Abstract
This paper develops an anticontrol approach to design a 3D continuous-time autonomous chaotic system with saddle-focus homoclinic orbit, based on two chaotification criterions for all orbits to be globally bounded with positive Lyapunov exponents. By using the Shil’nikov theorem, a Poincaré return map near the origin is found in the designed controlled system, confirming the existence of chaos in sense of the Smale horseshoe.
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