13 results about "Bifurcation diagram" patented technology

The application relates to encryption communication technology, and particularly discloses a construction, dynamic analysis and application method of a six-dimensional memristor hyperchaotic system. The method discovers that the new system has unique dynamic behaviors through a phase diagram, a bifurcation diagram and a Lyapunov exponent spectrum, generates symmetric coexistence cycles, chaos and hyperchaos double-wing attractors which depend on system parameters, shows extremely strong initial value sensitivity, has special symmetric extreme multistability and a memristor initial value enhancement behavior, generates symmetric four-wing attractors by adding a constant controller, shows more complexity and diversity, and finally, simulation is carried out through Multisim, the generated attractor is consistent with a phase diagram obtained through numerical simulation, and the feasibility of the new system is verified. The application has great advantages in encryption security and attack resistance.

The invention discloses a multi-gap design method for a power transmission system of an electric vehicle under a Tip in / out working condition, and relates to the technical field of new energy vehicles. The method comprises the following steps: establishing a system model comprising an input shaft spline, a two-stage fixed shaft helical gear pair reducer, a differential mechanism, a half shaft and the like, wherein the system model comprises multiple gaps such as an input shaft spline gap, a gear pair backlash, a differential mechanism backlash and the like; under the working conditions of rapid acceleration and rapid deceleration, the angular acceleration of a motor rotor, the angular acceleration of a first-stage driven gear of a speed reducer and the angular acceleration of a half shaft serve as transient impact evaluation indexes; and screening a target gap range of the periodic motion of the system through a bifurcation graph, Poincare mapping and a Lyapunov index, and performing multi-target optimization by taking the minimum evaluation index as a target to obtain an optimal gap combination. According to the method, transient impact can be effectively reduced, and the NVH performance and the driving comfort of the vehicle are improved.

The invention discloses a construction and implementation method of a hyperbolic tangent fractional order memristor chaotic system. The method comprises the following steps: firstly, designing a fractional order magnetic control memristor model containing a hyperbolic tangent function, and constructing a fractional order memristor chaotic system based on the model; through high-resolution order parameter scanning and in combination with Lyapunov exponent spectrum, bifurcation diagram, phase diagram and complexity analysis, rich dynamic behaviors and high sensitivity of the system under order change are revealed; a difference equation model of the system is obtained through a frequency domain approximation and discretization method, digital modeling is completed on a DSP Builder platform, and hardware description language codes executable by an FPGA are automatically generated; finally, the real-time iterative operation of the system is realized on the FPGA development board, and the physical realizability of the chaotic attractor is verified through the oscilloscope. The invention provides a high-precision and low-power-consumption hardware implementation scheme for the fractional order memristor chaotic system, and is suitable for the information security fields of secret communication, image encryption and the like.

The application discloses a design method of an alternating current stimulation Hodgkin-Huxley cardiac Purkinje fiber model, and the dynamic characteristics of the model under different alternating current parameters and different initial conditions are observed through a phase plane orbit, a waveform, a bifurcation diagram and a Lyapunov exponent spectrum, and multiple coexisting membrane action potential modes are revealed, corresponding to the same or different periodic coexisting attractors in a phase diagram. The model experiences period, quasi-period and forward or reverse period-doubling bifurcation with the change of an amplitude A or a frequency f, and it is proved that the cardiac Purkinje fiber model with alternating current injection has complex nonlinear characteristics. By changing a current I m , a sodium ion equilibrium potential E Na and a potassium ion equilibrium potential E K , heartbeat frequency rules are observed, and state conversion of the cardiac Purkinje fiber between normal, abnormal and sudden cardiac arrest is found. The application provides a reference for exploring the evolution rules of nonlinear dynamics in the HH CPF model, protecting life and heart health.

The present application belongs to the technical field of signal processing and detection, and specifically relates to a weak harmonic detection method based on a coupled chaotic system array, which couples the displacement and nonlinear restoring force of a Duffing system with the displacement and damping force of a Van der pol system to form a new coupled chaotic system for signal detection. The critical driving force of the coupled chaotic system is calculated by using a bifurcation diagram and a bisection method, and then the phase response interval is calculated. According to the size of the phase response interval, the coupled chaotic system array is designed, the to-be-detected signal is input, each subsystem in the array is selected, and it is judged whether the system undergoes a phase transition. If the signal makes the coupled chaotic system jump from a critical chaotic state to a large periodic state, it is indicated that the to-be-detected frequency signal exists. At this time, the amplitude of the harmonic is determined in the manner that the driving force amplitude is gradually reduced by a step size, and it is judged whether the system enters a chaotic state, so as to provide sensitivity and precision of weak harmonic detection.

The invention relates to the technical field of modern application of traditional Chinese medicine theories, and aims to solve the problem of insufficient quantitative research of the five-element theory of traditional Chinese medicine and the meridian theory under modern scientific contexts. Clinical twelve-meridian bio-electricity signals are collected, the chaos theory is used as the basis, a five-element generation-restriction mechanism is fused, and a five-dimensional nonlinear kinetic equation system is constructed; by establishing an acupuncture point-meridian-five-element two-stage mapping relation, quantitative characterization of five-element characteristic values is realized; parameter identification is completed by adopting a PSO-GA integrated optimization strategy, and chaos characteristics and evolution laws of a five-element system of a human body in healthy, sub-healthy and disease states are represented by calculating a Lyapunov index, calculating fractal dimensions, drawing a chaos bifurcation diagram, a phase diagram and the like. The method can be used for human health status assessment, provides a modeling thought for modernization of traditional Chinese medicine theories, and has clinical application value.

The application discloses a mapping method based on double discrete memristor, and relates to the technical field of memristor, two new double-memristor hyperchaotic mapping models of isomorphic sine-sine discrete memristor SSDM mapping and heterogeneous sine-cosine discrete memristor SCDM mapping are constructed by using two periodic discrete memristors; the mapping has a plane fixed point, and stability distribution is divided according to the second characteristic root in the parameter and initial value plane; bifurcation behavior depending on coupling strength, coexistence extreme multistability controlled by the initial value of the memristor are studied by using a bifurcation diagram, Lyapunov exponent, phase diagram and local attraction basin; under the control of the memristor, coexistence infinite heterogeneous attractors are self-replicated along a straight line and a plane; numerical results show that the SSDM and SCDM mappings can not only generate highly complex hyperchaotic attractors, but also exhibit extreme multistability behavior controlled by the initial condition of the memristor distributed on a straight line and a plane.

The application relates to the technical field of aircraft flight dynamics, and discloses a long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation, which comprises the following steps: establishing wing flexible deformation structure dynamics and flight dynamics coupling equations; based on the coupling equations, solving an initial accurate equilibrium point according to a Newton-Raphson iteration method; based on the initial accurate equilibrium point, solving a parameter variation equilibrium curve according to a pseudo-arc length continuation method; and based on the parameter variation equilibrium curve, establishing a bifurcation diagram according to a bifurcation theory to analyze long-endurance unmanned aerial vehicle global stability. The long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation can deeply analyze system nonlinearities and coupling properties and the like by establishing structure dynamics and flight dynamics coupling nonlinear dynamics equations considering wing flexible deformation, and can clearly show global system stability changes caused by parameter variation, so that the method is more comprehensive and effective.

The application relates to the technical field of signal processing, in particular to a chaotic neural network with complex-valued weights and application of the chaotic neural network in electrocardiogram classification. First, a complex Logistic chaotic mapping with complex-valued parameters is proposed, and bifurcation diagrams, Lyapunov exponents and chaotic attractors of the complex Logistic chaotic mapping are analyzed. Second, the ergodicity of CLCM and a new neuron function are used to optimize the weights of the CNN. Then, the method is verified by using the MIT-BIH database. Through band-pass filtering and double-threshold processing, the electrocardiogram signal is processed into a signal with a single waveform and a more prominent signal, which is used as the input of the designed CNN. The results show that the accuracy of the CNN with complex weights for electrocardiogram classification is improved. The complex weight chaotic neural network has the ability to prevent the network from falling into a local minimum, improves the recognition accuracy of the electrocardiogram, and has a high recognition accuracy.

The present application relates to the technical field of power signal processing and detection, and in particular to a weak harmonic detection method based on Yang system, aiming at the defect that the classical time-frequency domain analysis method cannot accurately detect the weak harmonic signal of power system in a severe noise environment, a Yang system is introduced, and the bifurcation diagram, phase trajectory, attractor distribution, fixed point coordinate and system state variable time trajectory diagram are used to analyze the change characteristics of system state. The appearance and disappearance of attractor distribution and fixed point are used as the conversion criterion of different chaotic states of the system, and a weak harmonic detection algorithm of power system is designed based on the criterion, the present application can realize the amplitude detection of each harmonic component without error in a noise environment of-100dB, and a general rule of dissipative type system for weak harmonic detection is given.

The present application belongs to the field of weak harmonic signal detection, and particularly to a weak harmonic detection method based on Chen system. The parameters a, b, c and the initial value (x0, y0, z0) of the system of the Chen system are set, the critical threshold of the control signal of the system is found out by using the dichotomy according to the bifurcation diagram of the system state variable changing with the amplitude f of the control signal, and the input signal weighting factor A is set according to the critical threshold. After the Chen system for signal detection is debugged, the control signal and the weighted input signal are input into the system at the same time, the system equation of the Chen system is solved, the x-z phase diagram of the system, the attractor distribution and the state variable time history diagram are drawn. The change of the fixed point position or the change of the attractor distribution of the system is judged, if the change occurs, the harmonic signal to be detected exists, at this time, the control signal amplitude f is reduced by a step and the system state is recalculated until the fixed point position or the attractor distribution of the system becomes the initial state, and the ratio of the difference of the control signal amplitude and the weighting factor is the amplitude of the harmonic signal to be detected. The signal can be detected without error under the noise of-60dB, and the detection error under the noise of-100dB can also be kept below 0.1%.

The application provides a variable scale convex peak phase identification method, a terminal and a system of an early fault signal, first, a to-be-detected signal of a target bearing under a variable scale Duffing system is acquired; then, a phase bifurcation diagram of the to-be-detected signal is drawn with the phase of a reference signal as a benchmark; then, the phase bifurcation diagram is identified to determine a period boundary value in the phase bifurcation diagram; finally, the initial phase of the to-be-detected signal is calculated according to the period boundary value. Through the phase bifurcation diagram and the variable scale convex peak phase identification method, the phase of the early fault signal is identified, so that the accuracy of frequency identification of the fault signal is ensured, and the influence on bearing fault identification is avoided.

The invention relates to the technical field of aircraft flight dynamics, and discloses a long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation, and the method comprises the steps: building a wing flexible deformation structure dynamics and flight dynamics coupling equation; based on the coupling equation, solving an initial precise equilibrium point according to a Newton-Raphson iteration method; based on the initial precise balance point, solving a parameter change balance curve according to a quasi-arc length continuation method; and based on the parameter change balance curve, establishing a bifurcation diagram according to a bifurcation theory, and analyzing the global stability of the long-endurance unmanned aerial vehicle. According to the long-endurance unmanned aerial vehicle stability analysis method considering wing flexible deformation, by establishing a structural dynamics and flight dynamics coupling nonlinear dynamics equation considering wing flexible deformation, based on numerical continuation and bifurcation theories, dynamic characteristics such as nonlinearity and coupling of a system can be deeply analyzed, and the stability of a long-endurance unmanned aerial vehicle is improved. The global change condition of the system stability caused by parameter change is determined, and the method is more comprehensive and effective.