A memristive map with coexisting chaos and hyperchaos*

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.

Automated summary

By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed in this study. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are discovered, along with capturing other regimes of coexistence such as coexisting chaos, quasi-periodic oscillation, and discrete periodic points. Additionally, the hyperchaotic attractors can be flexibly controlled to be unipolar or bipolar by newly embedded constants, providing potential applications in artificial intelligence.