Homoclinic Orbits in Several Classes of Three-Dimensional Piecewise Affine Systems with Two Switching Planes

Yanli Chen, Lei Wang and Xiaosong Yang
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Yanli Chen: School of Economics and Management, Yibin University, Yibin 644007, China
Lei Wang: Department of Mathematics and Physics, Hefei University, Hefei 230601, China
Xiaosong Yang: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

Mathematics, 2021, vol. 9, issue 24, 1-15

Abstract: The existence of homoclinic orbits or heteroclinic cycle plays a crucial role in chaos research. This paper investigates the existence of the homoclinic orbits to a saddle-focus equilibrium point in several classes of three-dimensional piecewise affine systems with two switching planes regardless of the symmetry. An analytic proof is provided using the concrete expression forms of the analytic solution, stable manifold, and unstable manifold. Meanwhile, a sufficient condition for the existence of two homoclinic orbits is also obtained. Furthermore, two concrete piecewise affine asymmetric systems with two homoclinic orbits have been constructed successfully, demonstrating the method’s effectiveness.

Keywords: piecewise affine systems; two switching planes; homoclinic orbit (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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