Design of Grid Multi-Wing Chaotic Attractors Based on Fractional-Order Differential Systems

Abstract

In this article, a new method for generating grid multi-wing chaotic attractors from fractional-order linear differential systems is proposed. In order to generate grid multi-wing attractors, we extend the method of constructing heteroclinic loops from classical differential equations to fractional-order differential equations. Firstly, two basic fractional-order linear systems are obtained by linearization at two symmetric equilibrium points of the fractional-order Rucklidge system. Then a heteroclinic loop is constructed and all equilibrium points of the two basic fractional-order linear systems are connected by saturation function switching control. Secondly, the theoretical methods of switching control and construction of heteromorphic rings of fractal-order two-wing and multi-wing chaotic attractors are studied. Finally, the feasibility of the proposed method is verified by numerical simulation.

Bipolar-growth multi-wing attractors and diverse coexisting attractors in a new memristive chaotic system

“…[2][3][4][5][6][7][8] In the past few decades, researchers have been exploring the chaos that can produce complex dynamical behavior, and it is worth mentioning that multi-scroll attractors and coexisting attractors have become a hot topic in nonlinear research. [9][10][11][12][13][14][15][16][17][18][19] The state variable can go through multiple orbital states and jump randomly in different transitions for the multi-scroll attractors. The coexisting attractors can provide multiple optional steady states for the system to respond to different needs, so it is very meaningful to construct multi-scroll systems with abundant coexisting attractors.…”