文章基本信息

标题：Necessary and sufficient condition for existence of periodic solutions of predator-prey dynamic systems with Beddington-DeAngelis-type functional response
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作者：Neslihan Nesliye Pelen ; A. Feza Güvenilir ; Billur Kaymakçalan 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2016
卷号：2016
期号：1
页码：15
DOI：10.1186/s13662-016-0747-0
语种：English
出版社：Hindawi Publishing Corporation
摘要：We consider two-dimensional predator-prey systems with Beddington-DeAngelis-type functional response on periodic time scales. For this special case, we try to find the necessary and sufficient conditions for the considered system when it has at least one w-periodic solution. This study is mainly based on continuation theorem in coincidence degree theory and will also give beneficial results for continuous and discrete cases. Especially, for the continuous case, by using the study of Cui and Takeuchi (J. Math. Anal. Appl. 317:464-474, 2006), to obtain the globally attractive w-periodic solution of the given system, an inequality is given as a necessary and sufficient condition. Additionally, for the continuous case in this study, the open problem given in the discussion part of the study of Fan and Kuang (J. Math. Anal. Appl. 295:15-39, 2004) is solved.
关键词：predator-prey dynamic systems ; Beddington-DeAngelis-type functional response ; continuation theorem ; globally attractive solution ; periodic solution ; time-scale calculus