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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Stability of traveling waves for systems of nonlinear integral recursions in spatial population biology

Pages: 895 - 925, Volume 16, Issue 3, October 2011      doi:10.3934/dcdsb.2011.16.895

 
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Judith R. Miller - Dept. of Mathematics and Statistics, Georgetown University, Washington DC 20057, United States (email)
Huihui Zeng - Dept. of Mathematics and Statistics, Georgetown University, Washington DC 20057, United States (email)

Abstract: We use spectral methods to prove a general stability theorem for traveling wave solutions to the systems of integrodifference equations arising in spatial population biology. We show that non-minimum-speed waves are exponentially asymptotically stable to small perturbations in appropriately weighted $L^\infty$ spaces, under assumptions which apply to examples including a Laplace or Gaussian dispersal kernel a monotone (or non-monotone) growth function behaving qualitatively like the Beverton-Holt function (or Ricker function with overcompensation), and a constant probability $p\in [0,1)$ (or $p=0$) of remaining sedentary for a single population; as well as to a system of two populations exhibiting non-cooperation (in particular, Hassell and Comins' model [6]) with $p=0$ and Laplace or Gaussian dispersal kernels which can be different for the two populations.

Keywords:  Traveling wave, stability, integrodifference equation.
Mathematics Subject Classification:  Primary: 92D25, 92D40; Secondary: 47G10.

Received: June 2010;      Revised: December 2010;      Available Online: June 2011.

 References