Generating Grid Multiwing Chaotic Attractors by Constructing Heteroclinic Loops Into Switching Systems

Over the last two decades, multiwing chaos generation has seen promising advances and becomes an active research field today. It is well known that there is a gap between theoretical design and engineering applications in multiwing chaos generation. That is, most theoretical designs of multiwing chaotic attractors with mathematical proofs or numerical verification have rather complex expressions; however, most engineering applications of multiwing chaotic attractors without theoretical supports have simple expressions. To bridge the gap between theoretical design and engineering applications in multiwing chaos generation, this paper introduces a novel practical approach for generating grid multiwing butterfly chaotic attractors from the multipiecewise Lü system by constructing heteroclinic loops. It should be particularly pointed out that the designed multiwing chaotic attractors exhibit typical heteroclinic chaos from the heteroclinic Shil´nikov theorem and also have clear potential engineering applications. The proposed method can be easily extended to the generalized Lorenz system family.