Forced waves in a Lotka-Volterra competition-diffusion model with a shifting habitat

By Fang-Di Dong, Bingtuan Li, Wan-Tong Li. 2021

48 citations recorded by the source corpus.

Abstract We establish the existence of traveling waves for a Lotka-Volterra competition-diffusion model with a shifting habitat. It is assumed that the growth rate of each species is nondecreasing along the x-axis, positive near ∞ and negative near −∞, and shifting rightward at a speed c. We show that under appropriate conditions, for the case that one species is competitively stronger near ∞ and the case that both species coexist near ∞, there exists a critical number c ¯ ( ∞ ) such that for any c > c ¯ ( ∞ ) there exists a forced traveling wave with speed c connecting the origin and a semi-trivial steady state and for c c ¯ ( ∞ ) such a traveling wave does not exist. We also show that when a coexistence steady state exists, for any c > 0 , there is a forced traveling wave with speed c connecting the origin and the coexistence steady state.

Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/7a78aabfa11ec7e83ebdcca4507acb4c7b9f6688

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In Genetics

In Public Health, Environmental and Occupational Health

In Sociology and Political Science

Citations in the corpus

Persistence of species in a predator-prey system with climate change and either nonlocal or local dispersal (2021, background): “[12], and the persistence and extinction of species were established in [36, 40].”