Coexistence of competing consumers on a single resource in a hybrid model
| Autor: | Yunfeng Geng, Frithjof Lutscher, Xiaoying Wang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Resource (biology)
Applied Mathematics Reproduction (economics) 010102 general mathematics Stable equilibrium Climate change Linear analysis 01 natural sciences Expression (mathematics) 010101 applied mathematics Population cycle Discrete Mathematics and Combinatorics 0101 mathematics Hybrid model Mathematical economics Mathematics |
| Zdroj: | Discrete & Continuous Dynamical Systems - B. 26:269-297 |
| ISSN: | 1553-524X |
| Popis: | The question of whether and how two competing consumers can coexist on a single limiting resource has a long tradition in ecological theory. We build on a recent seasonal (hybrid) model for one consumer and one resource, and we extend it by introducing a second consumer. Consumers reproduce only once per year, the resource reproduces throughout the"summer" season. When we use linear consumer reproduction between years, we find explicit expressions for the trivial and semi-trivial equilibria, and we prove that there is no positive equilibrium generically. When we use non-linear consumer reproduction, we determine conditions for which both semi-trivial equilibria are unstable. We prove that a unique positive equilibrium exists in this case, and we find an explicit analytical expression for it. By linear analysis and numerical simulation, we find bifurcations from the stable equilibrium to population cycles that may appear through period-doubling or Hopf bifurcations. We interpret our results in terms of climate change that changes the length of the"summer" season. |
| Databáze: | OpenAIRE |
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