Dynamic Behavior Analysis Of Memristor Coupling System And Its Application Researc

In the field of life and natural science,nonlinear dynamic systems are everywhere.Classical linear systems are often the simple abstractions of actual physical systems.For nonlinear systems,the superposition principle of linear systems is no longer applicable.It is possible to explain the real physical system after mastering the inherent law of nonlinear behavior,and thus accomplishes special functions and applications that linear systems do not possess.Chaos is a kind of special behavior in a nonlinear system.Lorenz system in meteorology has proved the existence of a stable chaotic system for the first time.Since then,chaos and fractal theory has been considered the best tool to study nonlinear problems.The research on chaos involves many interdisciplinary issues,among which the application of chaotic systems for image encryption and data communication has been studied for nearly 30 years.In this process,people have been looking for how to design nonlinear dynamic systems with simple structures and high complexity.Until 2008,a new type of nonlinear device memristor was successfully manufactured.The introduction of memristors can greatly enhance the nonlinear behavior of the system.The study of dynamic systems composed of memristors has become a frontier topic in the nonlinear field in recent years.For nonlinear circuits composed of memristors,most of them use the memristor model to replace the resistance of an existing chaotic system.There is a lack of special research methods for coupling memristors with other components or other memristor systems to form high-dimensional nonlinear dynamic systems,which has certain limitations for using memristors to design systems.This dissertation mainly focuses on the problem of coupling memristors to linear circuits with a physical background and investigates the complex nonlinear dynamical behaviors of the memristive system in terms of a mathematical model,the equivalent emulator circuit for the memristor,how to design a nonlinear dynamical system by coupling a memristor,the application of the memristive system,and the method of constructing a high-dimensional multi-memristor system by coupling the memristor.These behaviors are analyzed in detail using Lyapunov exponents,phase diagrams,Poincaré mappings,and attraction basins.The main work accomplished in this dissertation includes:1.A new system of memristor conservative circuits is constructed by replacing and coupling the memristor.The system exhibits a rich multi-topological quasi-periodic five-dimensional conservative flow and possesses constant and initial dependent offset-boosting properties.First,after introducing constant control variables,the system undergoes three different states of offset boosting behavior,which are hyperchaotic,chaotic,and quasi-periodic phase trajectory offset boosting;then,under certain parameter conditions,changing the initial value of the system,the system exhibits offset boosting behavior with homogeneous multistability and heterogeneous multistability.In the process of studying its nonlinear dynamics,it is revealed that transient chaos is one mechanism for the conservative system to generate chaos.Finally,the correctness of the numerical simulation and the realizability of the system is verified based on PSIM circuit simulation and DSP digital circuit.2.From the point of view of the physical circuit,the flux-controlled memristor is directly coupled to form a classical Wien-Bridge oscillation circuit.The system is simple in structure and has the characteristics of a typical chaotic attractor,coexisting symmetric attractor,bistable behavior,and wide-range chaos.In particular,by changing its parameters,the system can achieve amplitude and offset boost control for seven different attractors under a wide range of parameters,where the offset boosting exhibits a rare monotonic nonlinear offset behavior.In addition,the system is found to have the properties of symmetric coexisting attractors,bistability,and wide-range chaos.3.A novel triangular wave charge-controlled memristor and its coupled conservative non-Hamiltonian energy conservation dynamic system are designed.According to the input-output relationship of charge-controlled memristor,a new type of memristor model TWM based on triangular wave memristor function is designed.Numerical simulations and Multisim circuits show that the tight hysteresis curves are consistent with the three essential characteristics of the charge-controlled memristor for different frequencies and different initial values of the periodic excitation signal,indicating the correctness of the designed TWM model.In addition,a conservative dynamic system based on TWM is designed by coupling memristors from the perspective of a mathematical model.Changing its parameters,the phase diagram exhibits an extremely rich conservative flow.In addition,the system has super multistability that depends on the initial value of the memristor,where the extreme multi-stability consists of homomorphic multistability and heteromorphic multistability.And homomorphic multistability reflects the control effect of memristor initial value or other initial conditions on amplitude.Finally,using the superiority of the conservative system itself for encryption,the proposed conservative system based on triangular waves is made into a pseudo-random signal generator and used for image encryption.The ideal statistical properties of ciphertext,key sensitivity measure,and information entropy are obtained,which shows that the proposed system has good pseudo-randomness and complexity.4.The two memristors are directly coupled from the physical circuit point of view,and the double memristor MLC oscillation circuit with stacked attractors is designed.The MLC oscillation circuit is composed of four components: a flux-controlled memristor,a charge-controlled memristor,a linear capacitor,and a linear inductor.Under certain parameters and initial conditions,the system can produce a new type of stack attractor,and the formation mechanism of the stack attractor is also described.In terms of dynamic characteristics,the system shows relatively rich multiple transient transitions and quasi-periodic multi-steady behavior,and these dynamic characteristics have been experimentally verified by DSP digital circuits.Finally,based on the Lyapunov stability theory,the synchronization controller for the different systems is designed,and the application of synchronization and data transmission of two chaotic systems is realized.5.The problem of increasing the number of memristors and the dimensionality of the system in the memristive chaotic system is solved.Usually,nonlinear chaotic systems are required to have high complexity,and increasing the number of memristors and dimensionality can improve the complexity of the system.However,there is no general method to increase the number of memristors in a memristor chaotic system and to improve the dimensionality of the system.In this paper,a signal in the existing memristor chaotic circuit system is multiplied by a variable in a new memristor equation to form a nonlinear feedback term and then coupled to the memristor equation.In this way,the circuit increases the number of memristors and increases the variable space of two dimensions,which solves the problem of increasing the complexity of a chaotic system.To verify the correctness of the coupling method,the proposed coupling method is applied to a specific case,and a three-dimensional chaotic system containing a single memristor is upgraded to a five-dimensional chaotic system containing two memristors.The coupled five-dimensional system has extremely rich multiple transient transitions behavior and extreme multistability characteristics that vary with parameters and initial values.This method provides a new idea for the design of multi-memristor high-dimensional chaotic systems.