Dynamic analysis and circuit design of tunable multi-vortex chaotic systems based on memristors

This paper proposes a new four-dimensional chaotic system that consists of two active magnetically controlled memristors. The dynamic characteristics of the system, including equilibrium points, Lyapunov exponent spectrum, bifurcation diagram, double-parameter Lyapunov exponent, and attractor basin, are analyzed. The results indicate that the Lyapunov exponents of the system undergo abrupt changes. The bifurcation diagrams reveal the occurrence of sudden cusp bifurcations, and the diverse manifestations of two-parameter Lyapunov exponents under different parameter combinations further underscore the system’s complexity and variability. This chaotic system also possesses an infinite number of equilibrium points and coexisting attractors, demonstrating multiple stable states. By adjusting parameters, multi-vortex chaotic attractors with high controllability can be generated, enabling the transition from two-vortex to four-vortex and then to multi-vortex chaotic systems. As the number of vortices increases, the system’s dynamic characteristics become richer and more complex. Introducing pulse functions has realized mirrored multi-vortex scroll chaotic attractors, further enhancing the chaotic characteristics of the system. To verify the feasibility and practical value of the mathematical model, a circuit model of the system was constructed. Simulations were conducted using Multisim software, and the system was implemented as a digital circuit using FPGA to validate its feasibility.