- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 360182, 6 pages
Periodic Solutions of a Nonautonomous Plant-Hare Model with Impulses
1Sunshine College, Fuzhou University, Fuzhou, Fujian 350015, China
2College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350015, China
Received 25 July 2013; Revised 14 September 2013; Accepted 15 September 2013
Academic Editor: Thabet Abdeljawad
Copyright © 2013 Haihui Wu and Yan Zhou. 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.
- L. Chen, Mathematical Models and Methods in Ecology, Science Press, Beijing, China, 1998, (in Chinese).
- Y. Li, “Periodic solutions of a periodic delay predator-prey system,” Proceedings of the American Mathematical Society, vol. 127, no. 5, pp. 1331–1335, 1999.
- Y. Song, Y. Peng, and J. Wei, “Bifurcations for a predator-prey system with two delays,” Journal of Mathematical Analysis and Applications, vol. 337, no. 1, pp. 466–479, 2008.
- Y.-H. Xia, “Periodic solution of certain nonlinear differential equations: via topological degree theory and matrix spectral theory,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 22, no. 8, Article ID 940287, 2012.
- T. Zhang, J. Liu, and Z. Teng, “Stability of Hopf bifurcation of a delayed SIRS epidemic model with stage structure,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 293–306, 2010.
- Z. Zhang and J. Luo, “Multiple periodic solutions of a delayed predator-prey system with stage structure for the predator,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4109–4120, 2010.
- M. Fan, Q. Wang, and X. Zou, “Dynamics of a non-autonomous ratio-dependent predator-prey system,” Proceedings of the Royal Society of Edinburgh A, vol. 133, no. 1, pp. 97–118, 2003.
- H.-F. Huo, “Periodic solutions for a semi-ratio-dependent predator-prey system with functional responses,” Applied Mathematics Letters, vol. 18, no. 3, pp. 313–320, 2005.
- Y.-F. Gao and Y.-H. Xia, “Periodic solutions of a nonautonomous plant-hare model,” Journal of Zhejiang University, vol. 39, no. 5, pp. 507–511, 2012.
- D. Baĭnov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, Harlow, UK, 1993.
- Q. Wang, B. Dai, and Y. Chen, “Multiple periodic solutions of an impulsive predator-prey model with Holling-type IV functional response,” Mathematical and Computer Modelling, vol. 49, no. 9-10, pp. 1829–1836, 2009.
- L. Mahto, S. Abbas, and A. Favini, “Analysis of Caputo impulsive fractional order differential equations with applications,” International Journal of Differential Equations, vol. 2013, Article ID 704547, 11 pages, 2013.
- A. M. A. El-Sayed, E. Ahmed, and H. A. A. El-Saka, “Dynamic properties of the fractional-order logistic equation of complex variables,” Abstract and Applied Analysis, vol. 2012, Article ID 251715, 12 pages, 2012.
- J. Hui and L. S. Chen, “Existence of positive periodic solution of periodic time-dependent predator-prey system with impulsive effects,” Acta Mathematica Sinica (English Series), vol. 20, no. 3, pp. 423–432, 2004.
- 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.
- J. O. Alzabut and T. Abdeljawad, “Exponential boundedness for solutions of linear impulsive differential equations with distributed delay,” International Journal of Pure and Applied Mathematics, vol. 34, no. 2, pp. 203–217, 2007.
- J. O. Alzabut and T. Abdeljawad, “On existence of a globally attractive periodic solution of impulsive delay logarithmic population model,” Applied Mathematics and Computation, vol. 198, no. 1, pp. 463–469, 2008.
- R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, vol. 568 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977.