Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane \Sigma which admits an invariant hyperplane \Omega transversal to \Sigma containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2016 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:169467 |
| Online Access: | https://ddd.uab.cat/record/169467 https://dx.doi.org/urn:doi:10.1016/j.jde.2015.12.034 |
| Access Level: | Open access |
| Keyword: | Crossing periodic orbits Limit cycle Lyapunov-Schmidt reduction Piecewise differential system |
| Summary: | We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane \Sigma which admits an invariant hyperplane \Omega transversal to \Sigma containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n = 3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms. |
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