Hidden multistability in a hyperchaotic memristive system: theoretical analysis and electronic circuit implementation

Abstract To further increase the intricacy of chaotic dynamical systems and investigate the regulatory mechanisms of memristors in chaotic systems, a novel five-dimensional memristive hyperchaotic system with hidden attractors is built upon a four-dimensional chaotic system. First, the investigation begins by evaluating key dynamical metrics, including Lyapunov exponents, the Kaplan-Yorke dimension, dissipation rates, fixed-point configurations, and stability behavior. Second, the system’s dynamic behaviors are investigated by using the bifurcation diagrams, spectra of Lyapunov exponents, phase trajectories, and Poincaré mappings. The results show that the developed system not only exhibits parameter-dependent periodic attractors, quasi-periodic oscillations and chaotic attractors, revealing rich dynamic behavior transitions, but also exhibits coexisting attractors sensitive to initial conditions. Furthermore, the transient chaos and offset boost control are studied, and the effective control of the chaotic attractor space dimension is realized by introducing a control variable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>k</mml:mi> </mml:math> , which enables spatial translation of the attractor while preserving the original dynamics, as evidenced by unchanged Lyapunov exponent spectra. Finally, the results of circuit simulation and hardware experiment show that the attractor generated by the system is highly consistent with the numerical simulation in topology and dynamic characteristics, which fully verifies the correctness and physical feasibility of the theoretical model.