A class of memristive Hénon maps

Abstract Memristor, the electronic component, is introduced in the Hénon map and is studied extensively. Several chaotic maps are proposed by constructing the memristors through nonlinear functions such as absolute value functions, trigonometric functions, and activation functions. It is found that in a part of the proposed chaotic maps, the local offset boosting of the system variable can be guided by a single parameter. Not only that, the generation of homogeneous multistability can be controlled by the initial conditions of the systems. Moreover, the number of homogeneous attractors produced changes when the system parameters are varied. In addition, the control of chaos can be achieved by adjusting the excitation fRequency of the memristor. The theoretical results and numerical laws presented in this paper are verified by circuit implementation based on the microcontroller unit.