李盈科,滕志东,曼合布拜·热合木

• 1:新疆大学数学与系统科学学院
• 2:新疆农业大学数理学院

摘要(Abstract)：

研究了非自治的具有阶段结构的时滞捕食被捕食模型的周期解的存在问题.模型中阶段结构是针对被捕食者种群,而时滞是由于捕食者捕食食饵而转化成自身的一部分的过程引起的.利用Gaines及Mawhin的叠合度理论,文章得到了该模型周期解存在的充分条件.最后给出了一个实例以验证文章结果的可行性.

关键词(KeyWords)： 非自治捕食被捕食模型;阶段结构;正周期解;时滞;叠合度

Abstract:

Keywords:

基金项目(Foundation): Supported by The National Natural Science Foundation of P.R. China (60764003);; The Major Project of The Ministry of Education of P.R. China (207130);; The Scientific Research Programmes of Colleges in Xinjiang (XJEDU2007G01, XJEDU2006I05)

作者(Author): 李盈科,滕志东,曼合布拜·热合木

参考文献(References)：

• [1]Aiello W G,Freedman H I.A time delay of single-spacies growth with stage strcture[J].Math Biosci,1990,101:139-153.
• [2]MA Zhi-hui,Li Zhi-zhen,Wang Shu-fan,et al.Permanence of a predator-prey system with stage strcuture and time delay[J].Appl MathComput,2008,201:65-71.
• [3]Wei Feng Ying,Wang Ke.Permanence of variable coeffcients predator-prey system with stage strcuture[J].Appl Math Comput,2006,180:594-598.
• [4]Pei Yongzhen,Li Changguo,Chen Lansun.Continuous and impusive harvesting strategies in a stage-strcutured predator-prey model with timedelay[J].Mathematics and Computer in Simulation,2009.
• [5]Jiao Jiaojun,Meng Xinzhu,Chen Lansun.A stage-structured Holling mass defence predator-prey model with impulsive perturbations onpredators[J].Appl Math Comput,2007,189:1448-1458.
• [6]Song Xinyu,hao M,Meng X.A stage-strcutured predator-prey model with disturbing pulse and time delays[J].Appl Math Modelling,2009,33:211-4223.
• [7]Gaines R E,Mawhin J L.Conincidence Degree and Nonliear Differencial Equations[M].Springer-Verlag,Berlin,1997.
• [8]Li Y,Kuang Y.Periodic solutions of periodic Lotka-Volterra equationg and systems[J].J Math Anal Appl,2001,255:260-280.
• [9]Chen F,You M.Permanence extinction and periodic solution of the predator-prey system with Beddington-DeAngelis funtional response andstage strcuture for prey[J].Nonlinear Anal R W A,2008,9:207-221.
• [10]Yang S J,Shi B.Periodic solution for three-stage-structured a predator-prey system with time delay[J].J Math Anal Appl,2008,341:287-294.
• [11]Xiong X,Zhang Z.Existence and global attractiviy of a periodic solution for a redator-prey model with sex-structure[J].Comput Math Appl,2007,190:1231-1224.
• [12]xu R,Chaplain M A J,Davidson F A.Persistence and periodicity of a delayed ratio-dependent predator-prey model with stage strcuture andprey dispersal[J].Comput Math Appl,2004,159:823-846.
• [13]Bandyopadhyay M,Banerjee S.A stage-structured predator-prey model with discrete time delay[J].Comput Math Appl,2006,182:1385-1398.