A memristive map with coexisting chaos and hyperchaos* *Project supported by the National Natural Science Foundation of China (Grant No. 61871230), the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20181410), and the Postgraduate Research and Practice Innovation Project of Jiangsu Province, China (Grant No. SJCX21 0350).

Abstract

By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points are also captured. The hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants meanwhile the amplitude can also be controlled in combination with those coexisting attractors. Based on the nonlinear auto-regressive model with exogenous inputs (NARX) for neural network, the dynamics of the memristive map is well predicted, which provides a potential passage in artificial intelligence-based applications.