Dynamical analysis and applications of a novel 2-D hybrid dual-memristor hyperchaotic map with complexity enhancement

The dual-memristor hyperchaotic map has not yet received much attention and application, and its complexity and flexibility deserve further improvement. To this end, a novel two-dimensional hybrid dual-memristor (HDM) hyperchaotic map with complexity enhancement is constructed by connecting two different discrete memristors through self-feedback and sinusoidal transformation. The considered map has line invariant points related to the initial conditions of the discrete memristor, and it is Lyapunov stable or unstable. Taking the coupling strengths, memristor parameters, and initial conditions as tunable parameters, complex dynamical behaviors are investigated by numerical methods, including special bifurcation modes, a plethora of strange attractors, hyperchaotic attractors, and multi-stability behaviors. In particular, the performance evaluation of strange attractors with different topological structures is performed, and the complexity enhancement characteristic of the hyperchaotic attractor is confirmed by excellent dynamical performance indicators. In addition, without affecting the dynamical performance, the flexibility of the HDM map is effectively improved by switching control. Afterward, the pseudo-random number generator and image encryption strategy are proposed based on the hyperchaotic sequences generated by the HDM map to improve its practical application value. The proposed encryption strategy fully utilizes the high randomness, complexity, and flexibility of the hyperchaotic sequences, exhibiting remarkable applicability and robustness in encrypting both typical color and non-typical grayscale images. Comprehensive analyses, including histogram, correlation, and information entropy analyses, as well as differential, data loss, and noise attacks, are conducted to thoroughly evaluate the performance of the encryption strategy. The results indicate that the strategy achieves superior encryption effectiveness and high security. Finally, a microcontroller-based digital circuit experiment platform is developed for verifying the numerical results.