The University of Arizona

Homoclinic bifurcations in models of vegetation patterns

Homoclinic bifurcations in models of vegetation patterns

Series: Analysis, Dynamics, and Applications Seminar
Location: Math 402
Presenter: Paul Carter, Department of Mathematics, University of Arizona

The formation of vegetation patterns in semiarid regions can be modeled by two-component reaction diffusion PDEs describing the interaction of water and plant density. In this talk I will consider a class of reaction-diffusion-advection equations which model the formation of slowly traveling vegetation stripe patterns on sloped terrain; due to the differing timescales describing the dispersal of biomass versus the downhill advection of water, the resulting equations are singularly perturbed. I will focus primarily on the existence problem, and I will present preliminary results regarding the existence of periodic orbits as well as single and multipulse homoclinic orbits using geometric singular perturbation theory and Melnikov theory.

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