Advanced Studies in Pure Mathematics

Existence of traveling wave solution in a diffusive predator-prey model with Holling type-III functional response

Chi-Ru Yang and Ting-Hui Yang

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Abstract

In this work, we show the existence of traveling wave solution of a diffusive predator-prey model with Holling type III functional response. The analysis is based on Wazewski's principle in the four-dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator-prey system under the moving coordinates.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 523-532

Dates
Received: 15 December 2011
Revised: 26 February 2013
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934251

Digital Object Identifier
doi:10.2969/aspm/06410523

Mathematical Reviews number (MathSciNet)
MR3381320

Zentralblatt MATH identifier
1378.34070

Subjects
Primary: 34C37: Homoclinic and heteroclinic solutions 35K57: Reaction-diffusion equations 92D25: Population dynamics (general) 92D40: Ecology

Keywords
Traveling wave solution Wazewski's principle Lyapunov function LaSalle's invariance principle

Citation

Yang, Chi-Ru; Yang, Ting-Hui. Existence of traveling wave solution in a diffusive predator-prey model with Holling type-III functional response. Nonlinear Dynamics in Partial Differential Equations, 523--532, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410523. https://projecteuclid.org/euclid.aspm/1540934251


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