Multi-ring julia fractal chaotic systems with separated scrolls and nested scrolls

Abstract

Chaos and fractals are two branches of nonlinear science. However, few scholars have combined chaos and fractals for generating chaotic attractors with different topologies. The main goal of this paper is to combine fractals and chaos to generate separated multi-scroll attractors and nested multi-scroll attractors, as well as to compensate for the lack of randomness and complexity of general chaotic systems. Combining chaotic attractors with two different fractal processes, a class of multi-scroll chaotic attractors with different behaviors are generated, including multi-ring attractors, separated multi-ring attractors, and nested multi-ring attractors. The experiments of spectral entropy (SE) complexity indicates that the proposed multi-ring fractal systems have higher complexity than other chaotic systems. Furthermore, from the perspective of engineering applications, the random performance of one of the multi-ring fractal systems is tested by the NIST test suite. The results demonstrate that the multi-ring fractal system has promising randomness and is well-suited for image encryption applications. Finally, the numerical simulation results are well illustrated by the micro-controller unit (MCU) hardware experiments, which reveal the feasibility of the designed multi-ring attractors, separated multi-ring attractors, and nested attractors.