modelLogisticGrowth
Extends from Interfaces.Basics.GenericSourceOrSink (SinkOrSource template with one flow port), Icons.Source (General icon for sources).
Information
This information is part of the Business Simulation Library (BSL). Please support this work and ► donate.
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:
 |
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 < xthe 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).
Parameters
| Type | Name | Default | Description |
|---|---|---|---|
| Rate | r | unspecified | Maximum fractional growth rate |
| CapacityType | K | unspecified | Carrying capacity or maximum sustainable amount for the connected stock (>0) |
| Structural Parameters | |||
| Boolean | isCCR | true | = true, if the maximum fractional rate given is assumed to be a continuously compounding rate else the rate will be converted |
| Boolean | hasConstantInputs | false | = true, if constant parameters aure to be used instead of the real inputs u[1] and u[2] |
Connectors
| Type | Name | Default | Description |
|---|---|---|---|
| Connectors.FlowPort | massPort (from GenericSourceOrSink) | Inflow to or outflow from connected stock | |
| Interfaces.Connectors.RealMultiInput[2] | u | [1] maximum fractional growth rate [2] carrying capacity |
Components
| Type | Name | Default | Description |
|---|---|---|---|
| RealOutput | y (from ThreeSO_rate) | Rate information | |
| RealOutput | y1 (from ThreeSO_rate) | Rate information | |
| RealOutput | y2 (from ThreeSO_rate) | Rate information |
Contents
| Name | Description |
|---|---|
| CapacityType |
Revisions
- Added type choice for
Kand defaulted optional constant parameters tounspecified.