Existence of homoclinic orbits and heteroclinic cycle in a class of three-dimensional piecewise linear systems with three switching manifolds.
| Autor: | Zhu B; School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China., Wei Z; School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China., Escalante-González RJ; Electrical, Electronic and Mechatronics Department, Technological Institute of San Luis Potosí, San Luis Potosí, México., Kuznetsov NV; Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg, Russia. |
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| Jazyk: | angličtina |
| Zdroj: | Chaos (Woodbury, N.Y.) [Chaos] 2020 Dec; Vol. 30 (12), pp. 123143. |
| DOI: | 10.1063/5.0032702 |
| Abstrakt: | In this article, we construct a kind of three-dimensional piecewise linear (PWL) system with three switching manifolds and obtain four theorems with regard to the existence of a homoclinic orbit and a heteroclinic cycle in this class of PWL system. The first theorem studies the existence of a heteroclinic cycle connecting two saddle-foci. The existence of a homoclinic orbit connecting one saddle-focus is investigated in the second theorem, and the third theorem examines the existence of a homoclinic orbit connecting another saddle-focus. The last one proves the coexistence of the heteroclinic cycle and two homoclinic orbits for the same parameters. Numerical simulations are given as examples and the results are consistent with the predictions of theorems. |
| Databáze: | MEDLINE |
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