Mathematics Faculty Proceedings, Presentations, Speeches, Lectures

Title

Predator-Mediated Coexistence with Attractive or Repulsive Prey-Taxis

Event Name/Location

Frontiers of Mathematical Biology: Modeling, Computation and Analysis, Orlando, Florida, May 2-4, 2018

Document Type

Conference Proceeding

Publication Date

5-2-2018

Abstract

The interactions of species can have significant impact on species distribution and diversity. For example, resource competition between two species can lead to a competitive exclusion where one species is driven to extinction. However, it is known that the presence of a predator can mediate a coexistence between the competing species and the predator. How this predator mediated coexistence is influenced by other predator mediated effects is less studied. Here we compare the impact on predator mediated coexistence when the predator is either attracted or repulsed by one of the prey choices. We study a system of three populations involving two competing species with a common predator. All three populations are mobile via diffusion within a bounded spatial domain Ω, but the predator’s movement is influenced by one prey’s gradient representing either prey-taxis (attraction) or a prey defense mechanism that is repulsive to the predator which we term repulsive prey-taxis. We prove existence of positive solutions, and investigate pattern formation through a Turing style bifurcation analysis and numerical simulation.

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