Stability of traveling wavefronts for a 2D lattice dynamical system arising in a diffusive population model. (English) Zbl 1485.39016
Summary: This paper is concerned with the traveling wavefronts of a 2D two-component lattice dynamical system. This problem arises in the modeling of a species with mobile and stationary subpopulations in an environment in which the habitat is two-dimensional and divided into countable niches. The existence and uniqueness of the traveling wavefronts of this system have been studied in [the author and S.-L. Wu, Nonlinear Anal., Real World Appl. 12, No. 2, 1178–1191 (2011; Zbl 1243.34013)]. However, the stability of the traveling wavefronts remains unsolved. In this paper, we show that all noncritical traveling wavefronts with given direction of propagation and wave speed are exponentially stable in time. In particular, we obtain the exponential convergence rate.
MSC:
| 39A14 | Partial difference equations |
| 34K31 | Lattice functional-differential equations |
| 92D25 | Population dynamics (general) |
Citations:
Zbl 1243.34013References:
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