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Discrete Dynamics in Nature and Society
Volume 2018, Article ID 3403127, 7 pages
https://doi.org/10.1155/2018/3403127
Research Article

Permanence and Existence of Periodic Solutions for Nicholson’s Blowflies Model with Feedback Control and Delay on Time Scales

School of Mathematics and Statistics Science, Ludong University, Yantai, Shandong 264025, China

Correspondence should be addressed to Yong-Hong Fan; moc.anis@3991_hynaf

Received 21 April 2018; Accepted 26 July 2018; Published 7 August 2018

Academic Editor: Luca Pancioni

Copyright © 2018 Lin-Lin Wang and Yong-Hong Fan. 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. L.-L. Wang and Y.-H. Fan, “Permanence for a discrete Nicholson's blowflies model with feedback control and delay,” International Journal of Biomathematics, vol. 1, no. 4, pp. 433–442, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  2. S. Hilger, Ein Mab kettenkalkül mit Anwendung auf Zentrumsmannig faltigkeiten [Ph.D. thesis], Universität of Würzburg, 1988.
  3. R. P. Agarwal, M. Bohner, and D. O'Regan, “Time scale boundary value problems on infinite intervals,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 27–34, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. C. Wang and R. P. Agarwal, “Uniformly rd-piecewise almost periodic functions with applications to the analysis of impulsive D-dynamic system on time scales,” Applied Mathematics and Computation, vol. 259, pp. 271–292, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  5. C. Wang and R. P. Agarwal, “Almost periodic dynamics for impulsive delay neural networks of a general type on almost periodic time scales,” Communications in Nonlinear Science and Numerical Simulation, vol. 36, pp. 238–251, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  6. Y.-Y. Yu, L.-L. Wang, and Y.-H. Fan, “Uniform ultimate boundedness of solutions of predator-prey system with Michaelis-MENten functional response on time scales,” Advances in Difference Equations, Paper No. 319, 14 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  7. W. S. C. Gurney, S. P. Blythe, and R. M. Nisbet, “Nicholson's blowflies revisited,” Nature, vol. 287, no. 5777, pp. 17–21, 1980. View at Publisher · View at Google Scholar · View at Scopus
  8. K. Gopalsamy and P. X. Weng, “Feedback regulation of logistic growth,” International Journal of Science and Mathematics, vol. 1, pp. 177–192, 1993. View at Google Scholar
  9. B. S. Lalli, J. S. Yu, and M.-P. Chen, “Feedback regulation of a logistic growth,” Dynamic Systems and Applications, vol. 5, no. 1, pp. 117–124, 1996. View at Google Scholar · View at MathSciNet
  10. L. Liao, “Feedback regulation of a logistic growth with variable coefficients,” Journal of Mathematical Analysis and Applications, vol. 259, no. 2, pp. 489–500, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. W.-T. Li and L.-L. Wang, “Existence and global attractivity of positive periodic solutions of functional differential equations with feedback control,” Journal of Computational and Applied Mathematics, vol. 180, no. 2, pp. 293–309, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. F. D. Chen, “Permanence of a single species discrete model with feedback control and delay,” Applied Mathematics Letters, vol. 20, no. 7, pp. 729–733, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. X. Xie, C. Zhang, X. Chen, and J. Chen, “Almost periodic sequence solution of a discrete Hassell-Varley predator-prey system with feedback control,” Applied Mathematics and Computation, vol. 268, pp. 35–51, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. X. Mao, “Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control,” Automatica, vol. 49, no. 12, pp. 3677–3681, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  15. H. A. El-Morshedy and A. Ruiz-Herrera, “Geometric methods of global attraction in systems of delay differential equations,” Journal of Differential Equations, vol. 263, no. 9, pp. 5968–5986, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. X. Liu and Y. M. Zeng, “Linear multistep methods for impulsive delay differential equations,” Applied Mathematics and Computation, vol. 321, pp. 555–563, 2018. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. V. Lakshmikantham, S. Sivasundaram, and B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Boston, Mass, USA, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  18. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, Mass, USA, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  19. V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Application, Kluwer Academic, Dordrecht, The Netherlands, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  20. Y. Fan, Y. Yu, and L. Wang, “Some differential inequalities on time scales and their applications to feedback control systems,” Discrete Dynamics in Nature and Society, Art. ID 9195613, 11 pages, 2017. View at Publisher · View at Google Scholar · View at MathSciNet