42 results about "Bifurcation diagram" patented technology

The invention provides an active noise control method based on a generalized Lorentz system. In order to solve a problem of suppressing acoustic energy of radiation noises of a ship, the method employs a classical Lorentz system and adds a time-lag feedback controlled quantity and an external excitation unit based on the system; and a noise control effect is realized by using a chaotic dynamics determination method. For a transformed generalized Lorentz system, the output dynamic characteristics, including a phase trajectory chart, a bifurcation diagram and a Lyapunov exponent diagram, are observed by using Matlab programming; an external excitation amplitude parameter, a frequency parameter, and a corresponding parameter range in a cyclic motion, quasi-cyclic motion, or chaotic motion state of a system output are given; and noise source energy values and energy changing values at fixed frequencies before and after active sound source application are provided by using a spectrum curve and thus noise suppression effects under different sound source effects are represented.

The invention discloses a linear model establishment method for a nonlinear radiofrequency microwave circuit, which comprises the steps: firstly, selecting a quality factor Q value of a no-load resonance loop according to a double parameter bifurcation diagram; secondly, carrying out linearization on a normalization state equation to ensure open loop gain g <*> of an oscillator; thirdly, calculating an inductance L value; fourthly, calculating a value of resistance R; fifthly, utilizing the parameter values to establish a Colpitts circuit simulation model. A nonlinear exponential function n (X2) equal to e<X>2 -1is converted to a linear function by taylor series expansion, thus the linearization conversion process of the nonlinear radiofrequency microwave circuit is realized. The establishment of the traditional Colpitts circuit linearization model needs to respectively select five parameter values which are L, C1, C2, IL and R, and the invention can ensure all the parameter values of the circuit model only by selecting the values of the quality factor Q, a current source I0 and capacitance C2.

The invention relates to a method for establishing an adjustable bifurcation point controller based on an integer order network congestion model, which comprises the following steps: analyzing the stability characteristics of an uncontrolled integer order network congestion model and a unique equilibrium point x*; applying a PD<1 / n> controller with adjustable bifurcation points to the uncontrolledinteger-order network congestion model, wherein at least the stability, Hopf bifurcation and periodic oscillation range of the researched system are satisfied; linearizing the network congestion model with fractional order controllerat the equilibrium point x*, and the characteristic equation of the linearized controlled system is obtained; selecting the time delay taoas the bifurcation parameter, and carrying out the stability analysis and bifurcation analysis through the characteristic equation of the controlled network after linearization in the aforementioned steps. By setting appropriatecontroller parameters, the occurrence time of Hopf bifurcation is effectively advanced or delayed, so that the congestion system becomes controllable and the ideal behavior is realized.

The invention belongs to the field of electronic communication, and particularly relates to a multi-stability chaotic system with a discrete bifurcation diagram, which is provided with the discrete bifurcation diagram and a constant Lyapunov exponential spectrum and can generate two infinite coexistence attractors which have different structures and are distributed in parallel along a fourth axis.The system comprises a three-dimensional chaotic circuit and a memristor, and is characterized in that the three-dimensional chaotic circuit and the memristor are transformed into a new four-dimensional memristor chaotic system, and the four-dimensional memristor chaotic system is composed of a reverse operation module, an addition operation module, an integration operation module and the like which are formed based on an operational amplifier and a resistor or a capacitor, and an analog multiplier module. The multi-stability chaotic system with the discrete bifurcation diagram is simple in structure, can generate two infinite coexistence attractors which are different in structure and are distributed in parallel along a fourth axis, has the discrete bifurcation diagram, and further has aconstant Lyapunov exponential spectrum.

The invention discloses a CPLD-based oscilloscope display circuit for observing chaotic system bifurcations. The CPLD-based oscilloscope display circuit comprises a controllable resistance network circuit, a CPLD signal circuit, a parameter signal circuit, a signal position obtaining circuit and a signal obtaining circuit. The CPLD signal circuit is respectively connected with a controllable resistance network and the parameter signal circuit, the signal position obtaining circuit is connected with the signal obtaining circuit, the two external connection ends of the controllable resistance network are connected to the two ends of a to-be-measured resistor of a measured chaotic system in parallel, the signal position obtaining circuit and the signal obtaining circuit receive signals V1 generated by the measured chaotic system at the same time, the parameter signal circuit outputs signals Vx sent into the input end of an X shaft of an oscilloscope, and the signal obtaining circuit outputs signals Vy sent into the input end of a Y shaft of the oscilloscope. The CPLD-based oscilloscope display circuit is suitable for observing bifurcation diagrams of the chaotic system with changed resistance parameters. The CPLD-based oscilloscope display circuit can be used in on-line monitoring, and can be used for system researching and chaos teaching demonstrating. The CPLD-based oscilloscope display circuit is low in cost, convenient to operate and high in measurement speed.

The invention provides a method for discrete modeling, stability analysis and parameter design of a switching converter, and is illustrated by taking a single-phase full-bridge inverter and a BOOST converter as examples. This method uses Matlab to solve the state equation in the switching cycle of the converter, and obtains the analytical form of the stroboscopic mapping expression and numerical solution, and then draws the bifurcation diagram, folding diagram, phase diagram, Lyapunov index spectrum, and Poincaré cross-section pair Converter for stability analysis and parameter design. Compared with the method based on classical control theory, the method provided by the invention directly completes the process of modeling, analysis and design in the time domain. The modeling process preserves the nonlinear characteristics of the switching converter, and the obtained model is closer to the real circuit with higher accuracy. The analysis process is mainly completed in Matlab using the algorithm that comes with the software, which is simple and convenient with less manual calculation. The analysis results can be presented and verified in various forms such as bifurcation diagrams, folding diagrams, phase diagrams, Lyapunov exponent spectra, and Poincaré sections. In particular, the bifurcation diagram can visually show the changing trend and changing range of the system state variables when the converter parameters change. The results of the analytical method can be verified by the results of the numerical method, which ensures the credibility of the results. In addition, it is not difficult to see from the examples given that the applicable objects of this method are not limited to single-phase full-bridge inverters and BOOST converters, but can be extended to the modeling, analysis and design of other switching converters. Especially for some lower order switching converters.

The invention discloses a CPLD-based oscilloscope display circuit for observing chaotic system bifurcations. The CPLD-based oscilloscope display circuit comprises a controllable resistance network circuit, a CPLD signal circuit, a parameter signal circuit, a signal position obtaining circuit and a signal obtaining circuit. The CPLD signal circuit is respectively connected with a controllable resistance network and the parameter signal circuit, the signal position obtaining circuit is connected with the signal obtaining circuit, the two external connection ends of the controllable resistance network are connected to the two ends of a to-be-measured resistor of a measured chaotic system in parallel, the signal position obtaining circuit and the signal obtaining circuit receive signals V1 generated by the measured chaotic system at the same time, the parameter signal circuit outputs signals Vx sent into the input end of an X shaft of an oscilloscope, and the signal obtaining circuit outputs signals Vy sent into the input end of a Y shaft of the oscilloscope. The CPLD-based oscilloscope display circuit is suitable for observing bifurcation diagrams of the chaotic system with changed resistance parameters. The CPLD-based oscilloscope display circuit can be used in on-line monitoring, and can be used for system researching and chaos teaching demonstrating. The CPLD-based oscilloscope display circuit is low in cost, convenient to operate and high in measurement speed.

The invention discloses a linear model establishment method for a nonlinear radiofrequency microwave circuit, which comprises the steps: 1), selecting a quality factor Q value of a no-load resonance loop according to a double parameter bifurcation diagram; 2), carrying out linearization on a normalization state equation to ensure open loop gain g <*> of an oscillator; 3), calculating an inductance L value; 4), calculating a value of resistance R; 5), utilizing the parameter values to establish a Colpitts circuit simulation model. A nonlinear exponential function n (X2)= e<X2 -1> is converted to a linear function by taylor series expansion, thus the linearization conversion process of the nonlinear radiofrequency microwave circuit is realized. The establishment of the traditional Colpitts circuit linearization model needs to respectively select five parameter values which are L, C1, C2, IL and R, and the invention can ensure all the parameter values of the circuit model only by selecting the values of the quality factor Q, a current source I0 and capacitance C2.

The invention discloses a finite time correction function projection synchronization and parameter modulation control method, and relates to the technical field of chaotic secret communication. A strategy of combining finite time control and correction function projection synchronous control is adopted, and the method comprises the following steps: taking a fractional order laser Maxwell-Bloch chaotic system serves as a driving system, and conducting nonlinear dynamic behavior analysis on the system in combination with a time sequence diagram, a space phase diagram, a bifurcation diagram and the like; designing a synchronous controller of the driving system and the response system; and analyzing the performance and the stability of the finite time correction function projection synchronous controller. The correctness of the control method is verified through numerical simulation, synchronization of the two systems can be achieved in a short time, and the method has high robustness and is more suitable for being applied to actual secret communication.

The invention provides an active noise control method based on a generalized Lorentz system. In order to solve a problem of suppressing acoustic energy of radiation noises of a ship, the method employs a classical Lorentz system and adds a time-lag feedback controlled quantity and an external excitation unit based on the system; and a noise control effect is realized by using a chaotic dynamics determination method. For a transformed generalized Lorentz system, the output dynamic characteristics, including a phase trajectory chart, a bifurcation diagram and a Lyapunov exponent diagram, are observed by using Matlab programming; an external excitation amplitude parameter, a frequency parameter, and a corresponding parameter range in a cyclic motion, quasi-cyclic motion, or chaotic motion state of a system output are given; and noise source energy values and energy changing values at fixed frequencies before and after active sound source application are provided by using a spectrum curve and thus noise suppression effects under different sound source effects are represented.