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Journal of Mathematics
Volume 2016, Article ID 7308609, 11 pages
Research Article

Stability Analysis of the Periodic Solutions of Some Kinds of Predator-Prey Dynamical Systems

Department of Mathematics, Ondokuz Mayis University, Samsun, Turkey

Received 29 September 2016; Accepted 18 October 2016

Academic Editor: Ram Jiwari

Copyright © 2016 Neslihan Nesliye Pelen. 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.


Analysis of predator-prey dynamical systems that have the functional response which generalizes the other types of functional responses in two dimensions is mainly studied in this paper. The main problems for this study are to detect the if and only if conditions for attaining the periodic solution of the considered system and to find the condition for global asymptotic stability of this solution for some different types of predator-prey systems that are obtained from that system. To get the desired results, some aspects of semigroup theory for stability analysis and coincidence degree theory are used.