Competition for one nutrient with recycling and allelopathy in an unstirred chemostat

Hua  Nie; Feng-Bin Wang

doi:10.3934/dcdsb.2015.20.2129

Article Contents

2015, Volume 20, Issue 7: 2129-2155. Doi: 10.3934/dcdsb.2015.20.2129

This issue Previous Article Existence and uniqueness of steady flows of nonlinear bipolar viscous fluids in a cylinder Next Article Exponential stability of solutions to impulsive stochastic differential equations driven by $G$-Brownian motion

Competition for one nutrient with recycling and allelopathy in an unstirred chemostat

Hua Nie^1, and
Feng-Bin Wang^2,

1.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710119
2.
Department of Natural Science in the Center for General Education, Chang Gung University, Kwei-Shan, Taoyuan 333

Received: August 2014

Revised: January 2015

Published online: July 2015

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Abstract

In this paper, we study a PDE model of two species competing for a single limiting nutrient resource in a chemostat in which one microbial species excretes a toxin that increases the mortality of another. Our goal is to understand the role of spatial heterogeneity and allelopathy in blooms of harmful algae. We first demonstrate that the two-species system and its single species subsystem satisfy a mass conservation law that plays an important role in our analysis. We investigate the possibilities of bistability and coexistence for the two-species system by appealing to the method of topological degree in cones and the theory of uniform persistence. Numerical simulations confirm the theoretical results.

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Mathematics Subject Classification: Primary: 35B40, 35K57; Secondary: 92D25.

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