Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/56207
Title: Classification of the spreading behaviors of a two-species diffusion-competition system with free boundaries
Contributor(s): Du, Yihong  (author)orcid ; Wu, Chang-Hong (author)
Publication Date: 2022-02-03
DOI: 10.1007/s00526-021-02170-8
Handle Link: https://hdl.handle.net/1959.11/56207
Abstract: 

In this paper, we revisit the spreading behavior of two invasive species modelled by a diffusion-competition system with two free boundaries in a radially symmetric setting, where the reaction terms depict a weak-strong competition scenario. Our previous work (Du and Wu in Cal Var PDE 57:52, 2018) proves that from certain initial states, the two species develop into a "chase-and-run coexistence" state, namely the front of the weak species v propagates at a fast speed and that of the strong species u propagates at a slow speed, with their population masses largely segregated. Subsequent numerical simulations in Khan et al. (J Math Biol 83:23, 2021) suggest that for all possible initial states, only four different types of long-time dynamical behaviours can be observed: (1) chase-and-run coexistence, (2) vanishing of u with v spreading successfully, (3) vanishing of v with u spreading successfully, and (4) vanishing of both species. In this paper, we rigorously prove that, as the initial states vary, there are exactly five types of long-time dynamical behaviors: apart from the four mentioned above, there exists a fifth case, where both species spread successfully and their spreading fronts are kept within a finite distance to each other all the time. We conjecture that this new case can happen only when a parameter takes an exceptional value, which is why it has eluded the numerical observations of Khan et al. (J Math Biol 83:23, 2021) .

Publication Type: Journal Article
Grant Details: ARC/DP190103757
Source of Publication: Calculus of Variations and Partial Differential Equations, 61(2), p. 1-34
Publisher: Springer
Place of Publication: Germany
ISSN: 1432-0835
0944-2669
Fields of Research (FoR) 2020: 490410 Partial differential equations
490105 Dynamical systems in applications
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Publisher/associated links: https://link.springer.com/article/10.1007/s00526-021-02170-8
Appears in Collections:Journal Article
School of Science and Technology

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