Abstract
We establish the existence of traveling wave solution for a reaction-diffusion predator-prey system with Holling type-IV functional response. For simplicity, only one space dimension will be involved, the traveling solution equivalent to the heteroclinic orbits inR3. The methods used to prove the result are the shooting argument and the invariant manifold theory.
Highlights
The paper will study the traveling wave solution for a diffusive predator-prey system with Holling type-IV functional response, which is as follows: ut = d1uxx + Au (1 − u K ) Buw 1 + Eu2 (1) wt d2wxx w( 1
Gardner [8] proved the existence of traveling wave solutions for a diffusive predator-prey system with Holling type-II functional response by using the connection index
Li and Wu [15] studied a system with Holling type-III functional response and proved the existence of traveling wave solutions by using the shooting argument in R3 together with a Lyapunov function [16], LaSalle’s invariance principle [17], and the Hopf bifurcation theorem [18]
Summary
The paper will study the traveling wave solution for a diffusive predator-prey system with Holling type-IV functional response, which is as follows: ut. Gardner [8] proved the existence of traveling wave solutions for a diffusive predator-prey system with Holling type-II functional response by using the connection index. Holling type-II functional response, when the diffusive rates of the prey and the predator are not zero, possesses traveling wave solutions. Li and Wu [15] studied a system with Holling type-III functional response and proved the existence of traveling wave solutions by using the shooting argument in R3 together with a Lyapunov function [16], LaSalle’s invariance principle [17], and the Hopf bifurcation theorem [18].
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