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Control of environmental pollution to conserve a population. (English) Zbl 0998.92042
Summary: The model analyzed here represents the dynamics of a population in a polluted environment. Here the net growth rate of the population depends on the concentration of the pollutant in the organism and environment. From Theorem 1, we can observe that the persistence or extinction of the population is very much dependent on $u\left(t\right)$, the input of the pollutants into the environment. In Theorem 3, it is shown that it is possible to guarantee the persistence of the population by regulating $u\left(t\right)$. Here, effort is used as control to regulate $u\left(t\right)$. Apart from making the population persistent, it is also possible to control the asymptotic value of the population. This is illustrated through Theorem 4. It is assumed that the total consumption in the environment is constant and no effort is made to reduce the consumption to regulate $u\left(t\right)$. However, we can also consider the consumption as a dynamic variable and hence study the trade off between consumption and conservation.
##### MSC:
 92D40 Ecology 34D05 Asymptotic stability of ODE 34D23 Global stability of ODE
##### Keywords:
environment; population conservation