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1.2: The Logistic Equation - Mathematics LibreTexts

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The exponential growth law for population size is unrealistic over long times. Eventually, growth will be checked by the over-consumption of resources. We assume that the environment has an intrinsic …

The Logistic equation The exponential growth law for population size is unrealistic over long times. Eventually, growth will be checked by the over-consumption of resources. We assume that the environment has an intrinsic carrying capacity \(K\) , and populations larger than this size experience heightened death rates. To model population growth with an environmental carrying capacity \(K\) , we look for a nonlinear equation of the form \[\frac{d N}{d t}=r N F(N) \nonumber \] where \(F(N)\) provides a model for environmental regulation. This function should satisfy \(F(0)=1\) (the population g

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