Travelling waves for diffusive and strongly competitive systems: relative motility and invasion speed

Léo Girardin (1) , Grégoire Nadin (2)

1 ENS Cachan - École normale supérieure - Cachan
2 LJLL - Laboratoire Jacques-Louis Lions

Our interest here is to find the invader in a two species, diffusive and competitive Lotka Volterra system in the particular case of travelling wave solutions. We investigate the role of diffusion in homogeneous domains. We might expect a priori two dierent cases: strong interspecific competition and weak interspecific competition. In this paper, we study the first one and obtain a clear conclusion: the invading species is, up to a fixed multiplicative constant, the more diffusive one.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [cs.NA]

Léo Girardin, Grégoire Nadin. Travelling waves for diffusive and strongly competitive systems: relative motility and invasion speed. European Journal of Applied Mathematics, 2015, ⟨10.1017/S0956792515000170⟩. ⟨hal-01135087⟩