Degradation and subsequent regeneration of a forestry resource: A mathematical model

Shukla, J.B.; Freedman, H. I.; Pal, Vijay; Misra, O. P.; Agarwal, Manju; Shukla, Ashutosh K.

doi:10.1016/0304-3800(89)90031-8

Cited by 64 publications

(30 citation statements)

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“…In the absence of diffusion our w x model is more general than that of Huaping and Ma Zhien 12 . In the w x presence of diffusion our results agree with those in Hastings 11 , Shukla w x w x w x and Verma 19 , Shukla and Shukla 18 , Shukla et al 17 , and Freedman w x and Shukla 5 . The stability theory of the ordinary differential equation is w x used to analyse the model 13 .…”

Section: Introductionsupporting

confidence: 94%

Modelling the Interaction of Two Biological Species in a Polluted Environment

Dubey

Hussain

2000

Journal of Mathematical Analysis and Applications

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In this paper a mathematical model is proposed and analysed to study the effect of an environmental pollutant on two interacting biological species. The interaction between the two species is considered to be of three types, namely, competition, cooperation, and prey᎐predator. In each case criteria for local stability, instability, and global stability of the nonnegative equilibria of the system are obtained. The effect of diffusion on the equilibrium state of the system is also studied. ᮊ 2000 Academic Press

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Section: Introductionsupporting

confidence: 94%

Modelling the Interaction of Two Biological Species in a Polluted Environment

Dubey

Hussain

2000

Journal of Mathematical Analysis and Applications

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“…Some examples are oil pollution in the seas [19], degradation of forests [24,21], dumping of toxic waste in rivers and lakes [9,14] and the environmental fluctuation due to eutrophication in the Salton sea [3,7] causing pelican extinction.…”

Section: Introductionmentioning

confidence: 99%

Dynamical model of a single-species system in a polluted environment

Samanta

Maiti²

2004

JAMC

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Abstract. The effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view. Here we have studied dynamical model of a single-species population-toxicant system. Two cases are studied : constant exogeneous input of toxicant and rapidly fluctuating random exogeneous input of toxicant into the environment. The dynamical behaviour of the system is analyzed by using deterministic linearized technique, Lyapunov method and stochastic linearization on the assumption that exogeneous input of toxicant into the environment behaves like 'Coloured noise'.

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“…Therefore, some kind of effort must be adopted to conserve the resource [4,14,16,19,21,23,25]. In this section, a mathematical model is proposed to conserve the resource biomass by some efforts and by controlling environmental pollution by some mechanism.…”

Section: Conservation Modelmentioning

confidence: 99%

“…Dubey [4] proposed a model for control of toxicant and conservation of forestry resources. The survival (growth and existence) of a resource biomass-dependent species in a forest habitat, which is depleting due to industrialization pressure, has also been studied [24,25]. Shukla and Dubey [23] studied the depletion of a forestry resource in a habitat, which is caused by an increase in population density and pollutant emission into the environment.…”

Section: Introductionmentioning

confidence: 98%