Stability and cyclicity of polycycles in non-smooth planar vector fields
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909193009627136 |
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| author | Santana, Paulo |
| author_facet | Santana, Paulo |
| contents | In this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to planar non-smooth vector fields (also known as piecewise vector fields, or Filippov systems). The polycycles considered here may contain hyperbolic saddles, semi-hyperbolic saddles, saddle-nodes and tangential singularities of any degree. We determine when the polycycle is stable or unstable. We prove the bifurcation of at most one limit cycle in some conditions and at least one limit cycle for each singularity in other conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_11674 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stability and cyclicity of polycycles in non-smooth planar vector fields Santana, Paulo Dynamical Systems 34A36, 34C23, 34C37, 37C29, 37G15 In this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to planar non-smooth vector fields (also known as piecewise vector fields, or Filippov systems). The polycycles considered here may contain hyperbolic saddles, semi-hyperbolic saddles, saddle-nodes and tangential singularities of any degree. We determine when the polycycle is stable or unstable. We prove the bifurcation of at most one limit cycle in some conditions and at least one limit cycle for each singularity in other conditions. |
| title | Stability and cyclicity of polycycles in non-smooth planar vector fields |
| topic | Dynamical Systems 34A36, 34C23, 34C37, 37C29, 37G15 |
| url | https://arxiv.org/abs/2112.11674 |