Hidden complex multistable dynamical analysis and FPGA implementation of integer-fractional order memristive-memcapacitive chaotic system

Abstract A chaotic circuit based on a magnetic-controlled memristor and charge-controlled memcapacitor is proposed in this paper. The study reveals that it is a hyperchaotic system with hidden characteristics in integer-order. Furthermore, as the parameters change, the attractors exhibit rich evolutionary phenomena. Even after adjusting some parameters to very large values, the system still maintains hyperchaotic behavior. Interestingly, the basin of attraction shows the multistability of the system. Under initial value control, coexisting attractors are categorized into two types: those with initial offset-boosting behavior and nested attractors. When under parameter control, coexisting attractors are divided into two types: symmetric coexisting attractors and nested coexisting attractors. By analyzing the spectral entropy (SE) complexity of the system and using a complexity distribution diagram with two parameters and two initial values, the existence of multiple complex dynamic behaviors in the system has been verified. The fractional-order memristive-memcapacitive system based on the Grunwald-Letnikov algorithm and the five fractional-order values of q i ( i = 1, 2, 3, 4, 5) are taken as different in the numerical simulation, it also displays multiple coexisting phenomena similar to those of the integer-order. Finally, Matlab/Simulink and DSP Builder software platform are used to design the fractional-order five-dimensional chaotic memristive-memcapacitive system, and then combined with VHDL and Verilog HDL hardware language, the proposed circuit system is verified on the EP4CE115F29C7 FPGA main chip of Cyclone IV E series. The consistency of hardware implementation and software simulation shows the correctness and feasibility of the design.