
Mathematical Biosciences and Engineering, 2019, 16(6): 81798194. doi: 10.3934/mbe.2019413.
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The effects of impulsive toxicant input on a singlespecies population in a small polluted environment
College of Science, Harbin University of Science Technology, Harbin 150080, China
Received: , Accepted: , Published:
Special Issues: Modeling and Complex Dynamics of Populations
Keywords: pollution; extinction; persistence; impulsive toxicant input; surviving threshold
Citation: Dongmei Li, Tana Guo, Yajing Xu. The effects of impulsive toxicant input on a singlespecies population in a small polluted environment. Mathematical Biosciences and Engineering, 2019, 16(6): 81798194. doi: 10.3934/mbe.2019413
References:
 1. Z. Jiang, Can we prevent extinction?, Bull. Sci. Technol., 61 (2016), 1978–1982.
 2. Q. Zhao, G. Huang and Y. Ma, The ecological environment conditions and construction of an ecological civilization in China, Acta Ecol. Sin., 36 (2016), 6328–6335.
 3. T. G. Hallam, C. E. Clark and R. R. Lassider, Effects of toxicants on populations: A qualitative approach I equilibrium environmental exposure, Eool. Model, 8 (1983), 291–304.
 4. T. G. Hallam, C. E. Clark and G. S. Jordan, Effects of toxicants on populations: A qualitative approach Ⅱ first order kinetics, Math. Biol., 18 (1983), 25–37.
 5. T. G. Hallam and J. T. Deluna, Effects of toxicants on populations: A qualitative approachc. environmental and food chain pathways, J. Theor. Biol., 109 (1984), 411–429.
 6. F. Wei, A. H. Geritz and J. Cai, A stochastic singlespecies population model with partial pollution tolerance in a polluted environment, Appl. Math. Lett., 63 (2017), 130–136.
 7. Y. Feng and K. Wang, The survival analysis for singlespecies system in a polluted environment, J. Ann. Diff. Equ., 22 (2006), 154–159.
 8. J. He and K. Wang, The survival analysis for a singlespecies population model in a polluted environment, Nonlinear Anal.: Real World Appl., 10 (2009), 1555–1571.
 9. J. He and K. Wang, The survival analysis for a population in a polluted environment, Appl. Math. Model., 31 (2007), 2227–2238.
 10. Z. Luo, Y. Yu and Z. Ba, The thresholds of survival for a singlespecies population model in a polluted environment, J. Biomath., 26 (2011), 211–222.
 11. A. Kumar, A. K. Agrawal, A. Hasan, et al., Modeling the effect of toxicant on the deformity in a subclass of a biological species, Model. Earth Syst. Environ., 2 (2016), 40–40.
 12. V. Ducrot, E. Billoir, J. Garric, et al., From individual to population level effects of toxicants in the tubicifid branchiura sowerbyi using threshold effect models in a bayesian framework, Environ. Sci. Technol., 44 (2010), 3566–3571.
 13. B. Liu, L. Chen and Y. Zhang, The effects of impulsive toxicant input on a population in a polluted environment, J. Biol. Syst., 11 (2003), 265–274.
 14. H. Zhang, X. Meng and L. Chen, Impact of impulsive effect on a population dynamical behaviorin a polluted environment, J. Dalian Univ. Technol., 48 (2008), 147–153.
 15. L. Bao and X. Ban, The study on single population model with pulse input of environmental toxin, J. Jiangxi Norm. Univ. (Nat. Sci.), 36 (2012), 502–505.
 16. B. Liu, L. Xu and B. Kang, Dynamics of a stage structured pest control model in a polluted environment with pulse pollution input, J. Appl. Math., 2013 (2009), 1–12.
 17. J. Jiao and L. Chen, The extinction threshold on a single population model with pulse input of environmental toxin in a polluted environment, Math. Appl., 22 (2009), 11–19.
 18. Y. Xue, J Wang and Z. Jin, The persistent threshold of single population under pulse input of environment, Wseas Trans. Math., 1 (2007), 22–29.
 19. Y. Hou and J. Jiao, Dynamical analysis of a single population model with delayed growth response and pulse input in polluted environment, Math. Pract. Theory, 47 (2017), 119–127.
 20. X. Song, H. Guo and X. Shi, The Theory of Impulsive Differential Equation and Its Application, Science Press, Beijing, 2011.
 21. Y. Xiao, Y. Zhou and S. Tang, Biological Mathematical Principles, Xi'an Jiaotong University Press, Xi'an, 2012.
This article has been cited by:
 1. Wenxu Ning, Zhijun Liu, Lianwen Wang, Ronghua Tan, A stochastic mutualism model with saturation effect and impulsive toxicant input in a polluted environment, Journal of Applied Mathematics and Computing, 2020, 10.1007/s12190020013878
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