Nonlinear coexistence phenomenons and FPGA implementation with the hybrid of memristive-memcapacitive hyperchaotic system

Abstract A hybrid circuit based on the magnetic-controlled memristor and charge-controlled memcapacitor is proposed in this paper. The circuit has hyperchaotic behavior in a large scale parameter range. By studying the influence of system parameters and initial conditions on the hybrid circuit, a variety of complex dynamic behaviors can be found: chaos turns into period, spike bursting, chaos turns into spike bursting and so on. Interestingly, different basins of attraction show different shapes. Selecting different basins of attraction positions, the direction of the chaotic attractor changes, but the shape does not change, thus forming a symmetrical coexistence attractor. The coexistence bifurcation diagram and coexistence time-domain waveform diagram under different initial conditions are studied, in the case of positive and negative changes in the initial value v0, the chaotic characteristics of the two cases are consistent. Meanwhile, a series of spectral entropy complexity distributions are analyzed, and find that special shapes are consistent with the attractive basins. Finally, on the platform of Cyclone IV E series, the FPGA main chip of EP4CE115F29C7 is used to complete the hardware implementation of the hybrid memristive-memcapacitive hyperchaotic circuit.