Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 186232, 7 pages
http://dx.doi.org/10.1155/2014/186232
Research Article

Analysis of a Periodic Single Species Population Model Involving Constant Impulsive Perturbation

1Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, China
2Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000, China

Received 11 January 2014; Accepted 22 May 2014; Published 12 June 2014

Academic Editor: Sabri Arik

Copyright © 2014 Ronghua Tan et al. 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. R. Tan, Z. Liu, and R. Cheke, “Periodicity and stability in a single-species model governed by impulsive differential equation,” Applied Mathematical Modelling, vol. 36, no. 3, pp. 1085–1094, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. W. B. Wang, J. H. Shen, and J. J. Nieto, “Permanence and periodic solution of predator-prey system with holling type functional response and impulses,” Discrete Dynamics in Nature and Society, vol. 2007, Article ID 81756, 15 pages, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Z. Liu and R. H. Tan, “Impulsive harvesting and stocking in a Monod-Haldane functional response predator-prey system,” Chaos, Solitons & Fractals, vol. 34, no. 2, pp. 454–464, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Z. Liu, Y. Chen, Z. He, and J. Wu, “Permanence in a periodic delay logistic system subject to constant impulsive stocking,” Mathematical Methods in the Applied Sciences, vol. 33, no. 8, pp. 985–993, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Z. Li, T. Wang, and L. Chen, “Periodic solution of a chemostat model with Beddington-DeAnglis uptake function and impulsive state feedback control,” Journal of Theoretical Biology, vol. 261, no. 1, pp. 23–32, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  6. A. d'Onofrio, “On pulse vaccination strategy in the SIR epidemic model with vertical transmission,” Applied Mathematics Letters, vol. 18, no. 7, pp. 729–732, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. R. Shi, X. Jiang, and L. Chen, “A predator-prey model with disease in the prey and two impulses for integrated pest management,” Applied Mathematical Modelling, vol. 33, no. 5, pp. 2248–2256, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. A. Lakmeche and O. Arino, “Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 7, no. 2, pp. 165–187, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y. Zhang and J. Sun, “Stability of impulsive neural networks with time delays,” Physics Letters A, vol. 348, no. 1-2, pp. 44–50, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. A. Anguraj, S. Wu, and A. Vinodkumar, “The existence and exponential stability of semilinear functional differential equations with random impulses under non-uniqueness,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 2, pp. 331–342, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. S. Wu, D. Han, and X. Meng, “p-moment stability of stochastic differential equations with jumps,” Applied Mathematics and Computation, vol. 152, no. 2, pp. 505–519, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Wu and Y. Duan, “Oscillation, stability, and boundedness of second-order differential systems with random impulses,” Computers & Mathematics with Applications, vol. 49, no. 9-10, pp. 1375–1386, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. J. Shen, Z. Luo, and X. Liu, “Impulsive stabilization of functional-differential equations via Liapunov functionals,” Journal of Mathematical Analysis and Applications, vol. 240, no. 1, pp. 1–15, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  14. D. Xu, W. Zhu, and S. Long, “Global exponential stability of impulsive integro-differential equation,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 12, pp. 2805–2816, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. D. Xu and Z. Yang, “Impulsive delay differential inequality and stability of neural networks,” Journal of Mathematical Analysis and Applications, vol. 305, no. 1, pp. 107–120, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. H. Chen, “Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays,” Statistics & Probability Letters, vol. 80, no. 1, pp. 50–56, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. H. Chen, X. Zhang, and Y. Zhao, “The existence and exponential stability for random impulsive integrodifferential equations of neutral type,” Advances in Difference Equations, vol. 2010, Article ID 540365, 18 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. D. Ludwig, D. D. Jones, and C. S. Holling, “Qualitative analysis of insect outbreak systems: the spruce budworm and forest,” Journal of Animal Ecology, vol. 47, no. 1, pp. 1315–1332, 1978. View at Publisher · View at Google Scholar
  19. J. D. Murray, Mathematical Biology I: An introduction, vol. 17, Springer, Berlin, Germany, 3rd edition, 2002. View at MathSciNet
  20. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theroy of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific Publishing, Singapore, 1989. View at Publisher · View at Google Scholar · View at MathSciNet