On the existence of heteroclinic cycles in some class of 3-dimensional piecewise affine systems with two switching planes |
| |
Authors: | Yanli Chen Lei Wang Xiao-Song Yang |
| |
Institution: | 1.School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan,China;2.School of Mathematics,Yibin University,Yibin,China;3.Department of Mathematics and Physics,Hefei University,Hefei,China;4.Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan,China |
| |
Abstract: | Since complicated dynamical behavior can occur easily near homoclinic trajectory or heteroclinic cycle in dynamical systems with dimension not less than three, this paper investigates the existence of heteroclinic cycles in some class of 3-dimensional three-zone piecewise affine systems with two switching planes. Based on the exact determination of the stable manifold, unstable manifold and analytic solution, a rigorous analytic methodology of designing chaos generators is proposed, which may be of potential applications to chaos secure communication. Furthermore, we obtain three sufficient conditions for the existence of a single or two heteroclinic cycles in three different cases. Finally, some examples are given to illustrate our theoretical results. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|