AAM  >> Vol. 5 No. 1 (February 2016)

    一类具有周期系数的脉冲种群模型稳定性分析
    Stability Analysis of an Impulsively Population Control Model in Periodical Environment

  • 全文下载: PDF(439KB) HTML   XML   PP.15-23   DOI: 10.12677/AAM.2016.51003  
  • 下载量: 706  浏览量: 4,331   国家自然科学基金支持

作者:  

王娜,杨志春:重庆师范大学数学科学学院,重庆

关键词:
脉冲周期系数害虫灭绝周期解稳定性Impulsively Periodical Environment Pest-Extinction Periodic Solution Stability

摘要:
本文主要研究一类具有周期系数的脉冲种群控制模型的害虫灭绝周期解的稳定性问题。首先,建立在不同时刻收割庄稼、喷洒农药和释放天敌的一类具有周期系数的植物害虫天敌的脉冲控制模型。然后得到脉冲控制模型的两个害虫灭绝周期解,利用线性化方法、比较原理以及Floquet原理,分别给出害虫灭绝周期解局部稳定性和全局稳定性的一些充分条件。

In the paper, we study the stability of pest-extinction periodic solutions of an impulsively popula-tion control model in periodical environment. First, we formulate a plant-pest-natural enemy model in periodical environment with harvesting, spraying and releasing at different moments. Then, we obtain pest-extinction periodic solutions. Some sufficient conditions for local stability and globally stability of pest-extinction periodic solutions are determined by the comparison technique of impulsive differential equations and the Floquet theory.

文章引用:
王娜, 杨志春. 一类具有周期系数的脉冲种群模型稳定性分析[J]. 应用数学进展, 2016, 5(1): 15-23. http://dx.doi.org/10.12677/AAM.2016.51003

参考文献

[1] Jiao, J.J., Chen, L.S. and Cai, S.H. (2012) Dynamical Analysis of a Biological Resource Management Model with Im-pulsive Releasing and Harvesting. Advances in Difference Equations, 9, 1-15.
[2] Singh Jatav, K. and Dhar, J. (2013) Hybrid Approach for Pest Control with Impulsive Releasing of Natural Enemies and Chemical Pesticides: A Plant-Pest-Natural Enemy Model. Nonlinear Analysis: Hybrid Systems, 9, 1-14.
[3] Georgescu, P. and Morosanu, G. (2008) Impulsive Perturbations of a Three-Trophic Prey-Dependent Food Chain System. Mathematical and Computer Modelling, 48, 975-997.
http://dx.doi.org/10.1016/j.mcm.2007.12.006
[4] 杨志春. 具有脉冲和HollingⅢ类功能反应的捕食系统的持续生存和周期解[J]. Journal of Biomathematics, 2004, 19(4): 439-444.
[5] Liu, X.N. and Chen, L.S. (2004) Global Dynamics of the Periodic System with Periodic Impulsive Perturbations. Journal of Mathe-matical Analysis and Applications, 289, 279-291.
http://dx.doi.org/10.1016/j.jmaa.2003.09.058
[6] Tang, S.Y. and Chen, L.S. (2002) The Periodic Predator-Prey Lokta-Volterra Model with Impulsive Effect. Journal of Mechanics in Medicine and Biology, 2, 267-296.
http://dx.doi.org/10.1142/S021951940200040X
[7] Wang, W.M., Wang, X.Q. and Lin, Y.Z. (2008) Complicated Dynamics of a Predator-Prey System with Watt-Type Functional Response and Impulsive Control Strategy. Chaos Solitons and Fractals, 37, 1427-1441.
http://dx.doi.org/10.1016/j.chaos.2006.10.032
[8] Song, X.Y. and Li, Y.F. (2007) Dynamics Complexities of a HollingⅡ Two-Prey One-Predator System with Impulsive Effect. Chaos Solitons and Fractals, 33, 463-478.
http://dx.doi.org/10.1016/j.chaos.2006.01.019
[9] Liu, K.Y., Meng, X.Z. and Chen, L.S. (2008) A New Stage Structured Predator-Prey Gomportz Model with Time Delay and Impulsive Perturbations on the Prey. Applied Mathe-matics and Computation, 196, 705-719.
http://dx.doi.org/10.1016/j.amc.2007.07.020
[10] Bainov, D. and Simeonov, P. (1993) Impulsive Differential Equations: Periodic Solutions and Applications. Longman Scientific and Technical, England, 39-53.
[11] 宋新宇, 郭红建, 师向云. 脉冲微分方程理论及其应用[M]. 北京: 科学出版社, 2011: 19-23, 98-109.