NonlinearInteractionOutflows depend upon the product of the stocks and a factor 
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The NonlinearInteraction can be used by itself or in combination with the →LinearInteraction flow to model more complex interactions. The netflows to the connected stocks A (portA
) and B (portB
) are given by the following equations:
Note: Capital letters were chosen to represent the stocks (state variables) connected at portA
and portB
in the formula above. Also dot notation is used for a stock's rate of flowâ€”its first derivative with respect to time.
Coefficient  Unit  Description 

a_AB 
1 per second per base unit of B ( TypeB ) 
Factor used to determine the net flow to A 
b_AB 
1 per second per base unit of A ( TypeA 
Factor used to determine the net flow to B 
The coefficients can be given as parameters or as variables via the expandable connector dataIn
.
A nonlinear component is typically found in predatorprey models or models of infectious diseases, where the exponential growth rate for a population depends upon the size of another population (e.g., prey or susceptible population).
Amount [each]
then it is rather straight forward to enter a fractional rate per unit of A or B for the parameters a_AB, b_AB
and we can in fact leave TypeA, TypeB, refA, refB
at their default values.displayUnit
for one of the stocks, we can use the type selectors TypeA, TypeB
to select the appropriate units for the connected stocks and then set the references values refA, refB
using whatever displayUnit
we want.a_AB 
Value: unspecified Type: Rate (1/s) Description: Constant fractional rate for the netflow to A per unit of B (nonlinear coupling factor) 

refB 
Value: 1 Type: TypeB Description: Reference value for B, i.e., divisor for the fractional rate a_AB 
b_AB 
Value: unspecified Type: Rate (1/s) Description: Constant fractional rate for the netflow to B per unit of A (nonlinear coupling factor) 
refA 
Value: 1 Type: TypeA Description: Reference value for A, i.e., divisor for the fractional rate b_AB 
hasConstantFactorA 
Value: false Type: Boolean Description: = true, if the coupling factor for A is given by the constant parameter 
hasConstantFactorB 
Value: false Type: Boolean Description: = true, if the coupling factor for B is given by the constant parameter 
portA 
Type: FlowPort Description: Flow from/to Stock A 


portB 
Type: FlowPort Description: Flow to/from Stock B 

y_B 
Type: RealOutput_B Description: Rate for flow to and from B (positive value indicates inflow) 

y1_B 
Type: RealOutput_B Description: Rate for flow to and from B (positive value indicates inflow) 

y1_A 
Type: RealOutput_A Description: Rate for flow to and from A (positive value indicates inflow) 

y_A 
Type: RealOutput_A Description: Rate for flow to and from A (positive value indicates inflow) 

dataIn 
Type: InputConnector Description: Data bus for inputs 

u_a_AB 
Type: RealOutput Description: Nonlinear coupling factor for A 

u_b_AB 
Type: RealOutput Description: Nonlinear coupling factor for B 
netFlowA 
Type: ExogenousChange Description: Net flow to A 


netFlowB 
Type: ExogenousChange Description: Net flow to B 

levelA 
Type: FlowPortSensor Description: Amount in stock A 

levelB 
Type: FlowPortSensor Description: Amount in stock B 

product_A_B 
Type: Product_2 Description: Product of A and B 

netRateA 
Type: Product_2 Description: Rate of netflow A (positive = inflow) 

netRateB 
Type: Product_2 Description: Rate of netflow B (positive = inflow) 

parFactorA 
Type: ConstantConverter Description: Constant fractional rate A 

parFactorB 
Type: ConstantConverter Description: Constant fractional rate B 

unitMultiplierA 
Type: Gain Description: Constant should have units 1/UnitsA 

unitMultiplierB 
Type: Gain Description: Constant should have units 1/UnitsB 
BusinessSimulation.Examples Predatorprey dynamics 

LotkaVolterraEquationsRevisited BusinessSimulation.Examples Predatorprey dynamics with an additional predator 
BusinessSimulation.Flows.Interaction Combined linear and nonlinear interaction 
InputConnector
defined as encapsulated expandable connector
in v2.1.0.unspecified
in v2.1.0.