NonlinearInteraction

Outflows depend upon the product of the stocks and a factor

Diagram

Information

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 flow—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.

Examples

A nonlinear component is typically found in predator-prey 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).

Parameters (4)

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

Connectors (9)

	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

Components (9)

	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