Permanence and Global Attractivity of a Stage-Structured Predator-Prey Model With Continuous Harvesting on Predator and Impulsive Stocking on Prey
-
摘要: 研究了一个捕食者具连续收获与食饵具脉冲存放的阶段结构时滞捕食-食饵模型.根据生物资源管理的实际,改进了捕食者具阶段结构的捕食-食饵模型,即原来假设每个捕食者个体都具有相同的捕食食饵的能力.假设捕食者按年龄分为两个阶段,即幼体和成体,而且幼体无能力捕食食饵.得到了捕食者灭绝周期解全局吸引和系统持久的充分条件.结论说明了脉冲存放食饵对系统的持久起了重要的作用,并且为生物资源管理提供了策略基础.数值分析也进一步说明了系统的动力学性质.Abstract: A stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator is investigated.According to the fact of biological resource management,the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey was improved.It was assumed that the immature individuals and the mature individuals of the predator population were divided by a fixed age and that immature predator population does not have the ability to attack prey'sufficient conditions, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system,were obtained.The results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system,and provides tactical basis for the biological resource management.Furthermore,numerical analysis is inserted to illuminate the dynamics of the system.
-
Key words:
- stage-structured /
- impulsive stocking /
- continuous harvesting /
- global attractivity /
- permanence
-
[1] Nieto J J,Rodriguez-Lopez R.Periodic boundary value problems for non-Lipschitzian impulsive functional differential equations[J].J Math Anal Appl,2006,31(8):593-610. [2] Saker S H.Oscillation and global attractivity of impulsive periodic delay respiratory dynamics model[J].Chinese Ann Math,Ser B,2005,26(4):511-522. doi: 10.1142/S0252959905000403 [3] d'Onofrio A.A general framework for modeling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedical inferences[J].Physica D: Nonlinear Phenomena,2005,20(8):220-235. [4] GAO Shu-jing,CHEN Lan-sun.Pulse vaccination strategy in a delayed SIR epidemic model with vertical transmission[J].Discrete and Continuous Dynamical Systems,Ser B,2007,7(1):77-86. [5] Clark C W.Mathematical Bioeconomics[M].New York:Wiley,1990. [6] JIAO Jian-jun,MENG Xin-zhu,CHEN Lan-sun.A stage-structured Holling mass defence predator-prey 3 model with impulsive perturbations on predators[J].Applied Mathematics and Computation,2007,189(2):1448-1458. doi: 10.1016/j.amc.2006.12.043 [7] SON Xin-yu,LI Yong-feng.Dynamic complexities of a Holling Ⅱ two-prey one-predator system with impulsive effect[J].Chaos,Solitons and Fractals,2007,33(2):463-478. doi: 10.1016/j.chaos.2006.01.019 [8] Aiello W G,Freedman H I.A time-delay model of single-species growth with stage-structure[J].Math Biosci,1990,101(2):139-153. doi: 10.1016/0025-5564(90)90019-U [9] Freedman H I,Gopalsamy K.Global stability in time-delayed single species dynamics[J].Bull Math Biol,1986,48(5/6):485-492. [10] Beretta E,Kuang Y.Global analysis in some delayed ratio-dependent predator-prey system[J].Nonlinear Anal,1998,32(3):381-408. doi: 10.1016/S0362-546X(97)00491-4 [11] YANG Kuang.Delay Differential Equation With Application in Population Dynamics[M].N Y:Academic Press,1993,67-70. [12] Wang W,Chen L.A predator-prey system with stage structure for predator[J].Comput Math Appl,1997,33(8):83-91. [13] JIAO Jian-jun,PANG Guo-ping,CHEN Lan-sun,et al.A delayed stage-structured predator-prey model with impulsive stocking on prey and continuous harvesting on predator[J].Applied Mathematics and Computation,2008,195(1):316-325. doi: 10.1016/j.amc.2007.04.098 [14] SONG Xin-yu,CHEN Lan-sun.Optimal harvesting policy and stability for a single-species growth model with stage structure[J].Journal of System Sciences and Complex,2002,15(2):194-201. [15] DONG Ling-zhen,CHEN Lan-sun,SUN Li-hua.Extinction and permanence of the predator-prey system with stocking of prey and harvesting of predator impulsively[J].Math Methods Appl Sci,2006,29(4):415-425. doi: 10.1002/mma.688 [16] Wang W,Mulone G,Salemi F,et al.Permanence and stability of a stage-structured predator-prey model[J].J Math Anal Appl,2001,262(2):499-528. doi: 10.1006/jmaa.2001.7543 [17] Lakshmikantham V,Bainov D D,Simeonov P.Theory of Impulsive Differential Equations[M].Singapor:World Scientific,1989. [18] Bainov D,Simeonov P.Impulsive Differential Equations: Periodic Solutions and Applications[M].66.New York:Longman,1993. [19] Caltagirone L E,Doutt R L.Global behavior of an SEIRS epidemic model with delays,the history of the vedalia beetle importation to California and its impact on the development of biological control[J].Ann Rev Entomol,1989,34:1-16. doi: 10.1146/annurev.en.34.010189.000245
点击查看大图
计量
- 文章访问数: 2140
- HTML全文浏览量: 71
- PDF下载量: 536
- 被引次数: 0