Global phase portraits of the generalized van der Pol systems
We consider the generalized van der Pol systems x˙ = y, y˙ = -x + (1-x) f(y), where f ∈ R[y]. The classical van der Pol systems have f(y) = y. We first characterize when the origin of the generalized van der Pol systems is a center, and second we provide the global phase portraits in the Poincaré di...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:274774 |
| Online Access: | https://ddd.uab.cat/record/274774 https://dx.doi.org/urn:doi:10.1016/j.bulsci.2022.103213 |
| Access Level: | Open access |
| Keyword: | Van der Pol systems Center Lyapunov constant Poincaré compactification Blow ups |
| Summary: | We consider the generalized van der Pol systems x˙ = y, y˙ = -x + (1-x) f(y), where f ∈ R[y]. The classical van der Pol systems have f(y) = y. We first characterize when the origin of the generalized van der Pol systems is a center, and second we provide the global phase portraits in the Poincaré disc of the generalized van der Pol when f(y) = ay + ay for all a,a ∈ R. |
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