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Modelling the effect of toxicant on forestry resources. (English) Zbl 0870.92020

Summary: A mathematical model is proposed and analysed to study the effect of a toxicant on forestry resources. The effects of conservation of resource biomass and control of the concentration of toxicant in the environment are incorporated in the model. Using stability theory of ordinary differential equation, it is shown that if suitable efforts are made to conserve the recource biomass and to control the concentration of toxicant, an appropriate level of resource biomass density can be maintained. It is noted that a periodic emission of toxicant for small amplitude causes a periodic behaviour in the system. If no effort is made to conserve the resource and to control the undesired level of the concentration of toxicant, then it is found that in the case of constant spill of toxicant into the environment the resource biomass settles down to its equilibrium level, the magnitude of which depends upon the environmental concentration and the uptake concentration of toxicant. It is noted here that the resource biomass may go to extinction if the environmental concentration of toxicant continues without control.
To discuss the applicability of the model, a numerical example is also presented. This example shows that if suitable efforts are not applied to conserve the resource biomass and to control the concentration of toxicant, then the concentration of the toxicant in the environment and in the resource biomass increases and consequently the density of the resource biomass decreases. The model presented in this paper is applicable to the Doon Valley in the northern part of Uttar Pradesh, India, where the forestry resources are degrading due to continuous pressures of industrial growth and associated pollution.

MSC:

92D40 Ecology
93C95 Application models in control theory
34D05 Asymptotic properties of solutions to ordinary differential equations
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