Design and FPGA implementation of nested grid multi-scroll chaotic system

Abstract

Conventional multi-scroll chaotic systems are often constrained by the number of attractors and the complexity of generation, making it challenging to meet the increasing demands of communication and computation. This paper revolves around the modified Chua’s system. By modifying its differential equation and introducing traditional nonlinear functions, such as the step function sequence and sawtooth function sequence. A nested grid multi-scroll chaotic system (NGMSCS) can be established, capable of generating nested grid multi-scroll attractors. In contrast to conventional grid multi-scroll chaotic attractors, scroll-like phenomena can be initiated outside the grid structure, thereby revealing more complex dynamic behavior and topological features. Through the theoretical design and analysis of the equilibrium point of the system and its stability, the number of saddle-focused equilibrium points of index 2 is further expanded, which can generate (2 N+2) × M attractors, and the formation mechanism is elaborated and verified in detail. In addition, the generation of an arbitrary number of equilibrium points in the y-direction is achieved by transforming the x and y variables, which can generate M×(2 N+2) attractors, increasing the complexity of the system. The system’s dynamical properties are discussed in depth via time series plots, Lyapunov exponents, Poincaré cross sections, 0–1 tests, bifurcation diagrams, and attraction basins. The existence of attractors is confirmed through numerical simulations and FPGA-based hardware experiments.