Traveling waves of some Holling–Tanner predator–prey system with nonlocal diffusion

2018 ◽  
Vol 338 ◽  
pp. 12-24 ◽  
Author(s):  
Hongmei Cheng ◽  
Rong Yuan
Keyword(s):  
Traveling Waves ◽  
Nonlocal Diffusion ◽  
Predator Prey ◽  
Prey System

Topological Horseshoes of Traveling Waves for a Fast–Slow Predator–Prey System

2006 ◽  
Vol 19 (3) ◽  
pp. 623-654 ◽  
Author(s):  
Marcio Gameiro ◽  
Tomáš Gedeon ◽  
William Kalies ◽  
Hiroshi Kokubu ◽  
Konstantin Mischaikow ◽  
...  
Keyword(s):  
Traveling Waves ◽  
Predator Prey ◽  
Prey System ◽  
Topological Horseshoes

TRAVELING WAVES IN A REACTION-DIFFUSION PREDATOR-PREY SYSTEM WITH NONLOCAL DELAYS

2012 ◽  
Vol 05 (05) ◽  
pp. 1250043
Author(s):  
ZHE LI ◽  
RUI XU
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Iteration Scheme ◽  
Monotonicity Condition ◽  
Predator Prey ◽  
Wave Solutions ◽  
Prey System ◽  
Theoretical Results

This paper is concerned with the existence of traveling wave solutions in a reaction-diffusion predator-prey system with nonlocal delays. By introducing a partially exponential quasi-monotonicity condition and a new cross iteration scheme, we reduce the existence of traveling wave solutions to the existence of a pair of upper-lower solutions. By constructing a desirable pair of upper-lower solutions, we establish the existence of traveling wave solutions. Finally, some numerical examples are carried out to illustrate the theoretical results.

Traveling waves for a periodic Lotka–Volterra predator–prey system

2018 ◽  
Vol 98 (14) ◽  
pp. 2619-2638 ◽  
Author(s):  
Xinjian Wang ◽  
Guo Lin
Keyword(s):  
Traveling Waves ◽  
Predator Prey ◽  
Prey System
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