Research article Special Issues

The effects of impulsive toxicant input on a single-species population in a small polluted environment

  • Received: 31 December 2018 Accepted: 14 May 2019 Published: 10 September 2019
  • In this paper, we study a single-species population model with pulse toxicant input in a small polluted environment. The intrinsic rate of population change is affected by the environmental toxin load and toxin in the organisms which is influenced by toxin in the environment and the food chain. A new mathematical model is established. By the Pulse Compare Theorem, we find the surviving threshold of the population and obtain the sufficient conditions of persistence and extinction of the population.

    Citation: Dongmei Li, Tana Guo, Yajing Xu. The effects of impulsive toxicant input on a single-species population in a small polluted environment[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 8179-8194. doi: 10.3934/mbe.2019413

    Related Papers:

  • In this paper, we study a single-species population model with pulse toxicant input in a small polluted environment. The intrinsic rate of population change is affected by the environmental toxin load and toxin in the organisms which is influenced by toxin in the environment and the food chain. A new mathematical model is established. By the Pulse Compare Theorem, we find the surviving threshold of the population and obtain the sufficient conditions of persistence and extinction of the population.


    加载中


    [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 single-species 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 single-species system in a polluted environment, J. Ann. Diff. Equ., 22 (2006), 154–159.
    [8] J. He and K. Wang, The survival analysis for a single-species 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 single-species 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.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3150) PDF downloads(537) Cited by(5)

Article outline

Figures and Tables

Figures(4)  /  Tables(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog