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Sliding homoclinic orbits and bifurcations of three-dimensional piecewise affine systems |
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| Authors: | Wu Tiantian Huan Songmei Liu Xiaojuan |
| Institution: | 1.School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, People’s Republic of China ;2.School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China ;3.School of Mathematics and Statistics, Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Wuhan, 430074, People’s Republic of China ; |
| Abstract: | Sliding dynamics is a peculiar phenomenon to discontinuous dynamical systems, while homoclinic orbits play a role in studying the global dynamics of dynamical systems. This paper provides a method to ensure the existence of sliding homoclinic orbits of three-dimensional piecewise affine systems. In addition, sliding cycles are obtained by bifurcations of the systems with sliding homoclinic orbits to saddles. Two examples with simulations of sliding homoclinic orbits and sliding cycles are provided to illustrate the effectiveness of the results. |
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