Wave train selection behind invasion fronts in reaction-diffusion predator-prey models

PHYSICA D-NONLINEAR PHENOMENA

卷:239

Article

Merchant, Sandra M.¹ 

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

关键词: Reaction-diffusion;    Wave train selection;    Periodic travelling waves;    Population cycles;    Coherent structures;    Predator invasion;   

DOI  :  10.1016/j.physd.2010.04.014

来源: Elsevier

【 摘 要 】

Wave trains, or periodic travelling waves, can evolve behind invasion fronts in oscillatory reaction-diffusion models for predator-prey systems. Although there is a one-parameter family of possible wave train solutions, in a particular predator invasion a single member of this family is selected. Sherratt (1998) [13] has predicted this wave train selection, using a lambda-omega system that is a valid approximation near a supercritical Hopf bifurcation in the corresponding kinetics and when the predator and prey diffusion coefficients are nearly equal. Away from a Hopf bifurcation, or if the diffusion coefficients differ somewhat, these predictions lose accuracy. We develop a more general wave train selection prediction for a two-component reaction-diffusion predator-prey system that depends on linearizations at the unstable homogeneous steady states involved in the invasion front. This prediction retains accuracy farther away from a Hopf bifurcation, and can also be applied when the predator and prey diffusion coefficients are unequal. We illustrate the selection prediction with its application to three models of predator invasions. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free