Observational analysis reveals diverse dynamics and robust synchronization in a memristive chaotic system, indicating effective control approaches.
A four-dimensional memristive chaotic system with only a single nonlinear term is proposed to reveal diverse dynamical behaviors under variations of parameters and initial conditions and to realize efficient synchronization control. Based on dissipativity analysis and Lyapunov exponent computation, combined with bifurcation analysis and multistability exploration, it is shown that the system possesses infinitely many unstable equilibrium points and exhibits both homogeneous and heterogeneous multistability, including point, periodic, and chaotic attractors. Moreover, it is found that amplitude modulation of the system's output signals can be precisely achieved by adjusting internal parameters of the memristor. A predefined-time sliding mode surface with linear and bidirectional power-law nonlinear decay terms is constructed to address synchronization. Sufficient conditions for predefined-time convergence of synchronization errors are derived using Lyapunov stability theory, and a double-stage sliding mode controller with an adjustable upper bound on synchronization time is designed. The resulting control law features an adjustable upper bound for the synchronization time and enables rapid error suppression under arbitrary initial disturbances. Numerical simulations confirm that the synchronization errors converge within the predefined time without overshoot or chattering, demonstrating high precision and strong robustness.
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Lai et al. (2025) studied this question.