Necessary and sufficient condition for existence of periodic solutions of predator-prey dynamic systems with Beddington-DeAngelis-type functional response

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Pelen N. N., GÜVENİLİR A. F., Kaymakcalan B.

ADVANCES IN DIFFERENCE EQUATIONS, vol.2016, pp.1-19, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2016
  • Publication Date: 2016
  • Doi Number: 10.1186/s13662-016-0747-0
  • Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1-19
  • Keywords: predator-prey dynamic systems, Beddington-DeAngelis-type functional response, continuation theorem, globally attractive solution, periodic solution, time-scale calculus, PERMANENCE
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

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.