Design and Implementation of Grid Multiwing Hyperchaotic Lorenz System Family via Switching Control and Constructing Super-Heteroclinic Loops

This paper initiates a systematic methodology for generating various grid multiwing hyperchaotic attractors by switching control and constructing super-heteroclinic loops from the piecewise linear hyperchaotic Lorenz system family. By linearizing the three-dimensional generalized Lorenz system family at their two symmetric equilibria and then introducing the state feedback, two fundamental four-dimensional linear systems are obtained. Moreover, a super-heteroclinic loop is constructed to connect all equilibria of the above two fundamental four-dimensional linear systems via switching control. Under some suitable conditions, various grid multiwing hyperchaotic attractors from the real world applications can be generated. Furthermore, a module-based circuit design approach is developed for realizing the designed piecewise linear grid multiwing hyperchaotic Lorenz and Chen attractors. The experimental observations validate the proposed systematic methodology for grid multiwing hyperchaotic attractors generation. Our theoretical analysis, numerical simulations and circuit implementation together show the effectiveness and universality of the proposed systematic methodology.