NonlinearInteractionOutflows depend upon the product of the stocks and a factor 
This information is part of the Business Simulation Library (BSL).
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 amount of B 
Factor used to determine the net flow to A (positive rate = inflow) 
b_AB 
1 per second per amount of A 
Factor used to determine the net flow to B (positive rate = inflow) 
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).
a_AB 
Value: unspecified Type: Rate (1/s) Description: Constant fractional rate for the netflow to A per unit of B (nonlinear coupling factor) 

b_AB 
Value: unspecified Type: Rate (1/s) Description: Constant fractional rate for the netflow to B per unit of A (nonlinear coupling factor) 
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 

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: ConstantConverterRate Description: Constant fractional rate A 

parFactorB 
Type: ConstantConverterRate Description: Constant fractional rate B 
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.