Controllable multi-scroll chaotic attractors with multiple wings in Chua’s system

Abstract

Controllable chaotic attractors with special structures have great value in engineering applications. In this paper, the novel controllable chaotic attractors are generated by constructing parameter controlled index-2 saddle-foci in Chua’s system. The chaotic attractors simultaneously contain two types of topological units, namely scroll and wing. There are potential differences among index-2 saddle-foci, which can be confirmed by the differences among eigenvalues and coexisting attractors. We propose the formation mechanism of wing, that is, the particle located in a index-2 saddle-focus region with weaker potential field is influenced by other index-2 saddle-foci regions with stronger potential field, it will escape from the constraint of weaker potential field before forming a spiral motion and then only form wings. Based on the formation mechanism of wing, half-saddle-foci or regions without equilibrium points but close to half-saddle-foci are constructed to further weaken the attraction of potential field and generate controllable wings. The analog circuit experiments confirmed the results.