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Travelling waves in the Holling-Tanner model with weak diffusion. (English) Zbl 1371.35302
Summary: 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.

MSC:
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35C07 Traveling wave solutions
92D25 Population dynamics (general)
35F50 Systems of nonlinear first-order PDEs
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