.BusinessSimulation.SourcesOrSinks.LogisticGrowth

Information

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LogisticGrowth describes the growth of some population that is limited by the availability of some finite resource. While the population starts to grow exponentially at first at a given fractional rate of growth (either given by the constant parameter r or by the time-variant input u[1]), its growth rate will continously diminish until the population reaches its sustainable level (either given by the constant parameter K or the time-variant input u[2]), which is called the carrying capacity.

The rate of inflow to a connected stock is given by the so called Verhulst equation:

 The diagram below shows the s-shaped growth for a population x for different rates of growth:

LogisticGrowth for Different Rates r (x0 = 0.1)

Notes

• By default it is assumed, that the rate given is a continously compounding rate (isCCR = true). If this is not case, the rate will be converted using the →ForceOfInterest converter.


• While the component refers to growth it can easily be seen from the equation above, that for negative rates or for K < x the inflow to the stock can become negative. This is allowed and the modeler has to take care that the input or parameter values make sense for the process being modeled.

Acknowledgements

The logistic growth equation is originally due to the Belgian mathematican Pierre-François Verhulst (1804 - 1849).

Contents

Name	Description
CapacityType	Type for carrying capacity K

Revisions

• Added type choice for K and defaulted optional constant parameters to unspecified.