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Generating 3-D multi-scroll chaotic attractors: a hysteresis series switching method. (English) Zbl 1162.93353

Summary: This paper introduces a systematic method-a hysteresis series switching approach-for generating multi-scroll chaotic attractors from a three-dimensional linear autonomous system, including 1-D \(n\)-scroll, 2-D \(n-m\)-grid scroll, and 3-D \(n-m-l\)-grid scroll chaotic attractors. The chaos generation mechanism is studied by analyzing the system trajectories and the hysteresis switching dynamics of the controlled chaotic systems are explored. Moreover, a two-dimensional Poincaré return map is rigorously derived. This map and its maximum Lyapunov exponent are applied to verifying the chaotic behaviors of the generated 3-D multi-scroll chaotic attractors.

MSC:

93C10 Nonlinear systems in control theory
34C55 Hysteresis for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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