On the number of limit cycles for discontinuous piecewise linear differential systems in R^2n with two zones
We study the number of limit cycles of the discontinuous piecewise linear differential systems in R2n with two zones separated by a hyperplane. Our main result shows that at most (8n-6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small par...
| Authors: | , |
|---|---|
| Format: | article |
| Publication Date: | 2013 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:150645 |
| Online Access: | https://ddd.uab.cat/record/150645 https://dx.doi.org/urn:doi:10.1142/S0218127413500247 |
| Access Level: | Open access |
| Keyword: | Limit cycles, averaging method Discontinuous piecewise linear differential systems |
| Summary: | We study the number of limit cycles of the discontinuous piecewise linear differential systems in R2n with two zones separated by a hyperplane. Our main result shows that at most (8n-6)n-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not necessary. |
|---|