We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model incorporating a prey refuge. By using the shooting argument, invariant manifold theory, and the Hopf bifurcation theorem, we analyze the dynamic behavior of this model in the three-dimensional phase space. Numerical results are also presented to illustrate the theoretical results.
Xiujuan Wu. Yong Luo. Yizheng Hu. "Traveling Waves in a Diffusive Predator-Prey Model Incorporating a Prey Refuge." Abstr. Appl. Anal. 2014 (SI01) 1 - 13, 2014. https://doi.org/10.1155/2014/679131