scholarly journals Spatial dynamics of a nonlocal and delayed population model in a periodic habitat

2011 ◽  
Vol 29 (1) ◽  
pp. 343-366 ◽  
Author(s):  
Peixuan Weng ◽  
◽  
Xiao-Qiang Zhao ◽  
Keyword(s):  
Population Model ◽  
Spatial Dynamics ◽  
Delayed Population Model

scholarly journals Spatial Dynamics of a Nonlocal Dispersal Population Model in a Shifting Environment

2018 ◽  
Vol 28 (4) ◽  
pp. 1189-1219 ◽  
Author(s):  
Wan-Tong Li ◽  
Jia-Bing Wang ◽  
Xiao-Qiang Zhao
Keyword(s):  
Population Model ◽  
Spatial Dynamics ◽  
Nonlocal Dispersal

Traveling Waves Connecting Equilibrium and Periodic Orbit for a Delayed Population Model on a Two-Dimensional Spatial Lattice

2016 ◽  
Vol 26 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Cui-Ping Cheng ◽  
Wan-Tong Li ◽  
Zhi-Cheng Wang ◽  
Shenzhou Zheng
Keyword(s):  
Periodic Orbit ◽  
Traveling Waves ◽  
Population Model ◽  
Traveling Wave Solution ◽  
Heteroclinic Orbits ◽  
Two Dimensional ◽  
Regular Perturbation ◽  
Perturbation Problem ◽  
Spatial Lattice ◽  
Delayed Population Model

This paper is concerned with the existence of fast traveling waves connecting an equilibrium and a periodic orbit in a delayed population model with stage structure on a two-dimensional spatial lattice, under the assumption that the corresponding ODEs have heteroclinic orbits connecting an equilibrium point and a periodic solution. In this work, we rewrite the mixed functional differential equation as an integral equation in a Banach space and analyze the corresponding linear operator. Our approach eventually reduces a singular perturbation problem to a regular perturbation problem. The existence of traveling wave solution therefore is obtained by using the Liapunov–Schmidt method and implicit function theorem.

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