Existence of periodic solutions for a predator-prey system with sparse effect and functional response on time scales

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• 作者：Yu Tong^a ; Zhenjie Liu^b ; ^{liouj2008@126.com} ; Zhiying Gao^b ; Yonghong Wang^b
• 关键词：Time scale ; Predator&ndash ; prey system ; Beddington&ndash ; DeAngelis response ; Holling-type III response ; Sparse effect ; Coincidence degree
• 刊名：Communications in Nonlinear Science and Numerical Simulation
• 出版年：2012
• 出版时间：August, 2012
• 年：2012
• 卷：17
• 期：8
• 页码：3360-3366
• 全文大小：227 K

文摘

In this paper, we systematically investigates the existence of periodic solutions of a predator-prey system with sparse effect and Beddington-DeAngelis or Holling III functional response on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the systems. Moreover, when the time scale is chosen as or , the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.