A Universal Matrix Transformation Method for Generating Multistructure Chaotic Attractors

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.