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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 412409, 8 pages
Modeling the Dynamics of a Single-Species Model with Pollution Treatment in a Polluted Environment
1College of Mathematics and Information Science, Anshan Normal University, Anshan, Liaoning 114007, China
2Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
3Department of Mathematics, Beihang University, Beijing 100083, China
Received 19 November 2012; Accepted 25 December 2012
Academic Editor: Zhen Jin
Copyright © 2013 Bing Liu 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.
- T. G. Hallam, C. E. Clark, and R. R. Lassiter, “Effects of toxicants on populations: a qualitative approach. 1. Equilibrium environmental exposure,” Ecological Modelling, vol. 18, no. 4, pp. 291–304, 1983.
- T. G. Hallam, C. E. Clark, and G. S. Jordan, “Effects of toxicants on populations: a qualitative approach. II. First order kinetics,” Journal of Mathematical Biology, vol. 18, no. 1, pp. 25–37, 1983.
- Z. E. Ma, G. R. Cui, and W. D. Wang, “Persistence and extinction of a population in a polluted environment,” Mathematical Biosciences, vol. 101, no. 1, pp. 75–97, 1990.
- P. D. N. Srinivasu, “Control of environmental pollution to conserve a population,” Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, vol. 3, no. 3, pp. 397–411, 2002.
- L. Huaping and M. Zhien, “The threshold of survival for system of two species in a polluted environment,” Journal of Mathematical Biology, vol. 30, no. 1, pp. 49–61, 1991.
- D. Mukherjee, “Persistence and global stability of a population in a polluted environment with delay,” Journal of Biological Systems, vol. 10, no. 3, pp. 225–232, 2002.
- F. Wang and Z. Ma, “Persistence and periodic orbits for an SIS model in a polluted environment,” Computers & Mathematics with Applications, vol. 47, no. 4-5, pp. 779–792, 2004.
- Y. Xiao and L. Chen, “How do the spatial structure and time delay affect the persistence of a polluted species,” Applicable Analysis, vol. 82, no. 3, pp. 253–267, 2003.
- A. K. Pal and G. P. Samanta, “A single species population in a polluted environment,” International Journal of Biomathematics, vol. 3, no. 2, pp. 187–204, 2010.
- B. Liu, L. Chen, and Y. Zhang, “The effects of impulsive toxicant input on a population in a polluted environment,” Journal of Biological Systems, vol. 11, no. 3, pp. 265–274, 2003.
- F. Tao and B. Liu, “Dynamic behaviors of a single-species population model with birth pulses in a polluted environment,” The Rocky Mountain Journal of Mathematics, vol. 38, no. 5, pp. 1663–1684, 2008.
- X.-Z. Meng, Q.-L. Zhao, and L.-S. Chen, “Global qualitative analysis of new monod type chemostat model with delayed growth response and pulsed input in polluted environment,” Applied Mathematics and Mechanics, vol. 29, no. 1, pp. 75–87, 2008.
- B. Liu, L. Zhang, and Q. Zhang, “The effects of a single stage-structured population model with impulsive toxin input and time delays in a polluted environment,” Applicable Analysis, vol. 88, no. 8, pp. 1143–1155, 2009.
- Z. Zhao, L. Chen, and X. Song, “Extinction and permanence of chemostat model with pulsed input in a polluted environment,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1737–1745, 2009.
- B. Liu and L. Zhang, “Dynamics of a two-species Lotka-Volterra competition system in a polluted environment with pulse toxicant input,” Applied Mathematics and Computation, vol. 214, no. 1, pp. 155–162, 2009.
- B. Kang, B. Liu, and L. Xu, “Dynamics of an inshore-offshore fishery model with impulsive pollutant input in inshore area,” Nonlinear Dynamics, vol. 67, no. 4, pp. 2353–2362, 2012.
- B. Liu, Y. Duan, and S. Luan, “Dynamics of an SI epidemic model with external effects in a polluted environment,” Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, vol. 13, no. 1, pp. 27–38, 2012.
- S. Sun and L. Chen, “Permanence and complexity of the eco-epidemiological model with impulsive perturbation,” International Journal of Biomathematics, vol. 1, no. 2, pp. 121–132, 2008.
- Y. Xue, A. Kang, and Z. Jin, “The existence of positive periodic solutions of an eco-epidemic model with impulsive birth,” International Journal of Biomathematics, vol. 1, no. 3, pp. 327–337, 2008.
- J. Jia and H. Cao, “Dynamic complexities of Holling type II functional response predator-prey system with digest delay and impulsive harvesting on the prey,” International Journal of Biomathematics, vol. 2, no. 2, pp. 229–242, 2009.
- S. Tang, G. Tang, and R. A. Cheke, “Optimum timing for integrated pest management: modelling rates of pesticide application and natural enemy releases,” Journal of Theoretical Biology, vol. 264, no. 2, pp. 623–638, 2010.
- W. Gao and S. Tang, “The effects of impulsive releasing methods of natural enemies on pest control and dynamical complexity,” Nonlinear Analysis. Hybrid Systems. An International Multidisciplinary Journal, vol. 5, no. 3, pp. 540–553, 2011.
- Z. Hu and M. Han, “Periodic solutions and bifurcations of first-order periodic impulsive differential equations,” International Journal of Bifurcation and Chaos, vol. 19, no. 8, pp. 2515–2530, 2009.
- J. Lopez-Gomez, R. Ortega, and A. Tineo, “The periodic predator-prey Lotka-Volterra model,” Advances in Differential Equations, vol. 1, no. 3, pp. 403–423, 1996.