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一类带反馈控制的高维泛函微分方程的正周期解研究

, PP. 16-20

Keywords: 泛函微分方程,严格集压缩不动点定理,正周期解,反馈控制

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Abstract:

具反馈控制的泛函微分方程模型比传统的微分方程模型能更加真实地反映客观现实.基于种群生态学中的数学模型为基础,研究如下一类带反馈控制的高维泛函微分方程模型(t)=-P(t)x(t)+F(t,xt,u(t-δ(t))),(t)=-Q(t)u(t)+R(t)x(h(t,x(t-σ(t)))),其中,P(t)=(pij(t))n×n是非奇异矩阵.该模型包括了许多具反馈控制的时滞微分方程(系统)的生物数学模型,具有重要的理论和现实意义.利用严格集压缩不动点定理的方法,获得了其正周期解存在性的新的充分条件.

References

[1]  Wang L L, Li W T. Existence and global stability of positive periodic solutions of a predator-prey system with delays\[J\]. Appl Math Comput,2003,146:167-185.
[2]  鲁世平,李亚林. 一类中立型泛函微分系统周期解存在性问题\[J\]. 数学学报,2007,50(6):1231-1242.
[3]  郭承军,徐远通,郭志明. 一类三阶中立型微分方程多重周期解的存在性\[J\]. 数学学报,2009,52(4):737-750.
[4]  Lefschetz S. Stability of Nonlinear Control Systems\[M\]. New York:Academic Press,1965.
[5]  Wang L L, Fan Y H. Permanence and existence of periodic solutions for a generalized system with feedback control\[J\]. Applied Mathematics and Computation,2010,216:902-910.
[6]  Freedman H I, Wu J. Periodic solutions of single-species models with periodic delay\[J\]. SIAM J Math Anal,1992,23:689-701.
[7]  Gopalsamy K, Weng P X. Feedback regulation of logistic growth\[J\]. Internat J Math Sci,1993(1):177-192.
[8]  Li Y K. Positive periodic solutions for neutral functional differential equations with distributed delays and feedback control\[J\]. Nonlinear Analysis:Real World Applications,2008(9):2214-2221.
[9]  Li Y K, Zhang T W. Permanence of a discrete n-species cooperation system with time-varying delays and feedback controls\[J\]. Mathematical and Computer Modelling,2011,53:1320-1330.
[10]  Li Y, Zhu L. Positive periodic solutions for a class of higher-dimensional state-dependent delay functional differential equations with feedback control\[J\]. Appl Math Comput,2004,159:783-795.
[11]  Gatica J A. Fixed point theorems for mappings in ordered Banach spaces\[J\]. J Math Anal Appl,1979,71:547-557.
[12]  Guo D. Positive solutions of nonlinear operator equations and its applications to nonlinear integral equations\[J\]. Adv Math,1984,13:294-310.
[13]  Muhammad N I, Youssef N R. Periodic solutions of neutral nonlinear system of differential equations with functional delay\[J\]. J Math Anal Appl,2007,331:1175-1186.
[14]  Chen F D, Yang J H, Chen L J. On a mutualism model with feedback controls\[J\]. Applied Mathematics and Computation,2009,214:581-587.
[15]  Zeng Z J, Zhou Z C. Multiple positive periodic solutions for a class of state-dependent delay functional differential equations with feedback control\[J\]. Applied Mathematics and Computation,2008,197:306-316.
[16]  Nie L F, Peng J G, Teng Z D. Permanence and stability in multi-species non-autonomous Lotka-Volterra competitive systems with delays and feedback controls\[J\]. Mathematical and Computer Modelling,2009,49:295-306.

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