Dynamical analysis and FPGA implementation of a memristive non-Hamiltonian conservative hyperchaotic system with extreme multistability

Abstract

Recent studies indicate that coupling a memristor with a nonlinear circuit can generate more complex dynamical behaviors. However, research on high-dimensional memristor-based conservative systems remains scarce, and existing low-dimensional memristive systems have yet to exhibit rich dynamic characteristics. In this work, we integrate a magnetically controlled memristor into a conservative chaotic circuit, proposing a novel four-dimensional memristive non-Hamiltonian conservative hyperchaotic system (MHHS) with hidden chaotic dynamics. Through dissipation analysis, Lyapunov exponents, and energy evolution, we verify the system’s non-Hamiltonian conservative properties and hyperchaotic nature. The MHHS system demonstrates high sensitivity to initial conditions and parameters, exhibiting extreme multistability phenomena governed by Hamiltonian energy variations. Phase-space analysis reveals diverse multistable attractors under different initial conditions. Time-series analysis further identifies three distinct transition behaviors: (1) amplitude expansion, (2) quasiperiodic-to-hyperchaotic transitions, and (3) the coexistence of multiple topological states. The system’s chaotic sequences pass the NIST randomness tests, confirming strong pseudorandomness, while Shannon entropy (SE) complexity analysis highlights their high unpredictability. Finally, we implement the MHHS system on FPGA hardware using the fourth-order Runge–Kutta method, experimentally validating its physical realizability. This study not only advances the theoretical understanding of conservative hyperchaotic systems but also provides practical foundations for high-security chaos-based encryption applications.