Design of a memristive chaotic map and its adaptive regulation

Abstract The analysis of structure and dynamics in chaotic systems has long been a significant research direction in nonlinear science. Constructing a reliable chaotic system with rich dynamical characteristics is essential for secure communication applications. Existing memristor-based chaotic maps are typically obtained by incorporating discrete mathematical models of memristors into basic chaotic maps. In this study, a simple memristive nonlinear circuit is first designed, from which a memristive oscillator is derived. Subsequently, a memristive map is developed from this oscillator through a linear transformation of the variables. The reliability of the new map is validated through nonlinear dynamic analysis. The results demonstrate that the map exhibits complex nonlinear dynamics under different parameter settings. This finding is beneficial for the construction of memristor maps and the development of image encryption algorithms.