title: Travelling waves in the Holling-Tanner model with weak diffusion.
abstract: For a wide range of parameters, we study travelling 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 travelling waves of relaxation oscillation type are constructed using a recent generalization of the entry-exit function.
authors.affiliation: Department of Mathematics , Miami University , 301 South Patterson Avenue, Oxford, OH 45056, USA.
authors.forename: Anna
authors.initials: A
authors.lastname: Ghazaryan
authors.affiliation: Department of Mathematics , Miami University , 1601 University Boulevard, Hamilton, OH 45011, USA.
authors.forename: Vahagn
authors.initials: V
authors.lastname: Manukian
authors.affiliation: Department of Mathematics , North Carolina State University , 2108 SAS Hall, 2311 Stinson Drive, Raleigh, NC 27695, USA.
authors.forename: Stephen
authors.initials: S
authors.lastname: Schecter
keywords: diffusive Holling–Tanner model; entry–exit function; geometric singular perturbation theory; periodic wave train; predator–prey model; travelling front