Dynamical analysis and circuit implementation of a memristive chaotic system with infinite coexisting attractors

Abstract

Abstract In order to obtain a chaotic system with more complex dynamic characteristics and more suitable for engineering applications, this paper combines a general memristor containing a hyperbolic tangent function with a simple three-dimensional chaotic system to construct a four-dimensional memristive chaotic system with infinite coexisting attractors. The memristive chaotic system is thoroughly studied through numerical simulations of various nonlinear systems, including the Lyapunov exponent spectra, bifurcation diagram, C0 complexity, two-parameter bifurcation diagram and basins of attraction. The analysis reveals that this system has complex dynamical behavior. It includes not only periodic limit loops and chaotic attractors that depend on the variation of system parameters, but also the extreme multi-stability phenomenon of infinite coexisting attractors that depend on the variation of the initial conditions of the system. In addition, the chaos degradation and offset boosting control of the system are also studied and analyzed. Finally, the correctness and realizability of the memristive chaotic system are verified by circuit simulation and hardware circuit fabrication.The experimental results show that this memristive chaotic system can lay the foundation for practical engineering fields such as secure communication and image encryption.