About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 619721, 11 pages
http://dx.doi.org/10.1155/2013/619721
Research Article

Bifurcations and Periodic Solutions for an Algae-Fish Semicontinuous System

1School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325027, China
2Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, China
3Institute of Mathematics, Academia Sinica, Beijing 100080, China

Received 2 September 2013; Accepted 26 September 2013

Academic Editor: Carlo Bianca

Copyright © 2013 Chuanjun Dai 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. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Teaneck, NJ, USA, 1989. View at MathSciNet
  2. D. D. Baĭnov and P. S. Simeonov, Impulsive Differential Equations: Asymptotic Properties of the Solutions, vol. 28 of Series on Advances in Mathematics for Applied Sciences, World Scientific, River Edge, NJ, USA, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  3. D. Bainov and V. Covachev, Impulsive Differential Equations with a Small Parameter, vol. 24 of Series on Advances in Mathematics for Applied Sciences, World Scientific, River Edge, NJ, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  4. C. Dai, M. Zhao, and L. Chen, “Complex dynamic behavior of three-species ecological model with impulse perturbations and seasonal disturbances,” Mathematics and Computers in Simulation, vol. 84, pp. 83–97, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. X. Liu and L. Chen, “Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator,” Chaos, Solitons & Fractals, vol. 16, no. 2, pp. 311–320, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Baek and Y. Do, “Seasonal effects on a Beddington-DeAngelis type predator-prey system with impulsive perturbations,” Abstract and Applied Analysis, vol. 2009, Article ID 695121, 19 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. Shao, P. Li, and G. Tang, “Dynamic analysis of an impulsive predator-prey model with disease in prey and Ivlev-type functional response,” Abstract and Applied Analysis, vol. 2012, Article ID 750530, 20 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. H. Yu, S. Zhong, and R. P. Agarwal, “Mathematics and dynamic analysis of an apparent competition community model with impulsive effect,” Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 25–36, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. L. S. Chen, “Pest control and geometric theory of semi-dynamical systems,” Journal of Beihua University (Natural Science), vol. 12, pp. 1–9, 2011.
  10. C. Dai, M. Zhao, and L. Chen, “Homoclinic bifurcation in semi-continuous dynamic systems,” International Journal of Biomathematics, vol. 5, no. 6, Article ID 1250059, 19 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  11. P. S. Simeonov and D. D. Baĭnov, “Orbital stability of periodic solutions of autonomous systems with impulse effect,” International Journal of Systems Science, vol. 19, no. 12, pp. 2561–2585, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. H. Baek, “The dynamics of a predator-prey system with state-dependent feedback control,” Abstract and Applied Analysis, vol. 2012, Article ID 101386, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. S. Tang and R. A. Cheke, “State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences,” Journal of Mathematical Biology, vol. 50, no. 3, pp. 257–292, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C. Dai, M. Zhao, and L. Chen, “Dynamic complexity of an Ivlev-type prey-predator system with impulsive state feedback control,” Journal of Applied Mathematics, vol. 2012, Article ID 534276, 17 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Nie, J. Peng, Z. Teng, and L. Hu, “Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects,” Journal of Computational and Applied Mathematics, vol. 224, no. 2, pp. 544–555, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. C. Bianca and L. Rondoni, “The nonequilibrium Ehrenfest gas: a chaotic model with flat obstacles?” Chaos, vol. 19, no. 1, Article ID 013121, 10 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S. N. Rasband, Chaotic Dynamics of Nonlinear Systems, John Wiley & Sons, New York, NY, USA, 1990. View at MathSciNet
  18. C. Bianca and M. Pennisi, “The triplex vaccine effects in mammary carcinoma: a nonlinear model in tune with SimTriplex,” Nonlinear Analysis: Real World Applications, vol. 13, no. 4, pp. 1913–1940, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet