Department of Mathematics

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1996 - 19997

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End date: 1999

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Now showing 1 - 7 of 7
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    Simultaneous effect of two toxicants on biological species: a mathematical model
    (World Scientific, 1996) Dubey, Balram
    In this paper, a mathematical model to study the simultaneous effect of two toxicants (one is more toxic than the other) on the growth and survival of a biological species is proposed. The cases of instantaneous spill, constant and periodic emissions of each of the toxicant into the environment are considered. It is shown that in the case of an instantaneous spill of each of the toxicant into the environment, the species after its initial decrease in density may recover to its original level after a period of time, the magnitude of which depends on the toxicity and washout rate of each of the toxicant. However, if both the toxicants are emitted with constant rates, the species in the habitat is doomed to extinction sooner than the case of a single toxicant having the same influx and washout rates as one of them, the extinction rate becoming faster with the increase in toxicity and emission rate of the other toxicant. It is also shown that for a small amplitude periodic emission of the toxicant with a constant mean, the stability behavior of the system is same as that of the case of the constant emission. It is found further through the model study that if suitable efforts are made to reduce the emission rate of each of the toxicant at the source and its concentration in the environment by some removal mechanism, an appropriate level of species density can be maintained.
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    Effect of changing habitat on survival of species
    (Elsevier, 1996) Dubey, Balram
    In this paper, a mathematical model is proposed to study the growth and existence (survival) of resource-biomass-dependent species in a forested habitat which is being depleted due to the pressure of industrialization (population). It is shown that as the pressure of industrialization increases, the biomass density decreases, leading to lowering of the density of species and its eventual extinction if this pressure continues unabatedly. However, if suitable efforts are made to conserve the resource biomass and to control the pressure of industralization in the forested habitat, the survival of resource-biomass-dependent species can be ensured.
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    Effect of environmentally degraded soil on crop yield: The role of conservation, Ecol. Model., 86: 235-240, 1996.
    (Elsevier, 1996-05) Dubey, Balram
    In this paper the effect of fertile top soil degraded by environmental factors such as acid rain and wind on crop yield is studied by considering a single-sector economic growth model. It is shown that if these environmental factors continue to increase without control, the fertile top soil depth tends to zero and consequently the crop yield becomes negligible. However, if suitable measures are taken to fertilize the top soil and to control the acid rain, the crop yield may be maintained at a desired level.
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    Effect of changing habitat on species: Application to Keoladeo National Park, India, Ecol. Model.
    (Elsevier, 1996-04) Dubey, Balram
    In this paper, a mathematical model is proposed to study the effect of ecological changes caused by the excessive growth of wild grasses such as Paspalum distichum on the existence of various species in the Keoladeo National Wetland Park, Bharatpur, Rajasthan, India. In the model the growth rate of several species, such as floating vegetation (Nymphoides indicum, Nymphoides cristatum, Nymphaea nouchali and Nymphaea stellata), fishes, waterfowl, etc. and the corresponding carrying capacity of the wetland are assumed to decrease with the increase in biomass density of wild grasses. By analysing the model it is shown that if the wild grasses are not controlled, the existence of various other species will be threatened. It is shown through the model study that if the growth of wild grasses is controlled, either by allowing a managed number of buffaloes to graze them or by using some other mechanism to remove them, then the other species in the wetland will boom. Keeping in view the growth of Paspalum distichum and using the corresponding parameters for this wetland in the model, the number of buffaloes to be permitted for grazing has also been calculated for management purposes.
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    Modelling the depletion and conservation of forestry resources: effects of population and pollution
    (Springer, 1997-11) Dubey, Balram
    In this paper, a mathematical model is proposed to study the depletion of resources in a forest habitat due to the increase of both population and pollution. It is shown that if the rate of pollutant emission into the environment is either population dependent, constant, or periodic, the equilibrium biomass density of the resource settles down to a lower equilibrium than its original carrying capacity, the magnitude of which decreases as the equilibrium levels of the density of population and the concentration of pollutant increase. However, in the case of an instantaneous spill of pollutant into the environment, the equilibrium biomass density decreases with the increase of the equilibrium density of population only. It is found that if the population density and the emission rate of pollutant increase without control, the forestry resource may become extinct. A conservation model is also proposed, the analysis of which shows that the resource biomass can be maintained at a desired level by conserving the forestry resource and by controlling the growth of population and the emission rate of pollutant in the habitat.
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    Modelling the depletion of forestry resources: Effects of two interacting populations
    (Elsevier, 1997-08) Dubey, Balram
    In this paper, a general mathematical model to study the effects of two interacting populations on the depletion of resources is proposed and analysed. In modelling the system, it is assumed that the resource is a common food for both the populations while one of the population is a supplementary food for the other. A model to conserve the resource is also presented.
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    Models for the Survival of Species Dependent on Resource in Industrial Environments
    (Elsevier, 1999-03) Dubey, Balram
    In this paper, a mathematical model to study the survival of species dependent on a resource under the industrialization pressure in a given region with diffusion is proposed and analyzed. In the absence of diffusion, criteria for local stability, instability, and global stability are obtained. A model to conserve the resource biomass and to control the undesired level of industrialization pressure is also presented.