Trait selection and rare mutations: the case of large diffusivities

Idriss Mazari (1, 2)

1 SU - Sorbonne Université
2 LJLL - Laboratoire Jacques-Louis Lions

We consider a system of N competing species, each of which can access a different resources distribution. We fully characterize the existence and stability of steady-states for large diffu-sivities. Indeed, we prove that the resources distribution yielding the largest population size at equilibrium is, broadly speaking, always the winner when species disperse quickly. The methods used rely on an expansion of the solutions of the Lotka-Volterra sytem for large diffusivities.

Mots clés: principal eigenvalue; coexistence steady-states; sta-; Diffusive Lotka-Volterra system

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Idriss Mazari. Trait selection and rare mutations: the case of large diffusivities. Discrete and Continuous Dynamical Systems - Series B, 2019. ⟨hal-01672067v3⟩