Complex hidden dynamics in a memristive map with delta connection and its application in image encryption

Memristor, as a basic circuit component with strong nonlinearity, plays an important role in designing chaotic systems. In this study, three homogenous discrete memristors are coupled to establish a special triangular memristive network map (TMNM). The model has an infinite number of equilibrium points distributed in a three dimensional subspace, the generated attractors, thus, can be classified into hidden attractors. The dynamics related to coupling strength and initial condition of memristors are analyzed by dynamical maps, bifurcation diagrams, the Lyapunov exponents, and phase diagrams. As the coupling strength varies, the map exhibits two completely opposite bifurcation routes. The coexisting hyperchaotic, chaotic, quasi-periodic, and periodic attractors are observed under different initial conditions. In additional, partial and total amplitude control in this map can be respectively achieved by adjusting two independent system parameters. Without affecting the dynamic performance of the system, we introduce a constant controller in the original map to achieve signal polarity regulation. Finally, an image encryption scheme based on the TMNM is developed, and its security performance is verified by several evaluation criteria.