2012/11/16 by Benoît Sarels, Benoit Sarels, Sarels, Benoit
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · Physics and Astronomy · #FOS: Biological sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation #Populations and Evolution (q-bio.PE) #q-bio.PE #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1211.3858
15 pages, 3 figures
arxiv created 2012/11/16 · openalex publication_date 2012/11/16 · arxiv updated 2012/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study a simple one-dimensional model of reaction-diffusion with bistable non-linearity and in heterogeneous media. The bistable term accounts for the so-called Allee effect, and the heterogeneity in the media is localized. We recall the definition of a transition wave used in similar situations by well-known authors, and propose an alternative definition for discussion. We call it generalized traveling wave. As a consequence, we give new results of pinning in such media, due to Allee effect.