Bifurcations from families of periodic solutions in piecewise differential systems
Consider a differential system of the form x'=F0(t,x)+∑ki=1εiFi(t,x)+εk+1R(t,x,ε),where Fi:S1×D → Rm and R:S1×D×(-ε0,ε0)→ Rm are piecewise Ck+1 functions and T-periodic in the variable t. Assuming that the unperturbed system x'= F0(t,x) has a d-dimensional submanifold of periodic solutions...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:221298 |
| Acceso en línea: | https://ddd.uab.cat/record/221298 https://dx.doi.org/urn:doi:10.1016/j.physd.2020.132342 |
| Access Level: | acceso abierto |
| Palabra clave: | Lyapunov-Schmidt reduction Periodic solution Averaging method Nonsmooth differential system Piecewise smooth differential system |
| Sumario: | Consider a differential system of the form x'=F0(t,x)+∑ki=1εiFi(t,x)+εk+1R(t,x,ε),where Fi:S1×D → Rm and R:S1×D×(-ε0,ε0)→ Rm are piecewise Ck+1 functions and T-periodic in the variable t. Assuming that the unperturbed system x'= F0(t,x) has a d-dimensional submanifold of periodic solutions with d < m, we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated T-periodic solutions of the above differential system. |
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