Adjustable memristive multi-scroll hyperchaotic systems and their synchronization via adaptive super-twisting sliding mode control

This paper proposes a novel system construction method based on introducing memristors into a four-dimensional hyperchaotic conservative system. By leveraging the nonlinear characteristics of memristors to disrupt system conservatism, the transition from conservative systems to dissipative systems is achieved. On this basis, novel nonlinear functions are introduced to construct a one-dimensional memristive multi-scroll hyperchaotic system (1D-MMSHCS) and a two-dimensional memristive multi-scroll hyperchaotic system (2D-MMSHCS), respectively. Through equilibrium points analysis, coexisting attractors, bifurcation diagrams, and Lyapunov exponents, the complex dynamic behaviors of the memristive multi-scroll hyperchaotic systems are systematically revealed. To verify the hardware realizability of the memristive multi-scroll hyperchaotic systems, a digital hardware platform based on Field-Programmable Gate Array (FPGA) is developed, successfully implementing the 1D-MMSHCS and the 2D-MMSHCS. Addressing the synchronization problem of the more complex 2D-MMSHCS, unknown parameters can be estimated in real time through parameter adaptive mechanisms and dynamically adjust controller parameters, proposing an improved adaptive super-twisting sliding mode control method. Simulation results demonstrate that this method can achieve rapid system synchronization. The method also exhibits excellent robustness against time-varying bounded disturbances.