Traveling waves in delayed predator-prey systems with nonlocal diffusion and stage structure

Authors:
Guo-Bao Zhang;Wan-Tong Li;Guo Lin
Affiliations:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China;School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China;School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

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Traveling waves in diffusive predator-prey equations: periodic orbits and point-to-periodic heteroclinic orbits

SIAM Journal on Applied Mathematics

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Abstract

This paper is concerned with the existence of traveling wave solutions of a delayed predator-prey system with stage structure and nonlocal diffusion. By introducing the partial quasi-monotone condition and cross-iteration scheme, we first consider a class of delayed systems with nonlocal diffusion and deduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. When the result is applied to the predator-prey system, we establish the existence of traveling wave solutions, as well as its precisely asymptotic behavior. Our result implies that there is a transition zone moving from the steady state with no species to the steady state with the coexistence of both species.