A spatiotemporal coupling vibrator cluster emergent dynamics hardware implementation method based on ZYNQ

Abstract

The application discloses a kind of spatiotemporal coupling vibrator cluster emergent dynamics hardware implementation method based on ZYNQ, comprising: constructing the spatiotemporal coupling vibrator cluster model with environmental density influence, local environmental density is introduced as feedback quantity into effective space attraction coefficient;Model parameter configuration, running mode selection, initial state generation, environmental density calculation, cluster state iteration and double-channel output data organization are completed by the PS end of ZYNQ;Data transmission, streaming cache and synchronous digital-analog output are completed by the PL end of ZYNQ;The output signal is converted into two-way synchronous analog signal, and input oscilloscope is carried out point cloud trajectory, phase plane trajectory and time-domain waveform observation.The application can reproduce cluster emergent behavior such as synchronous aggregation, subgroup bounce, static separation, vortex motion and radial oscillation in real time on embedded hardware platform, with the advantages of strong real-time, high reconfigurability and easy hardware verification.

Description

Technical Field

[0001] This invention belongs to the fields of nonlinear cluster dynamics, heterogeneous on-chip systems and edge hardware simulation technology, specifically involving a hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ. Background Technology

[0002] With the development of nonlinear dynamics, complex systems, and edge computing technologies, emergent dynamic phenomena such as synchronization, clustering, separation, rotation, and radial oscillation in large-scale coupled oscillator systems have become important research objects for complex system modeling and hardware simulation. These systems typically consist of a large number of oscillator elements with spatial and phase states, and their overall behavior is driven by local interactions, phase coupling, and spatial interactions, reflecting the self-organizing evolution laws in complex cluster systems.

[0003] Existing coupled oscillator cluster models are mostly performed offline numerically on general-purpose computers to analyze phenomena such as phase synchronization, spatial clustering, subgroup separation, and vortex motion under different coupling parameters. Although some nonlinear dynamic systems have been ported to circuits, FPGAs, or embedded platforms for verification, the related implementations are mostly geared towards low-dimensional chaotic systems, single-neuron models, or small-scale dynamic modules, and lack sufficient support for real-time iteration, dual-channel output, and oscilloscope visualization and reproduction of large-scale spatiotemporally coupled oscillator clusters.

[0004] Furthermore, traditional coupled oscillator models typically rely primarily on phase difference and spatial distance to adjust the interaction strength between oscillators, rarely considering the feedback effect of local environmental density on spatial attraction. This makes it difficult to fully characterize the density constraint effect of clusters during local congestion, expansion and reorganization, subgroup bouncing, and radial breathing processes. Therefore, how to introduce local environmental density feedback into the spatiotemporal coupled oscillator model and map the improved high-dimensional cluster dynamics onto the ZYNQ heterogeneous on-chip system for real-time operation and observation is a technical problem that needs to be solved in the current technology. Summary of the Invention

[0005] The technical problem this invention aims to solve is: addressing the issue that existing spatiotemporally coupled oscillator cluster emergent dynamics mainly rely on offline numerical simulations, making real-time reproduction and observation on embedded edge hardware platforms difficult. This invention provides a hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ. This method constructs an improved spatiotemporally coupled oscillator cluster model by introducing an environmental density influence term, and uses the PS and PL terminals of ZYNQ to collaboratively complete model iteration, data transmission, dual-channel digital-to-analog output, and oscilloscope observation, thereby achieving hardware reproduction of large-scale cluster emergent behavior.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A hardware implementation method for the emergent dynamics of a spatiotemporally coupled oscillator cluster based on ZYNQ includes the following steps:

[0008] S1. Introduce an environmental density influence term to construct a spatiotemporal coupled oscillator cluster model with density feedback adjustment capability within a preset range, so that the spatial interaction between oscillators is simultaneously modulated by spatial distance, phase difference and environmental density within a preset range.

[0009] S2. The ZYNQ on-chip system's processing system is used to complete model parameter configuration, operation mode selection, initial state generation, environment density calculation, cluster state iteration, and dual-channel output data organization.

[0010] S3. Utilize the programmable logic terminals of the ZYNQ on-chip system to complete AXI data transmission, streaming buffering, dual-channel DAC synchronous control, and digital signal output;

[0011] S4. The two digital signals output from the programmable logic terminal are sent to the dual-channel DAC module. After digital-to-analog conversion, two synchronous analog signals are obtained. The point cloud trajectory, phase plane trajectory or time-domain waveform of the oscillator cluster are observed through an oscilloscope to realize the hardware reproduction of the spatiotemporally coupled oscillator cluster emergent dynamics.

[0012] As a preferred technical solution of the present invention: In step S1, the construction of the spatiotemporally coupled oscillator cluster model with density feedback adjustment capability within a preset range is specifically as follows:

[0013] S11. Suppose there are N oscillators in the cluster. At the nth discrete time, the state of the i-th oscillator is determined by its position in two-dimensional space. and internal phase A common description, in which, Used to describe the spatial position of the i-th oscillator in a two-dimensional plane. Let x be the x-coordinate of the i-th oscillator. Let be the ordinate position of the i-th oscillator. Used to describe the internal oscillation phase of the i-th oscillator;

[0014] Define the relative position vector and Euclidean distance between the i-th oscillator and the j-th oscillator as follows: and ,in, Let j be the two-dimensional spatial position of the j-th oscillator;

[0015] S12. Establish the spatial position update equation of the oscillator based on the spatial attraction term and the short-range repulsion term, and establish the phase update equation of the oscillator based on the natural frequency term and the range-weighted phase coupling term. The spatial position update equation and the phase update equation are respectively:

[0016] ;

[0017] Where h is the iteration step size, N is the cluster size, B is the short-range spatial repulsion strength, and K is the phase coupling strength. Let be the natural frequency of the i-th oscillator. Let be the effective spatial attraction coefficient between the i-th oscillator and the j-th oscillator. and These are represented as the internal oscillation phases of the i-th and j-th oscillators, respectively.

[0018] S13. The effective spatial attraction coefficient is expressed as the sum of the basic spatial attraction term, the phase-related spatial coupling term, and the environmental density influence term, i.e.:

[0019] ;

[0020] Where A is the basic spatial attraction strength, and J is the phase-dependent spatial coupling strength. This refers to the environmental density impact factor.

[0021] S14. Calculate the environmental density within a preset range for each oscillator using a Gaussian neighborhood kernel:

[0022] ;

[0023] in, For neighborhood perception scale

[0024] Furthermore, a bounded nonlinear function is used to construct an environmental density influence term, allowing the environmental density within a preset range to participate as a feedback quantity in adjusting the effective spatial attraction coefficient between oscillators.

[0025] ;

[0026] in, For environmental density feedback intensity, For density saturation parameters, The environmental density within a preset range for the i-th oscillator. The environmental density within a preset range for the j-th oscillator;

[0027] S15. Set the same-frequency mode and different-frequency mode. The same-frequency mode is used to generate synchronization, expansion and aggregation behavior under the condition of uniform frequency, while the different-frequency mode is used to generate subgroup separation, subgroup bouncing, static separation, vortex motion and radial oscillation behavior.

[0028] As a preferred technical solution of the present invention: In step S2, the processing system of the ZYNQ on-chip system completes the cluster state iteration, as follows:

[0029] S21. Initialize the spatial position, phase state, natural frequency, and model parameters of the oscillator cluster;

[0030] S22. In each discrete iteration, calculate the relative position, spatial distance and phase difference between any two oscillators, and calculate the environmental density within a preset range for each oscillator based on the Gaussian neighborhood kernel.

[0031] S23. Update the effective spatial attraction coefficient between oscillators according to the environmental density and phase difference within the preset range, and substitute the effective spatial attraction coefficient into the spatial position update process, and substitute the phase coupling term into the phase update process to obtain the spatial position and internal phase of all oscillators at the next moment.

[0032] S24. Constrain the phase range and spatial boundary of the oscillator, and extract the cluster state of the stable evolution stage after completing the transient iteration for subsequent dual-channel data organization and hardware output.

[0033] As a preferred technical solution of the present invention: in step S21, the model parameters include cluster size N, iteration step size h, basic spatial attraction strength A, short-range repulsion strength B, phase coupling strength K, phase-related spatial coupling strength J, and environmental density feedback strength. Neighborhood perception scale and density saturation parameter .

[0034] As a preferred technical solution of the present invention: In step S2, the processing system of the ZYNQ on-chip system completes the dual-channel output data organization, as follows:

[0035] S25. When the point cloud observation mode is selected, the processing system will use the horizontal and vertical coordinates of the oscillator in the stable evolution stage as dual-channel output data, namely the horizontal coordinate signal of the first channel and the vertical coordinate signal of the second channel.

[0036] S26. Center, sort, and scale the point cloud output data to make the output data fit the input range of the dual-channel DAC module.

[0037] S27. When the phase sequence parameter observation mode is selected, the processing system calculates the global phase sequence parameter based on the phase state of all oscillators:

[0038] ;

[0039] in, Denote the complex exponential form corresponding to the phase of the i-th oscillator, and denote its real part. and the virtual part Each is output as dual-channel data;

[0040] S28. Convert the generated dual-channel output data into a data format suitable for DAC output, write it into the DDR buffer according to the preset data arrangement, and configure the DMA read address, transmission length and start status so that the two signals maintain a fixed read order during DMA transmission.

[0041] As a preferred technical solution of the present invention, step S3 is as follows:

[0042] S31. The programmable logic terminal reads dual-channel output data from the DDR buffer through AXI DMA and converts it into an AXI-Stream data stream, which is then sent to the subsequent module of the programmable logic terminal.

[0043] S32. The AXI-Stream FIFO on the programmable logic side receives the data stream output by the AXI DMA and performs streaming buffering;

[0044] S33, the dual-channel DAC control module parses the dual-channel output data according to the input data stream, and generates the digital input data, clock signal and write control signal required by the two DACs respectively. The two output signals are kept synchronized in time by unifying the clock and synchronous writing control.

[0045] As a preferred embodiment of the present invention, the data transmission between the processing system terminal and the programmable logic terminal of the ZYNQ on-chip system, as well as the PL terminal output, are accomplished in the following manner:

[0046] The processing system configures the programmable logic peripherals through the AXI4-Lite interface. The configuration includes DMA start signal, DAC output enable signal, observation mode selection signal, and interrupt control signal.

[0047] As a preferred technical solution of the present invention, step S4 is specifically as follows:

[0048] The digital signal output from the programmable logic terminal of the S41 and ZYNQ on-chip system is converted into a current output after passing through the digital interface, latch, DAC core, reference and bias circuit of the dual-channel DAC module. Then, it is amplified by a first-stage I / V conversion and low-pass filtering, a second-stage operational amplifier, and a BNC interface to output two synchronous analog signals.

[0049] S42, two synchronous analog signals are input to the first and second channels of the oscilloscope respectively. In point cloud observation mode, they are used to display the spatial point cloud trajectory of the oscillator cluster. In phase sequence parameter observation mode, they are used to display the phase plane trajectory or dual-channel time domain waveform.

[0050] As a preferred technical solution of the present invention: in step S41, the dual-channel DAC module is an AN9767 dual-channel DAC module, and the AN9767 dual-channel DAC module contains an AD9767 dual-channel DAC chip.

[0051] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0052] This invention introduces environmental density feedback into a spatiotemporally coupled oscillator cluster model, enabling the effective spatial attraction between oscillators to be adjusted according to density changes within a preset range. This improves the model's ability to characterize emerging cluster behaviors such as synchronous aggregation, spatial expansion, subgroup separation, subgroup bouncing, vortex motion, and radial oscillation. In terms of hardware implementation, this invention constructs a PS-PL collaborative architecture based on a ZYNQ system-on-a-chip. The PS terminal handles model parameter configuration, environmental density calculation, cluster state iteration, and dual-channel data organization, while the PL terminal handles data buffering and transmission, dual-channel DAC control, and synchronous simulation output. This allows high-dimensional cluster dynamics processes, which previously relied on offline simulation on general-purpose computers, to run and be observed in real-time on an embedded hardware platform. Compared to traditional software simulation methods, this invention offers advantages such as flexible parameter configuration, good output continuity, strong dual-channel synchronization, compact hardware structure, and ease of embedded deployment, providing an effective approach for hardware verification and experimental observation of complex cluster dynamics. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the dynamic state of the oscillator cluster in the same-frequency mode; where, Figure 1 (a) is a schematic diagram of a disordered motion state. Figure 1 (b) is a schematic diagram of the phase wave state. Figure 1 (c) is a schematic diagram of in-phase motion. Figure 1 (d) is a schematic diagram of the synchronization cluster state; Figure 2 This is a schematic diagram of the dynamic state of the oscillator cluster under different frequency modes; where, Figure 2 (a) is a schematic diagram of a disordered motion state. Figure 2 (b) is a schematic diagram of the vortex motion state. Figure 2 (c) is a schematic diagram of the subgroup bouncing state. Figure 2 (d) is a schematic diagram of the static asynchronous cluster state; Figure 3 This is a flowchart of the cluster dynamics iteration of the processing system side of the ZYNQ system-on-a-chip; Figure 4 Flowchart for organizing dual-channel output data; Figure 5 This diagram illustrates the AXI communication mechanism based on AN9767 and the output of the PL terminal. Figure 6 This diagram illustrates the hardware experimental connection and oscilloscope observation method. Figure 7 This is an image showing the observation results of subgroup bouncing point cloud under heterogeneous frequency mode; among them, Figure 7(a) shows the oscilloscope point cloud observation under subgroup aggregation. Figure 7 (b) is an oscilloscope point cloud observation diagram under subgroup separation state; Figure 8 The figure shows the observation results of the subgroup bouncing phase sequence parameter under different frequency modes; Figure 9 This is a diagram showing the observation results of radial oscillation point cloud under heterogeneous frequency mode; among them, Figure 9 (a) shows the point cloud observation diagram of the oscilloscope under radial contraction. Figure 9 (b) shows the oscilloscope point cloud observation under radial expansion conditions; Figure 10 The figure shows the observation results of the radial oscillation phase sequence parameter under different frequency modes. Detailed Implementation

[0054] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the following embodiments are only used to illustrate preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Equivalent substitutions or improvements made to the cluster size, parameter values, data format, hardware model, interface form, and observation method without departing from the technical concept of the present invention should all fall within the scope of protection of the present invention.

[0055] like Figure 6 As shown, the present invention proposes a hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ, which includes the following steps:

[0056] S1. Introduce an environmental density influence term to construct a spatiotemporal coupled oscillator cluster model with density feedback adjustment capability within a preset range (local). This allows the spatial interaction between oscillators to be modulated simultaneously by spatial distance, phase difference, and environmental density within a preset range (local).

[0057] S2. The ZYNQ on-chip system's processing system is used to complete model parameter configuration, operation mode selection, initial state generation, environment density calculation, cluster state iteration, and dual-channel output data organization.

[0058] S3. Utilize the programmable logic terminals of the ZYNQ on-chip system to complete AXI data transmission, streaming buffering, dual-channel DAC synchronous control, and digital signal output;

[0059] S4. The two digital signals output from the programmable logic terminal are sent to the dual-channel DAC module. After digital-to-analog conversion, two synchronous analog signals are obtained. The point cloud trajectory, phase plane trajectory or time-domain waveform of the oscillator cluster are observed through an oscilloscope to realize the hardware reproduction of the spatiotemporally coupled oscillator cluster emergent dynamics.

[0060] This invention constructs a spatiotemporally coupled oscillator cluster model with environmental density influence.

[0061] The cluster is assumed to contain N oscillators, and the state of each oscillator is described by its two-dimensional spatial position and internal phase. In the spatiotemporally coupled oscillator cluster model, the spatial position is used to characterize the distribution state of the oscillators in the two-dimensional plane, and the internal phase is used to characterize the oscillation state of the oscillators. The update of the spatial position between the oscillators is determined by the spatial attraction term and the short-range repulsion term, and the phase update is determined by the natural frequency term and the distance-weighted phase coupling term.

[0062] This invention introduces an environmental density influence term into the effective spatial attraction coefficient.

[0063] The effective spatial attraction coefficient consists of a basic spatial attraction term, a phase-dependent spatial coupling term, and an environmental density influence term. The environmental density influence term is jointly determined by the local environmental density of the interacting oscillators and is modulated by a bounded nonlinear function, so that the spatial interaction strength between the oscillators is simultaneously affected by the phase relationship, spatial distance, and local environmental density.

[0064] This invention includes a same-frequency mode and a different-frequency mode.

[0065] In the same-frequency mode, all oscillators have the same natural frequency, which is used to generate synchronization, expansion and aggregation behavior under the same-frequency condition; in the different-frequency mode, the oscillator cluster is divided into two subgroups with opposite natural frequencies, which is used to generate heterogeneous cluster emergence behaviors such as subgroup separation, subgroup bouncing, static separation and radial oscillation.

[0066] This invention completes model parameter configuration, operation mode selection, initial state generation, environment density calculation, cluster state iteration, and output data organization on the processing system side of the ZYNQ on-chip system.

[0067] The processing system converts the cluster state in the stable evolution stage into dual-channel output data according to the observation mode. The dual-channel output data includes the horizontal and vertical coordinates in the point cloud observation mode, or the real and imaginary parts in the phase sequence parameter observation mode.

[0068] This invention constructs a data transmission, buffering, and dual-channel DAC synchronous output structure on the programmable logic terminal of a ZYNQ on-chip system.

[0069] The programmable logic terminal configures the PL peripherals through the AXI4-Lite interface and converts the dual-channel output data in the DDR buffer into an AXI-Stream data stream through AXI DMA;

[0070] The programmable logic terminal uses AXI-Stream FIFO for streaming buffering and generates the digital input data, clock signal and write control signal required by the two DACs through the dual-channel DAC control module; the DAC output interface sends the digital signal to the dual-channel DAC module, and after digital-to-analog conversion, it obtains two synchronous analog signals, which are then input to the oscilloscope for point cloud trajectory, phase plane trajectory or time domain waveform display.

[0071] The present invention will now be described in detail with reference to specific embodiments.

[0072] 1. Construct a spatiotemporally coupled oscillator cluster model with environmental density influence;

[0073] Suppose there are N oscillators in the cluster. At the nth discrete time, the spatial position and internal phase of the i-th oscillator are expressed as follows: and ,in Used to describe the spatial position of the i-th oscillator in a two-dimensional plane. Let x be the x-coordinate of the i-th oscillator. Let be the ordinate position of the i-th oscillator. Used to describe the internal oscillation phase of the i-th oscillator.

[0074] To calculate the spatial interaction between oscillators, the relative position vector and Euclidean distance between the i-th oscillator and the j-th oscillator are defined as follows: and ,in, Let be the two-dimensional spatial position of the j-th oscillator.

[0075] The spatial position update equation of the oscillator is established based on the spatial attraction and short-range repulsion terms, and the phase update equation of the oscillator is established based on the natural frequency and range-weighted phase coupling terms. The spatial position update equation and phase update equation of the i-th oscillator are respectively...

[0076] ;

[0077] Where h is the iteration step size, N is the cluster size, B is the short-range spatial repulsion strength, and K is the phase coupling strength. Let be the natural frequency of the i-th oscillator. Let be the effective spatial attraction coefficient between the i-th oscillator and the j-th oscillator. and These represent the internal oscillation phases of the i-th and j-th oscillators, respectively.

[0078] To further introduce the moderating effect of phase relationship on spatial aggregation behavior, the effective spatial attraction coefficient is expressed as the sum of the basic attraction term, the phase-related attraction term, and the environmental density influence term, i.e.;

[0079] ;

[0080] Where A is the basic spatial attraction strength, and J is the phase-dependent spatial coupling strength. This refers to the environmental density impact factor.

[0081] When J>0, oscillators with similar phases have a stronger spatial attraction; when J<0, oscillators with opposite phases or large phase differences are more likely to form spatial separation or expansion structures.

[0082] In actual cluster evolution, local density significantly affects the cluster's aggregation and expansion states. To enable the model to reflect the modulating effect of the local environment on spatial interactions, this invention further constructs an environment density influence term. This term is jointly determined by the local environment density of the interacting oscillators and modulated by a bounded nonlinear function, and its expression is:

[0083] ;

[0084] In the formula, For environmental density feedback intensity, For density saturation parameters, Let be the local environmental density of the i-th oscillator. Let be the local environmental density of the j-th oscillator.

[0085] To obtain the local environmental density, this invention uses a Gaussian neighborhood kernel to perform weighted statistical analysis on the spatial distribution of other oscillators surrounding the i-th oscillator, resulting in:

[0086] ;

[0087] in, The neighborhood perception scale is defined as follows: the closer an oscillator is to the i-th oscillator, the greater its contribution to the local environmental density; the farther away an oscillator is, the smaller its contribution.

[0088] In this way, local density can be used as an environmental feedback quantity to adjust the effective spatial attraction coefficient, so that the spatial interaction strength between oscillators is simultaneously affected by phase relationship, spatial distance and local environmental density. This approach can avoid excessive clustering in local regions, while enhancing the model's ability to represent emergent phenomena such as density adjustment, spatial expansion, subgroup bouncing and radial breathing.

[0089] like Figures 1-2 As shown, this embodiment sets up a same-frequency mode and a different-frequency mode, wherein:

[0090] exist Figure 1 middle, Figure 1 (a) is a schematic diagram of a disordered motion state. Figure 1(b) is a schematic diagram of the phase wave state. Figure 1 (c) is a schematic diagram of in-phase motion. Figure 1 (d) is a schematic diagram of the synchronization cluster state.

[0091] exist Figure 2 middle, Figure 2 (a) is a schematic diagram of a disordered motion state. Figure 2 (b) is a schematic diagram of the vortex motion state. Figure 2 (c) is a schematic diagram of the subgroup bouncing state. Figure 2 (d) is a schematic diagram of the static asynchronous cluster state.

[0092] In the same-frequency mode, the natural frequencies of all oscillators are:

[0093] ;

[0094] In heterogeneous frequency mode, the cluster is divided into two subgroups with opposite natural frequencies, which are:

[0095] .

[0096] 2. Complete the software iteration process on the processing system (PS) of the ZYNQ on-chip system;

[0097] like Figure 3 As shown, the PS-side software iteration process includes state array establishment, parameter initialization, initial state generation, interaction calculation, local environment density calculation, effective space attraction coefficient update, cluster state update, transient state discarding, and stable state extraction.

[0098] In a preferred embodiment, the cluster size is N=200, the iteration step size is h=0.1, the basic spatial attraction strength is A=1, the short-range repulsion strength is B=1, and the environmental density feedback strength is... =0.8, the neighborhood perception scale is =0.8, density saturation parameter is =0.25. The phase coupling strength K and the phase-correlated spatial coupling strength J are set according to the emergent behavior observed. The above parameters are only preferred values ​​and do not constitute a limitation on the scope of protection of this invention.

[0099] At each discrete iteration, the PS terminal reads the spatial position and phase state of all oscillators and calculates the relative position, Euclidean distance, and phase difference between any two oscillators. To avoid abnormal denominator terms due to excessively small distances, a very small positive number can be set as a lower limit for the distance. When the actual distance is less than this lower limit, it is used in the calculation.

[0100] Subsequently, the PS terminal calculates the local environmental density of each oscillator based on the Gaussian neighborhood kernel, and updates the effective spatial attraction coefficient based on the environmental density influence term and the phase correlation term. The PS terminal substitutes the effective spatial attraction coefficient into the spatial state update process and the phase coupling term into the phase state update process to obtain the spatial position and internal phase of all oscillators at the next moment. After the update is completed, the phase range and spatial boundary are constrained to ensure that the oscillators are always within the set two-dimensional observation area.

[0101] To reduce the impact of the initial state on the observation results, the PS terminal performs several transient iterations and extracts the oscillator state of the stable evolution stage after the transient phase ends, which is used for subsequent dual-channel data organization and hardware output.

[0102] 3. Dual-channel output data organization process;

[0103] like Figure 4 As shown, the PS terminal converts the high-dimensional cluster state in the stable evolution phase into two output data streams based on the observation modes. The observation modes include point cloud observation mode and phase sequence parameter observation mode.

[0104] When the point cloud observation mode is selected, the PS terminal uses the x-coordinate and y-coordinate of the oscillator during the stable phase as dual-channel raw data, where the first channel corresponds to the x-coordinate signal and the second channel corresponds to the y-coordinate signal, as shown in the following formula:

[0105] ;

[0106] To improve the oscilloscope display, the PS terminal performs centering, sorting, and amplitude scaling on the point cloud output data. This processing is only for display and does not alter the dynamic evolution of the oscillator cluster model itself. When the phase sequence parameter observation mode is selected, the PS terminal calculates the global phase sequence parameter based on the phase state of all oscillators, and uses the real and imaginary parts of this sequence parameter as dual-channel output data respectively. This phase sequence parameter is defined as:

[0107] ;

[0108] in, Denote the complex exponential form corresponding to the phase of the i-th oscillator, and denote its real part. and the virtual part They are output as dual-channel data respectively.

[0109] By treating the real and imaginary parts as dual-channel outputs, we obtain... After generating the observation data, the PS end converts the dual-channel data into a format suitable for DAC output and performs amplitude limiting to prevent the output value from exceeding the DAC input range. Subsequently, the PS end writes the two data streams into the DDR buffer according to a preset data arrangement. To ensure synchronous output of the two signals, the dual-channel data can be stored alternately or in partitions, maintaining a fixed read order during DMA transfer.

[0110] 4. Data transmission and output implementation of the ZYNQ on-chip system (PS) to the programmable logic (PL) terminal;

[0111] like Figure 5 As shown, the PS and PL terminals exchange data via the AXI bus. The PS terminal is responsible for generating the data to be output and managing the DDR buffer, while the PL terminal is responsible for data stream transmission, buffering, and DAC synchronization control.

[0112] The PS (Power Supply) terminal configures the PL (Programmer) peripherals via the AXI4-Lite interface. Configuration includes DMA start signal, DAC output enable signal, observation mode selection signal, and interrupt control signal. This control interface allows switching between point cloud observation mode and phase sequence parameter observation mode. After the dual-channel output data is written to the DDR buffer, the PS terminal configures the DMA read address, transfer length, and start status. The AXI DMA reads waveform data from the DDR buffer according to the configuration and converts it into an AXI-Stream data stream, which is then sent to the subsequent modules on the PL side.

[0113] The AXI-Stream FIFO at the PL end receives the data stream from the DMA output and buffers continuous data. This module reduces rate fluctuations between DDR reads and DAC outputs, ensuring the continuity and stability of subsequent dual-channel DAC outputs. The dual-channel DAC control module parses the data from the first and second channels based on the input data stream and generates the digital input data, clock signal, and write control signal required for each DAC. Through unified clocking and synchronous write control, the two output signals are kept synchronized in time.

[0114] The DAC output interface sends digital data to the AN9767 dual-channel DAC module. The AN9767 module contains the AD9767 dual-channel DAC chip. The digital signal passes through the digital interface, latch, DAC core, reference and bias circuits to form a current output, which then passes through a first-stage I / V converter and low-pass filter, a second-stage operational amplifier, and a BNC interface to output two synchronous analog signals.

[0115] 5. Hardware experimental connection and observation methods;

[0116] like Figure 6As shown, the hardware experimental system includes a ZYNQ development board, an AN9767 dual-channel DAC module, an oscilloscope, and a host computer. The host computer is used for program downloading, parameter setting, and debugging; the ZYNQ development board is used for cluster model iteration, data transmission, and control signal output; the AN9767 dual-channel DAC module is used to convert digital signals into analog signals; and the oscilloscope is used to display the cluster's emergent dynamics.

[0117] The PS-side software program and PL-side hardware design were compiled and synthesized separately, generating an executable program and a hardware configuration file. The hardware configuration file was loaded onto the ZYNQ platform using a download tool, and the PS-side program was run. The digital data, clock signal, and write control signal output from the PL-side were connected to the AN9767 dual-channel DAC module. The two analog outputs of the AN9767 module were connected to the first and second channels of an oscilloscope, respectively.

[0118] When performing point cloud observation, the oscilloscope is set to XY display mode, with the first channel as the horizontal axis input and the second channel as the vertical axis input, to display the spatial point cloud trajectory of the oscillator cluster. When performing phase sequence parameter observation, the oscilloscope is set to phase plane display or dual-channel time domain display, with the first channel corresponding to the real part of the global phase sequence parameter and the second channel corresponding to the imaginary part of the global phase sequence parameter, to characterize the overall phase synchronization and oscillation evolution characteristics of the cluster.

[0119] 6. Hardware observation results under typical parameters;

[0120] In a preferred embodiment, a different frequency operating mode is selected, and K=0.5 and J=0.8 are set. In this case, oscillators with the same natural frequency tend to form a local clustering structure, while two subgroups with opposite natural frequencies cannot completely merge due to the phase difference, and the system exhibits subgroup bouncing behavior.

[0121] Figure 7 The subgroup bounce point cloud observation results under this parameter are shown, where, Figure 7 (a) shows the oscilloscope point cloud observation under subgroup aggregation. Figure 7 (b) is an oscilloscope point cloud observation diagram under the subgroup separation state.

[0122] Figure 8 The observation results of the phase sequence parameter under this parameter are shown.

[0123] In another specific implementation, a different frequency operation mode is selected, and K=0.5 and J=-0.8 are set. In this case, the cluster undergoes periodic contraction and expansion under the combined effects of environmental density feedback, spatial attraction, and short-range repulsion, and the system exhibits radial oscillation behavior.

[0124] Figure 9The observation results of radial oscillation point cloud under this parameter are shown, where, Figure 9 (a) shows the point cloud observation diagram of the oscilloscope under radial contraction. Figure 9 (b) is an oscilloscope point cloud observation diagram under radial expansion state.

[0125] Figure 10 The observation results of the radial oscillation phase sequence parameter under this parameter are shown.

[0126] In addition to the typical parameter settings mentioned above, the phase coupling strength K, phase-related spatial coupling strength J, and environmental density feedback strength can be changed. Neighborhood perception scale and density saturation parameter Furthermore, multiple cluster emergence states, such as synchronous aggregation, synchronous expansion, static separation, and vortex motion, can be obtained on the same hardware platform.

[0127] In summary, this invention achieves hardware reproduction of the emergent dynamics of a spatiotemporally coupled oscillator cluster influenced by environmental density through an environmental density-based model, PS-side software iteration, DDR buffer data organization, AXIDMA data transmission, dual-channel DAC synchronous output at the PL end, and oscilloscope observation. This implementation transforms the cluster dynamics evolution process, which originally relied on offline numerical simulation, into a hardware experimental process that can be run and observed in real time on the ZYNQ platform, exhibiting good real-time performance, reconfigurability, and engineering application value.

[0128] The above description is merely a preferred embodiment of the present invention. For those skilled in the art, various improvements and modifications can be made to the parameter settings, hardware interfaces, output channels, observation methods, and module implementation forms without departing from the principles and technical solutions of the present invention; all such improvements and modifications should fall within the protection scope of the present invention.

Claims

1. A hardware implementation method for the emergent dynamics of a spatiotemporally coupled oscillator cluster based on ZYNQ, characterized in that, Includes the following steps: S1. Introduce an environmental density influence term to construct a spatiotemporal coupled oscillator cluster model with density feedback adjustment capability within a preset range, so that the spatial interaction between oscillators is simultaneously modulated by spatial distance, phase difference and environmental density within a preset range. In step S1, the construction of the spatiotemporally coupled oscillator cluster model with density feedback adjustment capability within a preset range is as follows: S11. Suppose there are N oscillators in the cluster. At the nth discrete time, the state of the i-th oscillator is determined by its position in two-dimensional space. and internal phase A common description, in which, Used to describe the spatial position of the i-th oscillator in a two-dimensional plane. Let x be the x-coordinate of the i-th oscillator. Let be the ordinate position of the i-th oscillator. Used to describe the internal oscillation phase of the i-th oscillator; Define the relative position vector and Euclidean distance between the i-th oscillator and the j-th oscillator as follows: and ,in, Let j be the two-dimensional spatial position of the j-th oscillator; S12. Establish the spatial position update equation of the oscillator based on the spatial attraction term and the short-range repulsion term, and establish the phase update equation of the oscillator based on the natural frequency term and the range-weighted phase coupling term. The spatial position update equation and the phase update equation are respectively: ； Where h is the iteration step size, N is the cluster size, B is the short-range spatial repulsion strength, and K is the phase coupling strength. Let be the natural frequency of the i-th oscillator. Let be the effective spatial attraction coefficient between the i-th oscillator and the j-th oscillator. and These are represented as the internal oscillation phases of the i-th and j-th oscillators, respectively. S13. The effective spatial attraction coefficient is expressed as the sum of the basic spatial attraction term, the phase-related spatial coupling term, and the environmental density influence term, i.e.: ； Where A is the basic spatial attraction strength, and J is the phase-dependent spatial coupling strength. This refers to the environmental density impact factor. S14. Calculate the environmental density within a preset range for each oscillator using a Gaussian neighborhood kernel: ； in, For neighborhood perception scale Furthermore, a bounded nonlinear function is used to construct an environmental density influence term, allowing the environmental density within a preset range to participate as a feedback quantity in adjusting the effective spatial attraction coefficient between oscillators. ； in, For environmental density feedback intensity, For density saturation parameters, The environmental density within a preset range for the i-th oscillator. The environmental density within a preset range for the j-th oscillator; S15. Set up same-frequency mode and different-frequency mode. The same-frequency mode is used to generate synchronization, expansion and aggregation behavior under the condition of uniform frequency, while the different-frequency mode is used to generate subgroup separation, subgroup bouncing, static separation, vortex motion and radial oscillation behavior. S2. The ZYNQ on-chip system's processing system is used to complete model parameter configuration, operation mode selection, initial state generation, environment density calculation, cluster state iteration, and dual-channel output data organization. S3. Utilize the programmable logic terminals of the ZYNQ on-chip system to complete AXI data transmission, streaming buffering, dual-channel DAC synchronous control, and digital signal output; S4. The two digital signals output from the programmable logic terminal are sent to the dual-channel DAC module. After digital-to-analog conversion, two synchronous analog signals are obtained. The point cloud trajectory, phase plane trajectory or time-domain waveform of the oscillator cluster are observed through an oscilloscope to realize the hardware reproduction of the spatiotemporally coupled oscillator cluster emergent dynamics.

2. The hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ according to claim 1, characterized in that, In step S2, the ZYNQ on-chip system's processing system completes the cluster state iteration, as follows: S21. Initialize the spatial position, phase state, natural frequency, and model parameters of the oscillator cluster; S22. In each discrete iteration, calculate the relative position, spatial distance and phase difference between any two oscillators, and calculate the environmental density within a preset range for each oscillator based on the Gaussian neighborhood kernel. S23. Update the effective spatial attraction coefficient between oscillators according to the environmental density and phase difference within the preset range, and substitute the effective spatial attraction coefficient into the spatial position update process, and substitute the phase coupling term into the phase update process to obtain the spatial position and internal phase of all oscillators at the next moment. S24. Constrain the phase range and spatial boundary of the oscillator, and extract the cluster state of the stable evolution stage after completing the transient iteration for subsequent dual-channel data organization and hardware output.

3. The hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ according to claim 2, characterized in that, In step S21, the model parameters include cluster size N, iteration step size h, basic spatial attraction strength A, spatial short-range repulsion strength B, phase coupling strength K, phase-related spatial coupling strength J, and environmental density feedback strength. Neighborhood perception scale and density saturation parameter .

4. The hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ according to claim 3, characterized in that, In step S2, the ZYNQ on-chip system's processing system completes the dual-channel output data organization, as follows: S25. When the point cloud observation mode is selected, the processing system will use the horizontal and vertical coordinates of the oscillator in the stable evolution stage as dual-channel output data, namely the horizontal coordinate signal of the first channel and the vertical coordinate signal of the second channel. S26. Center, sort, and scale the point cloud output data to make the output data fit the input range of the dual-channel DAC module. S27. When the phase sequence parameter observation mode is selected, the processing system calculates the global phase sequence parameter based on the phase state of all oscillators: ； in, Denote the complex exponential form corresponding to the phase of the i-th oscillator, and denote its real part. and the virtual part Each is output as dual-channel data; S28. Convert the generated dual-channel output data into a data format suitable for DAC output, write it into the DDR buffer according to the preset data arrangement, and configure the DMA read address, transmission length and start status so that the two signals maintain a fixed read order during DMA transmission.

5. The hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ according to claim 1, characterized in that, Step S3 is as follows: S31. The programmable logic terminal reads dual-channel output data from the DDR buffer through AXI DMA and converts it into an AXI-Stream data stream, which is then sent to the subsequent module of the programmable logic terminal. S32. The AXI-Stream FIFO on the programmable logic side receives the data stream output by the AXI DMA and performs streaming buffering; S33, the dual-channel DAC control module parses the dual-channel output data according to the input data stream, and generates the digital input data, clock signal and write control signal required by the two DACs respectively. The two output signals are kept synchronized in time by unifying the clock and synchronous writing control.

6. The hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ according to claim 5, characterized in that, Data transmission between the processing system and programmable logic (PL) terminals of the ZYNQ on-chip system, as well as PL output, are accomplished in the following manner: The processing system configures the programmable logic peripherals through the AXI4-Lite interface. The configuration includes DMA start signal, DAC output enable signal, observation mode selection signal, and interrupt control signal.

7. The hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ according to claim 1, characterized in that, Step S4 is as follows: The digital signal output from the programmable logic terminal of the S41 and ZYNQ on-chip system is converted into a current output after passing through the digital interface, latch, DAC core, reference and bias circuit of the dual-channel DAC module. Then, it is amplified by a first-stage I / V conversion and low-pass filtering, a second-stage operational amplifier, and a BNC interface to output two synchronous analog signals. S42, two synchronous analog signals are input to the first and second channels of the oscilloscope respectively. In point cloud observation mode, they are used to display the spatial point cloud trajectory of the oscillator cluster. In phase sequence parameter observation mode, they are used to display the phase plane trajectory or dual-channel time domain waveform.

8. The hardware implementation method for spatiotemporally coupled oscillator cluster emergent dynamics based on ZYNQ according to claim 7, characterized in that, In step S41, the dual-channel DAC module is an AN9767 dual-channel DAC module, which contains an AD9767 dual-channel DAC chip.

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