ASYMPTOTIC STABILITY OF TRAVELING WAVEFRONTS IN A DELAYED POPULATION MODEL WITH STAGE STRUCTURE ON A TWO-DIMENSIONAL SPATIAL LATTICE

作者：Cheng, Cui-Ping; Li, Wan-Tong^*; Wang, Zhi-Cheng

来源：Discrete and Continuous Dynamical Systems-Series B, 2010, 13(3): 559-575.

DOI：10.3934/dcdsb.2010.13.559

• Lattice differential equation
• traveling wave
• asymptotic stability
• energy estimates
• global interaction

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 a symptotic 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 wave front 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.

• 出版日期2010-5
• 单位兰州大学