| Abstract: |
| Motivated by evolutionary biology, we study general infinite-dimensional
dynamical systems involving two species - the resident and the invader. Sufficient conditions
for competitive exclusion phenomena are given when the two species play similar strategies. Those conditions are based on invasibility criteria, for instance, evolutionarily stable strategies in the framework of adaptive dynamics.
Such questions were first proposed and studied by Geritz and collaborators in the early 2000`s for a class of ordinary differential equations. We extend and generalize previous work in two directions. First, we consider analytic semiflows in infinite-dimensional spaces. Secondly, we device an argument based on the Hadamard graph transform method that does not depend on the monotonicity of the two-species system. Our results are applicable to a wide class of reaction-diffusion models as well as models with nonlocal diffusion operators. |
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