Co-existence of a Period Annulus and a Limit Cycle in a Class of Predator-Prey Models with Group Defense
| Autor: | Robert E. Kooij, André Zegeling |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Class (set theory)
Applied Mathematics Period (gene) Functional response Generalized Gause model Predation limit cycle Singularity functional response Modeling and Simulation Limit cycle bifurcation Annulus (firestop) Applied mathematics Quantitative Biology::Populations and Evolution Engineering (miscellaneous) Group defense Mathematics |
| Zdroj: | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 31(10) |
| ISSN: | 0218-1274 |
| Popis: | For a family of two-dimensional predator–prey models of Gause type, we investigate the simultaneous occurrence of a center singularity and a limit cycle. The family is characterized by the fact that the functional response is nonanalytical and exhibits group defense. We prove the existence and uniqueness of the limit cycle using a new theorem for Liénard systems. The new theorem gives conditions for the uniqueness of a limit cycle which surrounds a period annulus. The results of this paper provide a mechanism for studying the global behavior of solutions to Gause systems through bifurcation of an integrable system which contains a center and a limit cycle. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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