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Dynamical Models of Single-Species System in a Polluted Environment

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Deterministic, Stochastic and Thermodynamic Modelling of some Interacting Species

Part of the book series: Forum for Interdisciplinary Mathematics ((FFIM))

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Abstract

From the viewpoints of mathematics and experiments: the effect of toxicants on ecosystem (a community of living organisms with the environment where they lives), due to change in both terrestrial and aquatic environments caused by various kinds of stresses, is an absolutely essential issue. It is of great interest from both environmental and conservational points of view. Degradation of forests (due to acid rain), dumping of toxic (hazardous) waste in rivers and lakes and the environmental fluctuation because of eutrophication in the Salton sea leading to pelican extinction are some examples. In this chapter, we have studied dynamical behaviours of two single-species population models in polluted environment.

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References

  • Birkhoff, G., Rota, G.C.: Ordinary Differential Equations. Ginn, Boston (1982)

    MATH  Google Scholar 

  • Buonomo, B., Liddo, A.D., Sgura, I.: A diffusive-connective model for the dynamics of population-toxicant intentions: some analytical and numerical results. Math. Biosci. 157, 37–64 (1999)

    Article  MathSciNet  Google Scholar 

  • Erbe, L.H., Rao, V.S.H., Freedman, H.: Three species food chain models with mutual interference and time delays. Math. Biosci. 80, 57–80 (1986)

    Article  MathSciNet  Google Scholar 

  • Freedman, H.I.: Deterministic Mathematical Models in Population Ecology. HIFR Consulting Ltd., Edmonton (1987)

    MATH  Google Scholar 

  • Freedman, H., Rao, V.S.H.: The trade-off between mutual interference and time lags in predator-prey systems. Bull. Math. Biol. 45, 991–1004 (1983)

    Article  MathSciNet  Google Scholar 

  • Hale, J.K.: Theory of Functional Differential Equations. Springer-Verlag, New York (1977)

    Book  Google Scholar 

  • Liao, X.: Hopf and resonant codimension two bifurcation in Van Dar Pol equation with two time delays. Chaos Solitons Fractals 23, 857–871 (2005)

    Article  MathSciNet  Google Scholar 

  • Liu, W.: Criterion of Hopf bifurcations without using eigen values. J. Math. Anal. Appl. 182, 250–256 (1994)

    Article  MathSciNet  Google Scholar 

  • May, R.M.: Stability in randomly fluctuating versus deterministic environments. Am. Nat. 107, 621–650 (1973)

    Article  Google Scholar 

  • White, B.S.: The effects of a rapidly fluctuating random environment on systems of interacting species. SIAM J. Appl. Math. 32, 666–693 (1977)

    Article  MathSciNet  Google Scholar 

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Samanta, G. (2021). Dynamical Models of Single-Species System in a Polluted Environment. In: Deterministic, Stochastic and Thermodynamic Modelling of some Interacting Species. Forum for Interdisciplinary Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-16-6312-3_2

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