MULTI-DIRECTION CHAIN AND GRID CHAOTIC SYSTEM BASED ON JULIA FRACTAL
Xiangliang Xu, Guodong Li, Wanying Dai, Xiaoming Song
Abstract
In this paper, based on the multi-scroll chaotic system, multi-direction chain and grid chaotic attractors are generated by a new Julia fractal mapping process. The feasibility and effectiveness of the proposed method are verified by numerical simulation. This scheme not only realizes the combination of unidirectional and bidirectional distributed multi-scroll chaotic system and Julia fractal, but also applies to three-directional distributed 3D grid-like multi-scroll generalized Jerk system. This paper takes unidirectionally distributed multi-scroll chaos as an example. It discusses the influence of Julia fractals with coefficients and complex constants on the system and generalizes them to the higher-order Julia fractal mapping process. Then, three types of chaotic systems with controllable scroll numbers distributed in multiple directions are obtained. The results of the dynamic analysis method show that the post-fractal chaotic system not only increases the bifurcation interval of its parameters compared with the original chaotic system, but also increases the complexity of its sequence and the maximum Lyapunov exponent, and its attraction domain has a very complex fractal boundary. A kind of multi-directional chain chaotic attractor is realized by the Digital Signal Processors (DSP). The phase diagram of the oscilloscope is consistent with the result of numerical simulation, which verifies the possibility of this method in the digital circuit.