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

Files in This Item:
2 files
File Description SizeFormat 
Show full item record

SCOPUSTM   
Citations

33
checked on Sep 21, 2024

Page view(s)

1,568
checked on Jan 28, 2024
Google Media

Google ScholarTM

Check

Altmetric


Items in Research UNE are protected by copyright, with all rights reserved, unless otherwise indicated.