Bistability of a two-species Gilpin-Ayala competition model with stage structure. (English) Zbl 07905139
Summary: The dynamic behavior of bistability is considered for a two-species Gilpin-Ayala competition model with stage structure. By the theory of generalized saddle-point behavior for monotone semiflows, it is shown that there admits an invariant and \(K\)-unordered \(C^1\)-separatrix, which separates the basins of attraction of the two locally stable single-species steady states. This implies that bistability occurs for two species. When two delays vary in their existence regions, we prove that the stability switching of the positive equilibria does not arise. By comparing with classical two-species Gilpin-Ayala competition model, we find that the introduction of stage structure brings negative effect on permanence of one species, but positive effect on its competitor. Finally, some numerical examples are given to illustrate the effectiveness of our theoretical results.
MSC:
| 34D23 | Global stability of solutions to ordinary differential equations |
| 35K57 | Reaction-diffusion equations |
| 37C65 | Monotone flows as dynamical systems |
| 47H07 | Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces |
| 92D25 | Population dynamics (general) |
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