A memristive hyperchaotic system with multiple butterfly-shaped attractors: Modeling, analysis and hardware implementation

In this study, the design of a multi-butterfly hyperchaotic system based on hyperbolic-function memristors and its application to finite-time synchronization are investigated, with numerical simulations, experimental tests, and physical verification also performed. First, a mathematical model of the hyperbolic flux-controlled memristor is constructed and its basic characteristics are verified. Based on this memristor model, a novel chaotic system is proposed. Then, the dynamical characteristics of the proposed system are systematically analyzed, including dissipativity, equilibrium points, Lyapunov and bifurcation diagrams, spiking oscillations, symmetry, coexisting attractors and complexity, among others, which collectively reveal its rich dynamical behaviors and potential application value. Building on this, the circuit design, simulation verification and hardware circuit was physically implemented, which provides a theoretical basis for the actual implementation. Finally, the application of the chaotic system in finite-time synchronization is explored, and the feasibility and effectiveness of the system in the fields of information security and synchronization control are verified. The results show that the memristive chaotic system not only exhibits complex and diverse dynamic characteristics, but also provides a viable strategy for achieving high-speed and finite-time chaotic synchronization.