- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 126018, 18 pages
Existence and Attractiveness of Order One Periodic Solution of a Holling I Predator-Prey Model
College of Science, Shandong University of Science and Technology, Qingdao 266510, China
Received 16 April 2012; Accepted 13 August 2012
Academic Editor: Narcisa C. Apreutesei
Copyright © 2012 Huidong Cheng 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.
- J. Jiao and L. Chen, “A pest management SI model with periodic biological and chemical control concern,” Applied Mathematics and Computation, vol. 183, no. 2, pp. 1018–1026, 2006.
- X. Meng, L. Chen, and H. Cheng, “Two profitless delays for the SEIRS epidemic disease model with nonlinear incidence and pulse vaccination,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 516–529, 2007.
- P. Georgescu, H. Zhang, and L. Chen, “Bifurcation of nontrivial periodic solutions for an impulsively controlled pest management model,” Applied Mathematics and Computation, vol. 202, no. 2, pp. 675–687, 2008.
- X. Meng, L. Chen, and Q. Li, “The dynamics of a impulsive delay predator-prey model with variable coefficients,” Applied Mathematics and Computation, vol. 198, no. 1, pp. 61–374, 2008.
- B. Liu, Y. Zhang, and L. Chen, “Dynamic complexities of a Holling I predator-prey model concerning periodic biological and chemical control,” Chaos, Solitons and Fractals, vol. 22, no. 1, pp. 123–134, 2004.
- G. Jiang, Q. Lu, and L. Peng, “Impulsive ecological control of a stage-structured pest management system,” Mathematical Biosciences and Engineering, vol. 2, no. 2, pp. 329–344, 2005.
- A. d'Onofrio, “Pulse vaccination strategy in the SIR epidemic model: global asymptotic stable eradication in presence of vaccine failures,” Mathematical and Computer Modelling, vol. 36, no. 4-5, pp. 473–489, 2002.
- J. Jiao, X. Meng, and L. Chen, “A stage-structured Holling mass defence predator-prey model with impulsive perturbations on predators,” Applied Mathematics and Computation, vol. 189, no. 2, pp. 1448–1458, 2007.
- 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.
- J. Jiao and L. Chen, “Global attractivity of a stage-structure variable coefficients predator-prey system with time delay and impulsive perturbations on predators,” International Journal of Biomathematics, vol. 1, no. 2, pp. 197–208, 2008.
- X. Meng and Z. Li, “The dynamics of plant disease models with continuous and impulsive cultural control strategies,” Journal of Theoretical Biology, vol. 266, no. 1, pp. 29–40, 2010.
- C. S. Holling, “The functional response of p redator to prey density and its role in mimicry and population regulation,” Memoirs of the Entomological Society of Canada, no. 45, pp. 1–60, 1965.
- Y. Pei, L. Chen, Q. Zhang, and C. Li, “Extinction and permanence of one-prey multi-predators of Holling type II function response system with impulsive biological control,” Journal of Theoretical Biology, vol. 235, no. 4, pp. 495–503, 2005.
- Z. Xiong, Y. Xue, and S. Li, “A food chain system with Holling IV functional responses and impulsive effect,” International Journal of Biomathematics, vol. 1, no. 3, pp. 361–375, 2008.
- G. Jiang, Q. Lu, and L. Qian, “Complex dynamics of a Holling type II prey-predator system with state feedback control,” Chaos, Solitons & Fractals, vol. 31, no. 2, pp. 448–461, 2007.