Global stability of a reaction-diffusion predator-prey model with a nonlocal delay

Authors:
Rui Xu;Zhien Ma
Affiliations:
Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, PR China;Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 2
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Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model

SIAM Journal on Applied Mathematics
Convergence of solutions of reaction-diffusion systems with time delays

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On the Dynamics of an Impulsive Reaction-Diffusion Predator-Prey System with Ratio-Dependent Functional Response

Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications

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Abstract

In this paper, a reaction-diffusion predator-prey system with nonlocal delay due to the gestation of the predator and homogeneous Neumann boundary conditions is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive steady state and each boundary steady state is established. The existence of Hopf bifurcations at the positive steady state is also discussed. Sufficient conditions are derived for the global stability of the positive steady state and the semi-trivial steady state of the proposed problem by using the method of upper-lower solutions and its associated monotone iteration scheme, respectively. Numerical simulations are carried out to illustrate the main results.