Positive steady state solutions of a plant-pollinator model with diffusion

Lijuan  Wang; Hongling  Jiang; Ying  Li

doi:10.3934/dcdsb.2015.20.1805

Article Contents

2015, Volume 20, Issue 6: 1805-1819. Doi: 10.3934/dcdsb.2015.20.1805

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Positive steady state solutions of a plant-pollinator model with diffusion

1.
Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013

Received: August 31, 2014

Revised: November 30, 2014

Published: July 2015

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Abstract

In this paper, a plant-pollinator population system with diffusion is investigated, which is described by a cooperative model with B-D functional response. Using the Leray-Schauder degree theory, we discuss the existence of positive steady state solutions of the model. The result shows when the growth rate of plants is large and the death rate of pollinators is small, the plants and pollinators can coexist. By the regular perturbation theorem and monotone dynamical system theory, the uniqueness and stability of positive solutions have been studied. Especially, we show that the unique positive solution is a global attractor under some conditions. Furthermore, we present some numerical simulations, which is not only to check our theoretical results but also to supply some conjectures out of theoretical analysis.

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Mathematics Subject Classification: Primary: 35J57; Secondary: 92D25.

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