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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 1805 - 1819, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1805

 
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Lijuan Wang - Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013, China (email)
Hongling Jiang - Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013, China (email)
Ying Li - Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013, China (email)

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.

Keywords:  Plant-pollinator population model, steady state, positive solution, numerical simulation.
Mathematics Subject Classification:  Primary: 35J57; Secondary: 92D25.

Received: September 2014;      Revised: December 2014;      Available Online: June 2015.

 References