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Chaos and its control in an impulsive differential system. (English) Zbl 1142.93424
Summary: In this paper, the existence of chaos and its control in an autonomous impulsive differential system are discussed both theoretically and numerically. The existence of a snap-back repeller, as well as the chaos in the sense of Li-Yorke, is proved based on the qualitative analysis using the Poincaré map and the Lambert W-function. Moreover, the existence of the period-3 periodic window embedded in the chaotic region is also demonstrated. An algorithm of chaos control to stabilize the unstable periodic solutions is proposed. Detailed numerical results of chaotic attractors and stabilization of unstable periodic orbits by the impulsive effects, which are illustrated by an example, are in good agreement with the theoretical analysis.
MSC:
93D21Adaptive or robust stabilization
34A37Differential equations with impulses
37D45Strange attractors, chaotic dynamics