Design and FPGA realization of memristive multibutterfly chaotic system featuring coexisting attractors and complex multistability behavior

Abstract

Multibutterfly memristive chaotic systems (MMCSs) exhibit intricate multistable behavior and heightened randomness, making them highly advantageous for secure communications and image encryption. The paper provides a new five-dimensional chaotic system that incorporates two memristors into a 3D chaotic framework, leading to the creation of multibutterfly chaotic attractors. The quantity of multibutterfly chaotic attractors is capable of being managed by varying the parameters \(\mathrm M\) and \(\mathrm N\). We conduct an in-depth analysis of the five-dimensional MMCS dynamics through methods like Lyapunov exponents, Poincare maps, phase diagrams, and bifurcation diagrams. We depicted the basin of attraction for exploring the system’s coexisting attractors. Furthermore, the five-dimensional MMCS exhibits the coexisting attractors through variations in the initial values. By tuning parameters \(k_{1}\) and \(k_{2}\), the system’s amplitude can be adjusted. To validate the practical applicability of this system, we design a chaotic circuit based on the five-dimensional MMCS. The system is implemented on a Cyclone IV E series platform with the EP4CE15F23C8N FPGA as the primary chip. The FPGA implementation results align numerical simulations, confirming the practical applicability of the multibutterfly memristive chaotic circuit.