Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/22829
Title: Traveling waves for a generalized Holling-Tanner predator-prey model
Contributor(s): Ai, Shangbing (author); Du, Yihong  (author)orcid ; Peng, Rui (author)
Publication Date: 2017
DOI: 10.1016/j.jde.2017.08.021
Handle Link: https://hdl.handle.net/1959.11/22829
Abstract: We study traveling wave solutions for Holling-Tanner type predator-prey models, where the predator equation has a singularity at zero prey population. The traveling wave solutions here connect the prey only equilibrium (1, 0)with the unique constant coexistence equilibrium (u∗, v∗). First, we give a sharp existence result on weak traveling wave solutions for a rather general class of predator-prey systems, with minimal speed explicitly determined. Such a weak traveling wave (u(ξ), v(ξ))connects (1, 0)at ξ=-∞but needs not connect (u∗, v∗)at ξ=∞. Next we modify the Holling-Tanner model to remove its singularity and apply the general result to obtain a weak traveling wave solution for the modified model, and show that the prey component in this weak traveling wave solution has a positive lower bound, and thus is a weak traveling wave solution of the original model. These results for weak traveling wave solutions hold under rather general conditions. Then we use two methods, a squeeze method and a Lyapunov function method, to prove that, under additional conditions, the weak traveling wave solutions are actually traveling wave solutions, namely they converge to the coexistence equilibrium as ξ→∞.
Publication Type: Journal Article
Grant Details: ARC/DP150101867
Source of Publication: Journal of Differential Equations, 263(11), p. 7782-7814
Publisher: Academic Press
Place of Publication: United States of America
ISSN: 1090-2732
0022-0396
Fields of Research (FoR) 2008: 010110 Partial Differential Equations
Fields of Research (FoR) 2020: 490410 Partial differential equations
Socio-Economic Objective (SEO) 2008: 970101 Expanding Knowledge in the Mathematical Sciences
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
Appears in Collections:Journal Article
School of Science and Technology

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