42 results about "Bifurcation diagram" patented technology

The invention provides a discrete modeling, stability analysis and parameter design method for a switching converter, and the method is illustrated by taking a single-phase full-bridge inverter and a B00ST converter as examples. The method provided by the invention comprises the steps of solving a state equation in a switching period of the converter by virtue of Matlab to obtain a stroboscopic mapping expression and a numerical solution in an analytical form; and then drawing a bifurcation diagram, a folding diagram, a phase diagram, a Lyapunov exponent spectrum and a Poincare section for performing stability analysis and parameter design on the converter. The modeling, analysis and design processes are finished directly in a time domain. A nonlinear characteristic of the switching converter is reserved in the modeling process, so that the accuracy is higher. The analysis process is finished mainly by utilizing an algorithm of Matlab, so that the manual calculation amount is small and the analysis is simple and convenient. An analysis result can be presented and verified in various forms, and a result of an analytical method can be verified by a result of a numerical method, so that the credibility is ensured.

The invention discloses a voltage stability bifurcation analysis method for an AC / DC hybrid power distribution network. According to the method disclosed by the invention, the AC / DC hybrid power distribution network is equivalent to three portions; corresponding controllers are designed based on a differential algebra equation, wherein the controller comprises a voltage loop, a current loop and a stabilizer; voltage stability bifurcation analysis based on active power reference value variations is realized through setting system parameters and control parameters; a bifurcation inflection point and the limit power of voltage stability are determined based on an acquired bifurcation diagram, an optimal parameter of the stabilizer of the system is selected, a bandwidth value corresponding to the maximum stability margin of the system is found out, asymptotic stability analysis, static stability analysis, dynamic stability analysis and transient stability analysis of the system can be realized, a corresponding relation between the stabilizer parameter and the limit power of the system is acquired, feedback control signals of the stabilizer are set finally, and the system is controlled to operate in a range of the maximum stability margin.

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 method for realizing synchronous sliding mode secret communication based on a four-dimensional automatic switching chaotic system. The method comprises the steps of establishing the four-dimensional automatic switching chaotic system, analyzing dynamic characteristics of the four-dimensional automatic switching chaotic system with a bifurcation diagram, further analyzing and calculating a balance point of the four-dimensional automatic switching chaotic system, calculating a characteristic value of the balance point and a corresponding Lyapunov index with a Jacobian matrix to judge whether the four-dimensional automatic switching chaotic system is a chaotic system and judge phase space diagrams of different switching frequencies of the chaotic system, and finally designing a synchronous sliding mode controller based on the four-dimensional automatic switching chaotic system to realize synchronization of the automatic switching chaotic system in the same structure and with transmission signal modulation. An experiment simulation result shows that the method is effective, can recover a secret signal well, and has certain robustness.

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 provides a five-dimensional four-wing memristor hyper-chaotic system and a design, analysis and implementation method thereof. The five-dimensional four-wing memristor hyper-chaotic system has a multi-line balance point and three positive Lyapunov indexes and shows complex dynamic characteristics such as chaos, hyper-chaos, a limit ring and a period. The dynamic behavior of the novelfive-dimensional four-wing memristor hyper-chaotic system is realized by using the balance point, the phase diagram, the Poincare mapping, the Lyapunov exponent diagram and the bifurcation diagram.

The invention provides a novel bifurcation diagram drawing method suitable for a sliding mode variable structure control inverter. The method comprises the steps of 1, establishing a sliding mode variable structure control discrete iteration mapping model; 2, analyzing conventional bifurcation diagram drawing methods and determining the reasons for the inaccurate determination of stability domains and bifurcation behaviors thereof to find a solution; 3, researching the mechanism of the phenomenon of sudden change of states; 4, according to the mechanism of sudden change of states, deriving a method of variable-sampling point inverter bifurcation diagrams drawing and drawing a corresponding diagram. The invention provides the variable-sample point bifurcation diagram drawing method; it is proved that bifurcation diagrams drawn with the method can determine systematic stability work regions accurately and can be used for analyzing bifurcation behaviors of systems; finally the accuracy of theoretical analysis is verified through circuit experiments and research results provide reference for the research of nonlinear behaviors of sliding mode variable structure control inverters and drawing of bifurcation diagrams thereof.

The invention relates to the technical field of mechanical fault diagnosis, and in particular to a gear transmission system nonlinear stability-based fault diagnosis method. The method specifically comprises the following steps of: S1, establishing a multistage gear transmission system torsional dynamic equation which comprises a system motion differential equation and time-varying meshing stiffness (total stiffness, a crack model and a gear break model); S2, testing nonlinear features of a response signal; S3, carrying out sub-harmonic resonance and stability analysis; and S4, analyzing influences, on system stability, of faults, wherein the influences comprise but are not limited to influences, on sub-harmonic resonance, of planet gear break faults, influences, on sub-harmonic resonance,of fixed shaft crack faults, influences, on sub-harmonic resonance, of gear missing faults, influences, on sub-harmonic resonance, of wear faults and influences, on system stability, of coupling faults. According to the method, a multistage gear transmission system dimensionless dynamic equation with a two-stage fixed shaft gear and a one-stage planet gear is established from the angle of nonlinear dynamics, so that nonlinear characteristics such as bifurcation diagrams and the like of systems can be obtained.

The application discloses a bifurcation bracket. The bifurcation bracket comprises a main body, a first branch and the second branch. The first branch and the second branch are both connected to the same end of the main body. The main body, the first branch and the second branch are all mesh structures. The bifurcation bracket further includes a bifurcation area connected between the first branchand the second branch. The grid density of the bifurcation bracket in the bifurcation region is greater than the grid density in other regions of the bifurcation bracket. In this way, the contact areabetween the bifurcation area of the bifurcation bracket and the blood vessel wall at the bifurcation position is increased, and the bifurcation area can support the blood vessel wall at the bifurcation position. In addition, since the grid density of the bifurcation region is greater than that of other regions of the bifurcation bracket, embolism caused by the shedding of mural thrombus at the bifurcation position can be prevented.

The invention provides a dynamic behavior analysis method based on a small world network model. The invention discloses a fractional-order design method of the small world network model, and the method comprises a step of giving an integer-order small world network model of a controlled object and converting the original integer-order small world network model into a fractional-order small world network model through a fractional-order theory and method, a step of selecting a system delay parameter as a bifurcation parameter and carrying out stability and bifurcation analysis on a controlled system through a corresponding theory, and a step of obtaining corresponding conclusions through the analysis of a characteristic equation of the controlled system and finally verifying the correctnessof the theory and the characteristics of a dynamic behavior through MATLAB simulation. According to the method, the original integer-order model is in a transition to the fractional-order model for research, by selecting appropriate delay parameters and fractional-order exponents, the stability of the system is changed, and the increase or decrease of a stability domain can be controlled by specific parameter settings, and the controlled system has better operability.

The invention discloses a transient intrinsic orthogonal decomposition method applied to a coupled fault rotor-bearing system. The method comprises the following steps: firstly, establishing a 24-degree-of-freedom rotor-bearing system model with cracks and rub-impact coupling faults, then providing a transient intrinsic orthogonal decomposition (TPOD) dimensionality reduction method to carry out dimensionality reduction on the rotor-bearing system model, comparing the model with a single fault rotor system, namely a crack rotor, a rub-impact rotor and a fault rotor model containing nonlinear oil film force (an original system), and analyzing the dynamic characteristics of the rotor-bearing system with the coupling fault. The dimensionality of a coupling fault simplified model after dimensionality reduction is determined by adopting a POM energy method, and the effectiveness of a TPOD dimensionality reduction method is verified by comparing bifurcation diagrams. The dimension reduction model obtained through the method can well keep the dynamic characteristics of an original model, meanwhile, the dimension reduction model can be applied to a rotor model supported by a loose sliding bearing or a ball bearing, application of the dimension reduction method in a coupling fault rotor system is popularized, and the dimension reduction efficiency is improved.

The invention discloses a chaotic circuit with constant Liapunov exponent spectrum. The chaotic circuit comprises a signal source module, a linear module, a piecewise linear function module and a negative resistor module. The signal source module is connected with the linear module and the negative resistor module. The piecewise linear function module is connected with the linear module. The negative resistor module is connected with the linear module. The chaotic circuit comprises the linear module, the piecewise linear function module and the negative resistor module. A nonlinear component is added to the linear module, various theoretical parameter values in a state equation are converted into practically demanded circuit parameter values, the obtained circuit parameters are high in accuracy, and it is proved that the method of generating chaotic attractors through utilization of a circuit experiment is feasible. According to the chaotic circuit, various theoretical researches are carried out on the state equation of the chaotic circuit, a Liapunov exponent, a bifurcation diagram, a chaotic phase diagram and the like are obtained, and it is proved that the new chaotic circuit with the constant Liapunov exponent spectrum can be generated.

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 discloses a robust chaotic mapping system for image data encryption and a complexity optimization control method thereof, and the method comprises the following steps: 1, constructing achaotic mapping system, and calculating a system stationary point and a characteristic value expression thereof; 2, determining constant Lyapunov exponent characteristics of the mapping system in an infinite parameter range by analyzing the influence of system parameters on the characteristic values; 3, analyzing the position modulation effect of the parameters on the symmetrical non-zero fixed points of the mapping system, and determining the change rule of the signal amplitude along with the parameters; 4, a Matlab program is compiled, a Lyapunov exponent spectrogram and a bifurcation diagram about bifurcation parameters are drawn, and robust chaotic characteristics and amplitude control characteristics of the system are analyzed; And step 5, based on an iteration value domain matching condition and Lyapunov exponent definition, designing a complexity optimization control scheme of the robust chaotic mapping system with the Lyapunov exponent as a measurement criterion.

The invention discloses an aircraft structure damage diagnosis method based on a stable boundary and a POD method. On the basis of the POD method, an attractor method and a stability analysis method,a damage diagnosis technology of an aircraft sheet structure under a supersonic speed condition is provided, and nonlinear tools such as a bifurcation diagram, Poincare mapping, a Lyapunov index, a stability domain boundary and a high-order POD mode are utilized to obtain the influence rule of the structural damage degree, the damage range and the damage position on aeroelastic response, and a setof nonlinear structural damage diagnosis tool with high sensitivity and a structural damage criterion are attempted to be determined.

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.

Compared with an existing four-dimensional conservative chaotic system, the analog circuit based on the four-dimensional conservative chaotic system has five linear terms and one nonlinear function term, and is simple in structure and easy to realize. And the conservative property and chaos property of the system are confirmed by analyzing the dynamic characteristics such as dissipative property, phase diagram, equilibrium point, Lyapunov exponential spectrum and bifurcation diagram of the system. Compared with a common dissipative chaotic system, the method has a wider chaotic parameter interval, and a more reliable selection scheme can be provided for application of a conservative chaotic system in the fields of communication encryption and the like.

The invention discloses a 3D unbalanced conservative chaos self-adaptive synchronous controller system with multistability, and relates to a self-adaptive synchronous controller system. The invention designs a self-adaptive controller system, realizes synchronous control of the system, and verifies effectiveness of the method by using theoretical analysis and numerical simulation results; and a phase diagram, a Lyapunov index, a balance point, a symmetry and the like indicate the chaotic characteristic and the complex dynamic behavior of the system, the bifurcation diagram analysis discovers that the system can generate different hidden chaos coexistence attractors in the same phase space along with the difference of initial conditions, and the multistability of the system is verified. Due to the fact that few literatures about a multistable conservative chaotic system exist, the system enriches the types of the conservative chaotic system, and meanwhile the multistable conservative chaotic system has important application value in the field of synchronous communication and digital image encryption.

The invention discloses an improved Chua's system and an FPGA-based Chua's chaotic signal generator thereof, and provides an improved Chua's system which uses a composite hyperbolic tangent cubic nonlinear function, can generate a three-scroll chaotic attractor, and generates a three-scroll chaotic signal through a bifurcation diagram, a Lyapunov exponent, a phase diagram and a time domain diagram. The numerical value shows richer dynamic behaviors such as coexistence of multiple attractors, transient period, intermittent chaos, attractor offset and the like; and after constant excitation is added, the symmetric characteristic of the chaotic attractor is destroyed by the constant excitation. Compared with an existing Chua's system which generates multi-scroll Chua's chaotic signals by setting up an analog circuit, the invention provides an FPGA-based implementation mode of the improved Chua's system, so that the influence of factors such as temperature and component aging on result errors of a traditional Chua's analog circuit does not need to be considered.

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 relates to a two-dimensional complex number chaotic system. A two-dimensional chaotic system of a complex number field is provided by introducing of three diameters, the chaotic system of the complex number field has complex dynamic behavior, and the parameters are adjusted by analyzing a Lyapuvov index and a bifurcation diagram of the chaotic system to enable the chaotic system to produce both-wing chaotic attractors. The simple two-dimensional complex number chaotic system has wide application prospect and important application value in the fields such as radar, quantum secret communication and electronic countermeasures.

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 chaos generation method based on pulse control. The chaos generation method comprises the following steps: 1, constructing a model of a controlled nonlinear system; 2, establishing a univariate pulse controller; 3, drawing a parameter bifurcation diagram of the controlled dynamic system by taking the pulse interval and the state feedback pulse gain of the univariate pulse controller as analysis objects, obtaining a corresponding chaotic parameter range by utilizing the parameter bifurcation diagram, and selecting pulse controller parameters enabling the controlled nonlinear system to generate chaos; 4, analyzing the state of the controlled nonlinear system under the selected control parameter, verifying the chaotic characteristic, returning to the step 3 if the chaotic characteristic is not met, and reselecting the pulse control parameter in the chaotic parameter area; and otherwise, ending all the steps. Control energy is smaller than that of a continuous control chaos generation method, a chaos generation area is not limited to the vicinity of a periodic orbit of an original stable system, chaos can be generated and eliminated, and flexibility is better.

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 discloses a nonlinear kinetic analysis method for ship wave riding in regular waves. The nonlinear kinetic analysis method comprises the following steps: establishing a surging motion differential equation of a ship in the regular waves; based on a bifurcation nonlinear dynamics theory, calculating ship wave riding motion bifurcation characteristics by adopting a numerical method toobtain a bifurcation diagram of the relative speed between a ship and waves changing along with the rotating speed of a propeller, and according to the bifurcation diagram, obtaining a numerical propeller critical rotating speed when the ship sails thorugh the waves; combining a nonlinear dynamic Merlinkov method with a ship motion theory, analyzing ship surging motion based on a heteroclinic orbit, and calculating a theoretical propeller critical rotating speed when the ship sails thorugh waves so as to determine the reliability of the numerical propeller critical rotating speed; and determining conditions of ship wave riding instability according to the bifurcation diagram. According to the method, the stability domain of safe navigation of the ship is analyzed by adopting a nonlinear kinetic analysis method for the wave riding motion of the ship in regular waves, and an analysis method and a safe navigation basis are provided for safe navigation of the ship.

The invention provides a novel computer anti-virus propagation model in view of influence of anti-virus ability on the network. A two-dimensional mapping equation is obtained through analysis of relationships between system parameters. A dynamic behavior of the system is analyzed from the angles of a bifurcation diagram, a Lyapunov index and a parameter space three-dimensional bifurcation. Rich phenomena such as bifurcations and intermittent chaos can happen to the system, and the system has a chaos attractor. Finally, according to a two-dimensional chaotic system based on computer virus resistance, the fact that results such as a state and change of the system in a two-parameter space can facilitate understanding the rule that a computer virus is transmitted through a computer network is disscussed.