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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Birkhoff, G., Rota, G.C.: Ordinary Differential Equations. Ginn, Boston (1982)
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)
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)
Freedman, H.I.: Deterministic Mathematical Models in Population Ecology. HIFR Consulting Ltd., Edmonton (1987)
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)
Hale, J.K.: Theory of Functional Differential Equations. Springer-Verlag, New York (1977)
Liao, X.: Hopf and resonant codimension two bifurcation in Van Dar Pol equation with two time delays. Chaos Solitons Fractals 23, 857–871 (2005)
Liu, W.: Criterion of Hopf bifurcations without using eigen values. J. Math. Anal. Appl. 182, 250–256 (1994)
May, R.M.: Stability in randomly fluctuating versus deterministic environments. Am. Nat. 107, 621–650 (1973)
White, B.S.: The effects of a rapidly fluctuating random environment on systems of interacting species. SIAM J. Appl. Math. 32, 666–693 (1977)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-981-16-6312-3_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-6311-6
Online ISBN: 978-981-16-6312-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)