Homoclinic Bifurcations in Planar Piecewise-Linear Systems
| Autor: | Bin Xu, Fenghong Yang, Yun Tang, Mu Lin |
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| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Discrete Dynamics in Nature and Society, Vol 2013 (2013) |
| Druh dokumentu: | article |
| ISSN: | 1026-0226 1607-887X |
| DOI: | 10.1155/2013/732321 |
| Popis: | The problem of homoclinic bifurcations in planar continuous piecewise-linear systems with two zones is studied. This is accomplished by investigating the existence of homoclinic orbits in the systems. The systems with homoclinic orbits can be divided into two cases: the visible saddle-focus (or saddle-center) case and the case of twofold nodes with opposite stability. Necessary and sufficient conditions for the existence of homoclinic orbits are provided for further study of homoclinic bifurcations. Two kinds of homoclinic bifurcations are discussed: one is generically related to nondegenerate homoclinic orbits; the other is the discontinuity induced homoclinic bifurcations related to the boundary. The results show that at least two parameters are needed to unfold all possible homoclinc bifurcations in the systems. |
| Databáze: | Directory of Open Access Journals |
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