N种群Gilpin-Ayala脉冲竞争模型正周期解存在性和全局吸引性
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摘要
基于一类具脉冲的N种群Gilpin-Ayala竞争模型,对农业病虫害防治周期周期解存在性的充分必要条件和正周期解的全局吸引性进行研究。利用延拓定理得出该模型至少存在一个周期解的结论,并利用Lyapunov泛函方法得出该模型周期解的全局吸引性和稳定性结论都成立,为进一步阐明此具脉冲竞争模型的周期解全局渐近稳定性且唯一性提供了充足的依据。通过上述方法证明了具脉冲的N种群Gilpin-Ayala竞争模型的正周期解存在性和全局吸引性成立,同时给出具体实例进一步论证了该模型的可行性。研究具有较强的实用性,为农业病虫害防治周期性的研究提供了理论依据。
Based on a pulsed N-population Gilpin-Ayala competition model,the sufficient necessary conditions for the existence of periodic solutions of agricultural pest control and the global attractiveness of positive periodic solutions are studied. The extension theorem is used to conclude that there is at least one periodic solution in the model,and Lyapunov's functional method is used to conclude that the global attraction and stability of the periodic solution of the model are valid. It provides a sufficient basis for further elucidating the global asymptotic stability and uniqueness of the periodic solution with pulse competition model. The existence and global attractiveness of the positive periodic solution of the pulsed N-population GilpinAyala competition model are proved by the above methods. The research has a strong practicability,which provides a theoretical basis for the study of agricultural pest control periodicity.
Based on a pulsed N-population Gilpin-Ayala competition model,the sufficient necessary conditions for the existence of periodic solutions of agricultural pest control and the global attractiveness of positive periodic solutions are studied. The extension theorem is used to conclude that there is at least one periodic solution in the model,and Lyapunov's functional method is used to conclude that the global attraction and stability of the periodic solution of the model are valid. It provides a sufficient basis for further elucidating the global asymptotic stability and uniqueness of the periodic solution with pulse competition model. The existence and global attractiveness of the positive periodic solution of the pulsed N-population GilpinAyala competition model are proved by the above methods. The research has a strong practicability,which provides a theoretical basis for the study of agricultural pest control periodicity.
引文
[1]GILPIN M E,AYALA F J.Global models of growth and competition[J].Proc.Natl.Acad.Sci.,1973,70:3590-3593.
[2]WANG K H,GUI Z J.Periodic solution of n-species Gilpin-Ayala competition system with impulsive perturbations[J].Journal of Software Engineering and Applications,2012,5(12):26-29.
[3]胡猛,王健.一类时滞Gilpin-Ayala系统的概周期解的存在性[J].兰州理工大学学报,2013,39(1):142-146
[4]LIU L.Permanence,stationary distribution and extinction for one-dimensional stochastic Gilpin-Ayala systems[C]//中国自动化学会控制理论专业委员会、中国系统工程学会.第三十三届中国控制会议论文集(D卷),2014:5-5.
[5]魏美华,常金勇,张巧卫.一类具有种内竞争率的竞争扩散模型稳态解的存在性和稳定性[J].数学的实践与认识,2014,44(15):295-301.
[6]丁彦林.时间尺度上带有反馈控制和脉冲的企业集群竞争模型的持久性分析[J/OL].宜宾学院学报:1-7[2019-04-26].https://doi.org/10.19504/j.cnki.issn1671-5365.20181128.001.
[7]GAINES R E,MAWHIN J L.Coincidence degree and nonlinear differential equations[M].Springer-Verlag,New York,1977.
[8]LASHMIKANTHAM V,BAINO D D,SIMENOV P S.Theorey of impulsive differential equations[M].World Scientific,Singapore,1989.
[9]WANG Q,DAI B X,CHEN Y M.Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response[J].Math.Comput.Modelling,2009,49:1829-1836.
[10]WENG P X.Existence and global stability attractivity of positive periodic integrodifferential systems with feed-back controls[J].Comput.Math.Appl.,2000,40:747-759.
[11]ZHANG S W,TAN D J,CHEN L S.The periodic n-species Gilpin-Ayala competition system with impulsive effect[J].Chaos Solitons&Fractals,2005,26(2):507-517.
[12]姚晓洁,秦发金.具有收获率的脉冲竞争模型的4个正概周期解[J].华南师范大学学报:自然科学版,2018,50(2):94-99.
[13]郑紫微,林洁,陈昱闽,等.具有偏利关系的Gilpin-Ayala系统的稳定性[J].海峡科学,2018(3):78-80.
[14]刘锋.亚正定阵在Gilpin-Ayala系统稳定性中的应用[J].数学的实践与认识,2005,35(8):123-126.
[15]周孔容,雷镜朝.Gilpin-Ayala竞争模型全局稳定性分析[J].四川大学学报:自然科学版,1987,24(4):361-366.
[16]张俊杰,马满军.具Gilpin-Ayala模型的正解唯一性与周期吸引性[J].湖南文理学院学报:自然科学版,2012,24(1):7-10.
[17]郑紫微,林洁,陈昱闽,等.具有偏利关系的Gilpin-Ayala系统的稳定性[J].海峡科学,2018(3):78-80.
[2]WANG K H,GUI Z J.Periodic solution of n-species Gilpin-Ayala competition system with impulsive perturbations[J].Journal of Software Engineering and Applications,2012,5(12):26-29.
[3]胡猛,王健.一类时滞Gilpin-Ayala系统的概周期解的存在性[J].兰州理工大学学报,2013,39(1):142-146
[4]LIU L.Permanence,stationary distribution and extinction for one-dimensional stochastic Gilpin-Ayala systems[C]//中国自动化学会控制理论专业委员会、中国系统工程学会.第三十三届中国控制会议论文集(D卷),2014:5-5.
[5]魏美华,常金勇,张巧卫.一类具有种内竞争率的竞争扩散模型稳态解的存在性和稳定性[J].数学的实践与认识,2014,44(15):295-301.
[6]丁彦林.时间尺度上带有反馈控制和脉冲的企业集群竞争模型的持久性分析[J/OL].宜宾学院学报:1-7[2019-04-26].https://doi.org/10.19504/j.cnki.issn1671-5365.20181128.001.
[7]GAINES R E,MAWHIN J L.Coincidence degree and nonlinear differential equations[M].Springer-Verlag,New York,1977.
[8]LASHMIKANTHAM V,BAINO D D,SIMENOV P S.Theorey of impulsive differential equations[M].World Scientific,Singapore,1989.
[9]WANG Q,DAI B X,CHEN Y M.Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response[J].Math.Comput.Modelling,2009,49:1829-1836.
[10]WENG P X.Existence and global stability attractivity of positive periodic integrodifferential systems with feed-back controls[J].Comput.Math.Appl.,2000,40:747-759.
[11]ZHANG S W,TAN D J,CHEN L S.The periodic n-species Gilpin-Ayala competition system with impulsive effect[J].Chaos Solitons&Fractals,2005,26(2):507-517.
[12]姚晓洁,秦发金.具有收获率的脉冲竞争模型的4个正概周期解[J].华南师范大学学报:自然科学版,2018,50(2):94-99.
[13]郑紫微,林洁,陈昱闽,等.具有偏利关系的Gilpin-Ayala系统的稳定性[J].海峡科学,2018(3):78-80.
[14]刘锋.亚正定阵在Gilpin-Ayala系统稳定性中的应用[J].数学的实践与认识,2005,35(8):123-126.
[15]周孔容,雷镜朝.Gilpin-Ayala竞争模型全局稳定性分析[J].四川大学学报:自然科学版,1987,24(4):361-366.
[16]张俊杰,马满军.具Gilpin-Ayala模型的正解唯一性与周期吸引性[J].湖南文理学院学报:自然科学版,2012,24(1):7-10.
[17]郑紫微,林洁,陈昱闽,等.具有偏利关系的Gilpin-Ayala系统的稳定性[J].海峡科学,2018(3):78-80.