Title: Dynamics of an almost periodic delayed predator-prey model with Beddington-DeAngelis functional response

Authors: Liyan Pang

Addresses: School of Mathematics and Computer Science, Ningxia Normal University, Guyuan, Ningxia 756000, China

Abstract: Using the continuation theorem of coincidence degree theory and constructing a suitable Lyapunov functional, sufficient conditions are established for the existence, uniqueness and global asymptotic stability of positive almost periodic solution to a predator-prey model with Beddington-DeAngelis functional response and time delays. Further, the multiplicity of positive almost periodic solutions for the aforementioned model is considered. The main results obtained in this paper are completely new, and the method used in this paper provides a possible method to study the existence, uniqueness, uniform asymptotical stability and multiplicity of positive almost periodic solution of the models in biological populations. Finally, some examples and numerical simulations are given to illustrate the feasibility and effectiveness of our main results.

Keywords: coincidence degree; Lyapunov functional; multiplicity; asymptotic stability; positive almost periodic solution; predator-prey systems; Beddington-DeAngelis functional response; time delays; biological populations.

DOI: 10.1504/IJDSDE.2016.081814

International Journal of Dynamical Systems and Differential Equations, 2016 Vol.6 No.4, pp.285 - 304

Received: 23 Feb 2016
Accepted: 02 May 2016
Published online: 26 Jan 2017 *

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