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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 619721, 11 pages
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- L. S. Chen, “Pest control and geometric theory of semi-dynamical systems,” Journal of Beihua University (Natural Science), vol. 12, pp. 1–9, 2011.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- S. N. Rasband, Chaotic Dynamics of Nonlinear Systems, John Wiley & Sons, New York, NY, USA, 1990.
- 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.