LogisticGrowthLogistic growth model 
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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 timevariant 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 timevariant 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 sshaped growth for a population x for different rates of growth:
isCCR = true
). If this is not case, the rate will be converted using the →ForceOfInterest converter.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.The logistic growth equation is originally due to the Belgian mathematican PierreFrançois Verhulst (1804  1849).
r 
Value: unspecified Type: Rate (1/s) Description: Maximum fractional growth rate 

K 
Value: unspecified Type: CapacityType (#) Description: Carrying capacity or maximum sustainable amount for the connected stock (>0) 
isCCR 
Value: true Type: Boolean Description: = true, if the maximum fractional rate given is assumed to be a continuously compounding rate else the rate will be converted 
hasConstantInputs 
Value: false Type: Boolean Description: = true, if constant parameters aure to be used instead of the real inputs u[1] and u[2] 
y 
Type: RealOutput Description: Rate information 


y1 
Type: RealOutput Description: Rate information 

y2 
Type: RealOutput Description: Rate information 

massPort 
Type: FlowPort Description: Inflow to or outflow from connected stock 

u 
Type: RealMultiInput[2] Description: [1] maximum fractional growth rate [2] carrying capacity 
population 
Type: FlowPortSensor Description: Current level of the connected stock 


cloud 
Type: Cloud Description: System boundary 

growing 
Type: Switching Description: Process of logistic growth 

fractionalGrowthRate 
Type: Product_2 Description: Actual fractional rate of growth 

relativePopulation 
Type: Division_Guarded Description: Population as percentage of carrying capacity 

residualCapacity 
Type: Gap Description: Percentage of the carrying capacity left for growth 

one 
Type: ConstantConverter Description: 100 percent 

growthRate 
Type: Product_2 Description: Rate of growth 

carryingCapacity 
Type: ConstantConverter Description: Constant carrying capacity (optional) 

maxFractionalGrowthRate 
Type: ConstantConverter Description: Constant maximum rate of growth (optional) 

convertedRate 
Type: ForceOfInterest Description: Discrete compounding rate being converted to CCR 

identicalRate 
Type: PassThrough Description: Use indicated rate if it is continuously compounding 
BusinessSimulation.CausalLoop Sshaped logistic growth process 
K
and defaulted optional constant parameters to unspecified
.