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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) ; 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 |
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Appears in Collections: | Journal Article School of Science and Technology |
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