Dynamic analysis and finite-time control of a memristor-based six-dimensional hyperchaotic system

Memristors possess memory and nonlinear characteristics. Constructing high-dimensional nonlinear circuit systems using memristors can enhance the nonlinear coupling relationships among state variables and generate more complex dynamic behaviors. However, as the system's dimensions and nonlinear coupling relationships increase, synchronization control of high-dimensional hyperchaotic systems becomes more difficult. Meanwhile, synchronization control methods for high-dimensional hyperchaotic systems often suffer from complex controller structures, model dependence, and an uncertain convergence time. Therefore, this paper designs a six-dimensional hyperchaotic circuit using memristors and circuit components to enhance the nonlinear characteristics and dynamic complexity of the system. By applying Kirchhoff's current law and Kirchhoff's voltage law, the dynamic equations of the circuit state variables are established. Furthermore, the dynamic analysis, Multisim circuit simulation, and FPGA (Field Programmable Gate Array) hardware implementation results verify that the system exhibits hyperchaotic behavior. In addition, this paper proposes a finite-time synchronization control scheme with a simple structure and an explicit convergence time estimate, which enables the synchronization of hyperchaotic systems within a finite time. Based on Lyapunov stability theory and matrix inequalities, sufficient conditions for finite-time synchronization are derived. Numerical simulations further verify the effectiveness and feasibility of the proposed scheme.