Dynamical analysis and hardware verification of a spatial multi-scroll chaotic system without equilibria

Abstract

With the wide application of multi-scroll chaotic systems, a growing emphasis on the development of such systems has been spurred in recent years. Here, a spatial hyperchaotic multi-scroll hidden system is established by introducing three multi-stable memristors into a simple chaotic system. Despite the absence of an equilibrium point in the proposed system, the introduction of three multi-stable memristors expands an original single-scroll attractor into a three-dimensional space, resulting in the emergence of a spatial multi-scroll hidden attractor (SMSHA). The formation mechanism of SMSHA is comprehensively discussed, revealing that each scroll in SMSHA originates from the virtual equilibrium points generated by the stable equilibrium points of the incorporated memristors. Furthermore, the number of scrolls is intricately linked to that of stable equilibrium points of the memristors. More significantly, numerical analyses using various nonlinear analysis tools reveal that the proposed system has complex dynamics, including homogeneous and heterogeneous multi-stability, and partial amplitude control. Finally, the hardware system based on microcontroller is implemented to validate the numerical findings.