2018/12/13 by Léo Girardin, Girardin, Léo · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1812.05336
openalex publication_date 2018/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent paper by Cantrell, Cosner and Yu, two-component KPP systems with\ncompetition of Lotka--Volterra type were analyzed and their long-time behavior\nlargely settled. In particular, the authors established that any constant\npositive steady state, if unique, is necessarily globally attractive. In the\npresent paper, we give an explicit and biologically very natural example of\noscillatory three-component system. Using elementary techniques or\npre-established theorems, we show that it has a unique constant positive steady\nstate with two-dimensional unstable manifold, a stable limit cycle, a\npredator--prey structure near the steady state, periodic wave trains and\npoint-to-periodic rapid traveling waves. Numerically, we also show the\nexistence of pulsating fronts and propagating terraces.\n