A Universal Matrix Transformation Method for Generating Multistructure Chaotic Attractors
Ning Wang, Mengkai Cui, Yan Yang, Fatemeh Parastesh, Herbert Ho‐Ching Iu, Quan Xu
Abstract
The systematic control of chaotic phase orbits in desired location and orientation favors of the generation of multiwing/scroll attractors for potential industrial applications, which is an attractive but challenging work. In this article, we present a universal matrix transformation method for generating multistructure chaotic attractors. First, several basic transformation matrices or their composite forms are chosen to implement multiplex control of a seed. On this foundation, applying it in a general 3-D system and further obtaining the universal transformed system. Taking the Lorenz system, Chua's system, and Rössler system as the seeds, we construct various multistructure attractors with custom-shaped distributions via stringing together multiple separate units. The novelties are that the method is universal, has wide applicability, and does not introduce any extra variables for state-extension. Numerical phase orbits and hardware implementations verified the feasibility of the method. A pseudorandom number generator with qualified performance is implemented to support its potential applications.