Research On Multi-scroll Jerk Chaotic System Based On Memristor

The memristor is a nonlinear resistor with memory function,low power consumption and nanometer size.In recent years,many researches have been published on constructing various chaotic systems by memristors.Compared with the traditional chaotic circuits,the memristor-based chaotic circuits not only exhibit sensitivity to parameters,but also have strong sensitivity to the initial state of the memristor in the circuit,therefore,the memristive chaotic circuits have more complex and diverse dynamic characteristics.How to maximize the advantages of memristor in the design of chaotic circuit to obtain chaotic signals with higher complexity and stronger pseudo-randomness is a problem that need to be considered.Constructing a memristive multi-scroll chaotic system is a hot topic in chaotic circuit field.Based on the Jerk chaotic system,a kind of no-equilibrium memristive composite multi-scroll hidden attractors chaotic system and a kind of memristive hyperchaotic system which can generate multi-scroll attractors are proposed.The concrete research contents and results summarized as follows:(1)A memristive Jerk chaotic system which can generate compound multi-scroll hidden attractors is proposed.The dynamic characteristics of the system are analyzed by several common chaotic characterization methods such as phase diagram,equilibrium point,bifurcation diagrams and Lyapunov exponents.It is found that although the system equation is simple,it has extremely rich and complex dynamic behaviors.By changing only one system parameter,chaotic,hyperchaotic,periodic and quasi-periodic can be observed,including the state switching from hidden single-scroll attractor to hidden compound six-scroll attractors.Fixing the system parameters and changing the initial state of the memristor,the interesting nonlinear phenomenon of the coexistence of infinitely many hidden attractors is observed,which means the emergence of multistability and extreme multistability.In addition,the phenomenon of transient chaos is observed by changing the time of system simulation.Finally,the hardware circuit is designed by using discrete components,and the experimental results verify the correctness of the numerical simulation results.(2)Two kinds of novel non-ideal voltage-controlled multi-piecewise cubic nonlinearity memristors and their mathematical models are proposed,and the correctness of the memristor model is verified by simulation experiments.By adding the memristor to a three-dimensional Jerk system,a novel memristive multiscroll hyperchaotic Jerk system is established without introducing any other ordinary nonlinear functions,from which multi-scroll hyperchaotic attractors are achieved.The dynamic behaviors of the proposed system are analyzed by several conventional numerical analysis methods,and it is found that the system has complex dynamic characteristics.The results indicate that the system exhibits chaotic,hyperchaotic and periodic dynamics,and the phenomenon of transient chaos can be also found in system.Simultaneously,the system can produce the extreme multistability phenomenon of coexisting infinity multiple attractors.The circuit simulations and the hardware experimental results verify the correctness of the numerical simulation results.