Research And Design Of Memristor Multi-scroll Chaotic System And Hidden Attractor Multi-scroll Chaotic System

Compared with the traditional chaotic system,the multi-scroll chaotic system has more complex dynamical characteristics,so it is more suitable for the applications such as random number generator,image encryptions,secure communications,etc.However,the problems of these general multi-scroll chaotic systems are complicated circuit implementation,large power consumption and difficulty in integration.Using memristor to replace the nonlinear part of the general chaotic system,we can reduce the energy consumption and size of the chaotic circuit.Therefore,designing the multi-scroll chaotic circuit based on memristor has very important practical significance.In recent years,hidden attractor chaotic systems have been discovered one after another.It is impossible to obtain the hidden attractor multi-scroll chaotic systems by extending the unstable saddle-focus equilibrium point.Therefore,some new method needed to be found to obtain the hidden attractor multi-scroll chaotic systems.Based on the researchings of memristor,memristor multi-scroll chaotic system and hidden attractor chaotic system,two multi-piecewise linear smooth memristor models,a memristor multi-scroll chaotic system and a hidden attractor multi-scroll hyper-chaotic system are proposed.The main innovations of this paper are as follows:(1)Two new multi-piecewise linear smooth memristor models are proposed.The hardware circuit of the two kinds of memristor models was built using discrete components,and the correctness of the two memristor model designs are verified.Based on the two memristor models,a new memristor multi-scroll chaotic system which can produce 2N-scroll and 2N+1-scroll chaotic attractors is proposed.By using Lyapunov exponent,bifurcation diagram,and attractor phase diagram,the basic dynamic characteristics of the designed chaotic system are studied.It is found that the designed chaotic system has extremely complex dynamic characteristics including period-doubling bifurcation,point attractor,limit cycles,coexistence of multi-scroll chaotic attractors,etc.Finally,an electronic circuit of the memristor multi-scroll chaotic system is performed.The circuit experimental results are in good agreements with the Matlab simulation results.(2)A hidden attractor multi-scroll hyper-chaotic system is proposed.Compared with other hidden attractor hyper-chaotic systems,the chaotic system we proposed can produce N + M + 2-scroll hidden attractors.Compared with other hidden attractor multi-scroll chaotic systems,the chaotic system proposed by us is a hyper-chaotic system.It has a simple circuit structure,and can be easily implemented.By using Lyapunov exponent,bifurcation diagram,and attractor phase diagram,the basic dynamic characteristics of the designed chaotic system are studied.Finally,an electronic circuit of the hidden attractor multi-scroll hyper-chaotic system is performed.The circuit experimental results are in good agreements with the Matlab simulation results.