Abstract

CORTES-GARCIA, Christian  and  RAMIREZ-FIERRO, Allison. Traveling wave type solution in a Model Diffusive Predator-Prey type Holling II. Rev. Mat [online]. 2021, vol.28, n.2, pp.209-236. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v28i2.38645.

This paper demonstrates the existence of traveling waves as solutions for a predator - prey model with a Holling II predation function and a onedimensional diffusive term for predators. When performing a qualitative analysis on the model without diffusion, it follows that the model with diffusion presents periodic solutions. Similarly, by assuming a traveling wave-type solution to the diffusion model, it is shown that it has a heteroclinical orbit that connects two equilibrium points, attracted to one of them, and therefore presents wave fronts.

Keywords : Gause model; limit cycle; Hartman Grobman theorem; LaSalle principle; Hopf bifurcation theorem..

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