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Design and Implementation of Compound Chaotic attractors

This paper reports an autonomous-system-based approach for creating compound chaotic attractors from a class of generalized Lorenz systems via switching control. A state variable scale transformation is proposed for these systems to ensure that all attractors have comparable sizes. Coordinate transformation in the z-axis direction is also used, so that every pair of adjacent chaotic attractors have a common connected domain in the same phase space. Then, by switching control, the intended compound chaotic attractors can be generated. A circuit for a compound Lorenz–Chen–Lu chaotic attractor is designed and implemented for demonstration, which verifies the effectiveness of the proposed simulation-based technique. The aim of this report is to demonstrate the possibility of accomplishing such a very challenging task, leaving the extremely difficult underlying theory to future studies.