Feedback Control-Based Parallel Memristor-Coupled Sine Map and Its Hardware Implementation

Discrete memristors can be coupled with one-dimensional (1D) chaotic maps to construct chaotic or hyperchaotic map models. However, the literature on coupling 1D maps with multiple memristors to construct three-dimensional (3D) or higher dimensional chaotic maps is very sparse. To this end, this paper proposes a new framework to construct a 3D hyperchaotic map model by coupling two different memristors with 1D maps through a parametric feedback control approach. The stability analysis of fixed point shows that the stability of 3D chaotic map depends on the initial state of two different model memristors and the parameters of the chaotic map. The control parameter-dependent hyperchaotic behavior and the initial state-dependent boosting bifurcation behavior are revealed using numerical simulations. Meanwhile, the feedback parameters of the chaotic map can modulate the dynamical behavior of the chaotic map. In addition, experimental results obtained from a micro-controller based platform are presented to verify the validity of the proposed design.