Perturbation theory of the quadratic Lotka-Volterra double center
| Autor: | Lubomir Gavrilov, Jean-Pierre Françoise |
|---|---|
| Přispěvatelé: | Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
limit cycles
Applied Mathematics General Mathematics Double centers Dynamical Systems (math.DS) Center (group theory) Quadratic system Bifurcation function Quadratic equation Bifurcation theory Iterated integrals Bautin ideal FOS: Mathematics iterated integrals Perturbation theory [MATH]Mathematics [math] Mathematics - Dynamical Systems 34C05 37F75 34M35 Mathematical physics Mathematics |
| Zdroj: | Communications in Contemporary Mathematics Communications in Contemporary Mathematics, 2021, 24 (5), pp.2150064. ⟨10.1142/S0219199721500644⟩ |
| ISSN: | 0219-1997 |
| Popis: | We revisit the bifurcation theory of the Lotka-Volterra quadratic system \begin{eqnarray} X_0 :\left\{\begin{aligned} \dot{x}=& - y -x^2+y^2 ,\\ \dot{y}= &\;\;\;\;x - 2xy \end{aligned} \right. \end{eqnarray} with respect to arbitrary quadratic deformations. The system $X_0$ has a double center, which is moreover isochronous. We show that the deformed system $X_0$ can have at most two limit cycles on the finite plane, with possible distribution $(i,j)$, where $i+j\leq2$. Our approach is based on the study of pairs of bifurcation functions associated to the centers, expressed in terms of iterated path integrals of length two. 40 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|