Dynamics Research Based On The Four-dimensional Memristive Chaotic System

The memristor is a kind of nonlinear circuit element,it has the advantages of high speed,low consumption,easy integration,simple structure,etc.It is of great significance for information storage,secure communication,logic operation and neural network.By introducing the memristor model into chaotic systems that can produce a variety of dynamical behaviors,including multistability and extremely multistability.Because the system can produce a good pseudo-random chaotic sequence,it is generally used in the fields of image encryption and secure communication.Therefore,it is necessary for us to construct a memristor chaotic system with complex dynamical behavior.In this paper,the memristive chaotic system is constructed by different memristor models,and its characteristics are analyzed and studied.The main research work is as follows:(1)The generalized memristor device has the advantages of unrestricted,simple circuit structure and easy application in various circuits.We design a four-dimensional memristive chaotic system based on the generalized memristor bridge.Then,the bifurcation diagram and Lyapunov exponent spectrum are used to simulate the system.The results show that the system has complex dynamical phenomena,such as coexisting attractors,offset boosting and chaotic bursting.In addition,the circuit of memristive chaotic system is built in the environment of Multisim software,and the circuit simulation is carried out.The results of circuit simulation correspond to those of numerical simulation,which proves the feasibility and effectiveness of the system.(2)By introducing a memristor with cosine memristor function,a four-dimensional memristor chaotic system is obtained.The system has a line equilibrium point,which means that the system contains chaotic hidden attractors.Through a series of numerical simulation analysis of the memristive chaotic system,it is observed that the system has an extremely multi-stability phenomenon,which indicates that the system generates an infinite number of single and double wing chaotic hidden attractors.Then by adjusting the initial valueu(0)of the memristor and the initial value x(0)and z(0)of the system,we can effectively control the sequence of attractors as well as their location and topology.Secondly,the spectral entropy complexity of chaotic sequences with different system initial values is analyzed.Finally,the circuit simulation also proves that multistability can be realized by voltage control.These results show that the proposed memristive chaotic system has high complexity and sensitivity.(3)A local active memristor model of N-type is proposed.The local active and nonvolatile properties of the memristor are verified by the hysteresis loop,DC V-I diagram and Power-Off-Plot(POP)diagram.The observed local active properties can be used to design chaotic oscillating circuits.Based on the small signal analysis method,the equivalent circuit of memristor is established near the operating point of local active region.In addition,we further investigate a series of dynamical behaviors of the memristor when introduced into a chaotic system,which exhibits nested coexisting attractors.Finally,the system circuit is designed according to the state equation of the system,and the analog circuit is built in the environment of Multisim software for simulation,thus verifying the correctness of the memristor chaotic system.