Fast–Slow Dynamics for Intraguild Predation Models with Evolutionary Effects
| Autor: | Jianhe Shen, Cheng Hsiung Hsu, Ting Hui Yang |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Singular perturbation
Work (thermodynamics) Partial differential equation 010102 general mathematics Scale (descriptive set theory) 01 natural sciences 010101 applied mathematics Transcritical bifurcation Ordinary differential equation Quantitative Biology::Populations and Evolution Statistical physics Relaxation (approximation) 0101 mathematics Analysis Intraguild predation Mathematics |
| Zdroj: | Journal of Dynamics and Differential Equations. 32:895-920 |
| ISSN: | 1572-9222 1040-7294 |
| DOI: | 10.1007/s10884-019-09744-3 |
| Popis: | This work is concerned with the fast–slow dynamics for intraguild predation models with evolutionary effects. Assuming the survival pressure of the weaker predator induces evolution of it to the intraguild predator, then the system can be viewed as a singularly perturbed problem with two different time scales—predation time scale and evolution time scale. Using the geometric singular perturbation theory, we first completely analyze the limiting slow–fast dynamics of the system which involve the existence of turning points. Then, an application of the geometric singular perturbation theory gives rise to the birth of relaxation oscillations caused by the turning points and the associated delay of stability loss. From our main results, one can see that evolution enhances survival rates of inferior competitors. |
| Databáze: | OpenAIRE |
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