The Krylov-Bogoliuvob-Mitropolsky averaging method for polynomial dynamical systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915227530952704 |
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| author | Alvarez, Frank Ernesto Ricard, Mariano Rodriguez |
| author_facet | Alvarez, Frank Ernesto Ricard, Mariano Rodriguez |
| contents | We describe the transformation of a polynomial planar dynamical system into a second order differential equation by means of a polynomial change of variables. We then, by means of the Krylov-Bogoliubov-Mitropolsky averaging method, identify sufficient conditions involving said change of variables so that a limit cycle exists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00268 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Krylov-Bogoliuvob-Mitropolsky averaging method for polynomial dynamical systems Alvarez, Frank Ernesto Ricard, Mariano Rodriguez Dynamical Systems Analysis of PDEs 34C07, 34C29, 37G15, 34E10 We describe the transformation of a polynomial planar dynamical system into a second order differential equation by means of a polynomial change of variables. We then, by means of the Krylov-Bogoliubov-Mitropolsky averaging method, identify sufficient conditions involving said change of variables so that a limit cycle exists. |
| title | The Krylov-Bogoliuvob-Mitropolsky averaging method for polynomial dynamical systems |
| topic | Dynamical Systems Analysis of PDEs 34C07, 34C29, 37G15, 34E10 |
| url | https://arxiv.org/abs/2504.00268 |