Abstract
In this paper, we study a generalized two-species contest-competition model with an Allee effect. We provide a complete analysis of the global dynamics of the system. In particular, we determine all the invariant manifolds, the extinction, the exclusion and the coexistence regions. We use tools from topology and dynamical systems to show that all orbits must converge to one of the equilibrium points of the system. The analysis shows that there are several potential scenarios including competition coexistence, exclusion and extinction.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1127-1151 |
| Number of pages | 25 |
| Journal | Journal of Difference Equations and Applications |
| Volume | 20 |
| Issue number | 8 |
| DOIs | |
| State | Published - 2014 |
| Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Algebra and Number Theory
- Applied Mathematics
Keywords
- Allee effect
- extinction region
- global dynamics
- monotonicity