Global phase portraits of the quadratic systems having a singular and irreducible invariant curve of degree 3
| Autor: | Llibre, Jaume, Pantazi, Chara |
|---|---|
| Přispěvatelé: | Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. UPCDS - Grup de Sistemes Dinàmics de la UPC |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Separatrices
Canonical regions Applied Mathematics Global phase portrait Matemàtiques i estadística::Topologia::Varietats topològiques [Àrees temàtiques de la UPC] Three-manifolds (Topology) Varietats topològiques de dimensió 3 Cubic curve Curves Algebraic Singular curve Polycycles Modeling and Simulation Poincaré disk Corbes algebraiques Poincaré Conjectura de Engineering (miscellaneous) Poincaré conjecture |
| Popis: | Any singular irreducible cubic curve (or simply, cubic) after an affine transformation can be written as either y2=x3 , or y2=x2(x+1) , or y2=x2(x-1) . We classify the phase portraits of all quadratic polynomial differential systems having the invariant cubic y2=x2(x+1) . We prove that there are 63 different topological phase portraits for such quadratic polynomial differential systems. We control all the bifurcations among these distinct topological phase portraits. These systems have no limit cycles. Only three phase portraits have a center, 19 of these phase portraits have one polycycle, three of these phase portraits have two polycycles. The maximum number of separartices that have these phase portraits is 26 and the minimum number is nine, the maximum number of canonical regions of these phase portraits is seven and the minimum is three. C. Pantazi is also partially supported by the grant PID-2021-122954NB-100 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|