Memristor-based Gauss chaotic maps with hidden/self-exited dynamics

Discrete memristors can be used to improve the chaos complexity of existing chaotic maps due to their special nonlinearities of internal states. In this paper, a unified memristor-based Gauss mapping model is presented by coupling discrete memristors with Gauss map and then four two-dimensional (2-D) memristive Gauss maps using four different memristance functions are derived. The memristor-based Gauss mapping model possesses two specific cases of infinitely many line fixed points and no fixed points, resulting in the appearance of hidden dynamics or self-exited dynamics. To address the stability analysis of this kind of hidden dynamics, we use a dimension-reduction conversion method to study the hidden period-doubling bifurcations therein. Afterwards, we simulate and discuss the hidden/self-exited dynamics of the four 2-D memristive Gauss maps using several numerical tools, and perform performance tests and hardware experiments of the generated hidden/self-exited chaotic/hyperchaotic attractors. The results demonstrate that the discrete memristor can make the four 2-D memristive Gauss maps produce complex dynamical behaviours and greatly improve the chaos complexity of the one-dimensional (1-D) Gauss map.