The Research Of Multistability In A 4D Memristive Chaotic System

Memristor is one of the basic circuit elements except resistors,capacitors and inductors.It was first proposed by Chua in 1971,the researchers of HP Company reported the implementation of memristor on?Nature?In May 2008,The research results shocked the International Electrical and electronic industry,Together with the basic position of memristor in circuit theory,and its application in the fields of computer information storage,massive data processing,artificial neural network,etc.,which arouse people's passion in the research of memristor.The multi-stability can be used for image processing,or be regarded as another source of randomness and applied in many information engineering,for neural networks,multi-stability means that there are multiple memories in the network,so it is very important to study the multi-stability in the circuit.So far,there are few studies on the stability of the circuit in the memory circuit at home and abroad,in order to reveal its inherent behavioral characteristics in greater depth,it will be very important to study the mechanism and evolution of its dynamics.In this paper,we discuss the complex dynamical behavior of a class of 4D memory chaotic circuits.The problem of different types of multi-stability problems in 4D memristive chaotic circuits is proposed,such as the multi-stability problem of chaotic attractors and limit cycles,the multi-stability problem of torus and chaotic attractors,the multi-stability problem of the limit cycle and the hyperchaos,etc.The problem of attracting domain for the multi-stability and the existence of the attractor are studied when the attracting domain is too small.Finally,the existence of hyperchaos is proved by strict theoretical and physical experiment methods.The specific research methods are as follows: First of all,in order to find parameters that the system can produce more complex dynamic behaviors,we use CAPD(Computer Assisted in Dynamics group)group to search for a series of parameters.Secondly,using the power spectrum,Lyapunov exponent spectrum and bifurcation diagram to find out the complex dynamical behaviors may be introduced by the system.Then,in order to ensure the efficient and accuracy of numerical calculation,we use the CPU + GPU large-scale computing ability and the multi-precision GMP and MPFR library with 128 decimal places to calculate the domain of the attractors,and the existence of the attractor is proved by the interval Newton method when the attracting domain is small.Finally,in order to prove the hyperchaotic property of the system,we not only use the topological horseshoe to verify the existence of hyperchaos in theory,but also apply Multisim software and physical circuit building two practical way,the accuracy of numerical calculation is verified in the end.