Stability of traveling wavefronts for a 2D lattice dynamical system arising in a diffusive population model

• Main Author: Haiqin Zhao
• Format: Article
• Language: English
• Published: SpringerOpen 2019-10-01
• Series: Advances in Difference Equations
• Subjects: Lattice differential system; Traveling wavefronts; Quiescent stage
• Online Access: http://link.springer.com/article/10.1186/s13662-019-2379-7

Abstract 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 (Zhao and Wu in Nonlinear Anal., Real World Appl. 12: 1178–1191, 2011). 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.