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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 741043, 11 pages
http://dx.doi.org/10.1155/2013/741043
Research Article

Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse

1Department of Mathematics, National University of Defense Technology, Changsha 410073, China
2Department of Mathematics, Hengyang Normal University, Hengyang, Hunan 421008, China

Received 14 June 2013; Revised 1 August 2013; Accepted 2 August 2013

Academic Editor: Yong Ren

Copyright © 2013 Zhenguo Luo and Liping Luo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Weng, “Existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls,” Computers & Mathematics with Applications, vol. 40, no. 6-7, pp. 747–759, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  2. F. Yang and D. Q. Jiang, “Existence and global attractivity of positive periodic solution of a Logistic growth system with feedback control and deviating arguments,” Annals of Differential Equations, vol. 17, no. 4, pp. 337–384, 2001.
  3. F. Chen, “Positive periodic solutions of neutral Lotka-Volterra system with feedback control,” Applied Mathematics and Computation, vol. 162, no. 3, pp. 1279–1302, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. C. Wang and J. Shi, “Periodic solution for a delay multispecies logarithmic population model with feedback control,” Applied Mathematics and Computation, vol. 193, no. 1, pp. 257–265, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. Hu, Z. Teng, and H. Jiang, “Permanence of the nonautonomous competitive systems with infinite delay and feedback controls,” Nonlinear Analysis: Real World Applications, vol. 10, no. 4, pp. 2420–2433, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. J. Yan and A. Zhao, “Oscillation and stability of linear impulsive delay differential equations,” Journal of Mathematical Analysis and Applications, vol. 227, no. 1, pp. 187–194, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. W. Zhang and M. Fan, “Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays,” Mathematical and Computer Modelling, vol. 39, no. 4-5, pp. 479–493, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Q. Wang and B. X. Dai, “Existence of positive periodic solutions for a neutral population model with delays and impulse,” Nonlinear Analysis: Theory, Methods and Applications, vol. 69, pp. 3919–3930, 2008.
  9. Y. Zhang and J. Sun, “Stability of impulsive functional differential equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 12, pp. 3665–3678, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. Zhu, X. Meng, and L. Chen, “The dynamics of a mutual interference age structured predator-prey model with time delay and impulsive perturbations on predators,” Applied Mathematics and Computation, vol. 216, no. 1, pp. 308–316, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. D. B. Lakshmikantham and P. Simeonov, Theory of Impulsive Differential Equations, World Scientific Publisher, Singapore, 1989.
  12. D. Baĭnov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66, Longman, Harlow, UK, 1993. View at MathSciNet
  13. M. Benchohra, J. Henderson, and S. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2, Hindawi Publishing Corporation, New York, NY, USA, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  14. Z. J. Liu, “Positive periodic solutions for a delay multispecies logarithmic population model,” Chinese Journal of Engineering Mathematics, vol. 19, no. 4, pp. 11–16, 2002. View at Zentralblatt MATH · View at MathSciNet
  15. S. Lu and W. Ge, “Existence of positive periodic solutions for neutral logarithmic population model with multiple delays,” Journal of Computational and Applied Mathematics, vol. 166, no. 2, pp. 371–383, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. F. Chen, “Periodic solutions and almost periodic solutions for a delay multispecies logarithmic population model,” Applied Mathematics and Computation, vol. 171, no. 2, pp. 760–770, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. F. Chen, “Periodic solutions and almost periodic solutions of a neutral multispecies logarithmic population model,” Applied Mathematics and Computation, vol. 176, no. 2, pp. 431–441, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. W. Zhao, “New results of existence and stability of periodic solution for a delay multispecies Logarithmic population model,” Nonlinear Analysis: Real World Applications, vol. 10, no. 1, pp. 544–553, 2009.
  19. Q. Wang, Y. Wang, and B. Dai, “Existence and uniqueness of positive periodic solutions for a neutral logarithmic population model,” Applied Mathematics and Computation, vol. 213, no. 1, pp. 137–147, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Y. Luo and Z. Luo, “Existence of positive periodic solutions for neutral multi-delay logarithmic population model,” Applied Mathematics and Computation, vol. 216, no. 4, pp. 1310–1315, 2010. View at Publisher · View at Google Scholar · View at MathSciNet