Traveling Waves in the Holling-tanner Model with Weak Diffusion

For wide range of parameters, we study traveling waves in a diffusive version of the Holling-Tanner predator-prey model from population dynamics. Fronts are constructed using geometric singular perturbation theory and the theory of rotated vector fields. We focus on the appearance of the fronts in various singular limits. In addition, periodic traveling waves of relaxation oscillation type are constructed using a recent generalization of the entry-exit function. Anna Ghazaryan , Vahagn Manukian , and Stephen Schecter c a Department of Mathematics, Miami University, 301 S. Patterson Ave, Oxford, OH 45056, USA, Ph. 1-513-529-0582, [email protected] b Department of Mathematics, Miami University, 1601 University Blvd, Hamilton, OH 45011, USA, Ph. 1-513-785-3220, [email protected] c Department of Mathematics, North Carolina State University, 2108 SAS Hall, 2311 Stinson Drive, Raleigh, NC 27695, USA, Ph. 1-919-515-6533, [email protected]