2023/06/01 by Li, Hongliang, Zhao, Min, Yuan, Rong
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2306.00666
In this paper, a ratio-dependent Holling-Tanner system with nonlocal diffusion is taken into account, where the prey is subject to a strong Allee effect. To be special, by applying Schauder's fixed point theorem and iterative technique, we provide a general theory on the existence of traveling waves for such system. Then appropriate upper and lower solutions and a novel sequence, similar to squeeze method, are constructed to demonstrate the existence of traveling waves for c>c*. Moreover, the existence of traveling wave for c=c* is also established by spreading speed theory and comparison principle. Finally, the nonexistence of traveling waves for c