Fractional-order Hybrid Memristors Chaotic System Design And FPGA Implementation

Fractional-order chaotic systems can better reflect their inherent properties and physical characteristics,and their associative memory and information storage capacity are more prominent compared to integer-order systems.A memristor is a basic circuit element with nonlinearity.A chaotic or fractional-order chaotic system combined with a memristor can enhance its memory and storage capacity.Field Programmable Gate Array（FPGA）has the advantages of high reliability,large capacity and low power consumption.Therefore,the memristor chaotic circuits and fractional-order memristor chaotic circuits can be stably and accurately implemented using FPGA technology.In this paper,a simple memristor hyperchaotic circuit with attractor evolution and large-scale parameter range is constructed by using the new designed memristor model and other circuit components,and its in-depth research and digital implementation are carried out.Moreover,a five-dimensional fractional-order hybrid memristors chaotic system is designed,its nonlinear dynamical behavior is studied,and the fractional-order system is implemented using FPGA technology.The main research of this paper is as follows:（1）A novel four-dimensional simple memristor hyperchaotic circuit consisting of two capacitors,an inductor,and a magnetic-controlled memristor is designed.Three parameters（a,b,c）are specially set as the research objects of the model.Through numerical simulation and analysis,it is found that the circuit exhibits a rich attractor evolution phenomenon and large-scale parameter range capability.At the same time,the complexity of the circuit is analyzed,and it is confirmed that the circuit contains a significant amount of dynamic behaviors.By setting the internal parameters of the circuit to remain constant,a lot of coexisting attractors are found under symmetric initial conditions.Then,the results from the basin of attraction reflect the chaotic property of the circuit as well as the multistability.Finally,based on the time-domain method,a simple memristor chaotic circuit is designed using FPGA technology,and it is verified that the experimental results have the same phase trajectory as the numerical calculation results.（2）A hybrid memristors circuit consisting of a magnetic-controlled memristor and charge-controlled memristor and other circuit elements is designed.In order to construct a relatively complex dynamical system,an absolute value and a square root algorithm are especially embedded in the magnetic-controlled model.First,the novel five-dimensional memristor circuit is analyzed for the existence of chaotic phenomena based on integer order,and then the Grunwald-Letnikov algorithm is used to implement the fractional-order memristor chaotic system.Five fractional order values of₄)（4）=1,2,3,4,5)are taken as the same and different in the numerical simulation,respectively.It is found that the fractional-order system contains a large number of chaotic attractors,and each fractional order affects the chaotic properties of the system to different degrees.The nonlinear dynamic characteristics of the fractional order system are demonstrated using bifurcation diagrams,0-1 testing,SALI detection,and complexity analysis methods.Finally,based on frequency domain method,the commensurate and non-commensurate fractional-order memristor chaotic systems are implemented by FPGA technology,and the results of numerical calculations and hardware implementation are consistent and feasible.In summary,the theoretical analysis,numerical simulation,and digitization of the circuit have verified the feasibility and correctness of the design of the simple memristor hyperchaotic circuit and the fractional-order hybrid memristor chaotic system.Therefore,the research results of this paper have broad application prospects in the fields of secure communication and electronic engineering.