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Abstract and Applied Analysis
Volume 2012, Article ID 963486, 33 pages
Research Article

Dynamics of Mutualism-Competition-Predator System with Beddington-DeAngelis Functional Responses and Impulsive Perturbations

1School of Mathematics Science, Harbin Normal University, Harbin 150500, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China
3Foundation Department, Harbin Finance University, Harbin 150030, China

Received 17 March 2012; Revised 10 May 2012; Accepted 14 May 2012

Academic Editor: Ferhan M. Atici

Copyright © 2012 Xiaoming Fan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We explore the dynamics of a class of mutualism-competition-predator interaction models with Beddington-DeAngelis functional responses and impulsive perturbations. Sufficient conditions for existence of positive periodic solution are established by using a continuation theorem in coincidence degree theory, which have been extensively applied in studying existence problems in differential equations and difference equations. In addition, sufficient criteria are given for the global stability and the globally exponential stability of system by employing comparison principle and Lyapunov method.