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2010, Volume 13, Issue 3: 559-575. Doi: 10.3934/dcdsb.2010.13.559
This issue Previous Article Spatial structures and generalized travelling waves for an integro-differential equation Next Article Three-dimensional sphere $S^3$-attractors in Rayleigh-Bénard convection

Asymptotic stability of traveling wavefronts in a delayed population model with stage structure on a two-dimensional spatial lattice

  • 1.

    School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000

  • 2.

    School of Mathematic and Statistics, Lanzhou University, Lanzhou, Gansu 730000

Received:  November 30, 2008
Revised:  December 31, 2009
Published:  September 2010
Abstract Related Papers Cited by
    Abstract
  • Recently, we derived a lattice model for a single species with stage structure in a two-dimensional patchy environment with infinite number of patches connected locally by diffusion and global interaction by delay (IMA J. Appl. Math., 73 (2008), 592-618.). The important feature of the model is the reflection of the joint effect of the diffusion dynamics, the nonlocal delayed effect and the direction of propagation. In this paper we study the asymptotic stability of traveling wavefronts of this model when the immature population is not mobile. Under the assumption that the birth function satisfies monostable condition, we prove that the traveling wavefront is exponentially stable by means of weighted energy method, when the initial perturbation around the wave is suitably small in a weighted norm. The exponential convergent rate is also obtained.
    Mathematics Subject Classification: Primary: 35B40, 35K57; Secondary: 35R20, 92D25.

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