modelComplexInteraction

Interaction with linear and nonlinear terms

Extends from Interfaces.PartialCLD.Interaction (Partial interaction for causal loop diagramming).

Information

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Using →ComplexInteraction this component allows to logically connect two flows influencing two stocks A (connected to portA) and B (connected to portB). The formula for the resulting flows (using Newton's dot notation) has linear and nonlinear terms:

The coefficients are given by parameters, which are multiplied either with 1 (hasFactor = false) or an exogenous factor u (hasFactor = true). Upon setting hasRateOutput = true the component will report the current rate of flows via output connectors (y_A, y_B).

Notes

Using a_0 = -1, b_0 = 1 (other coefficients set to zero), and hasFactor = true a bidirectional flow can be modeled, whose rate is given by the input u (positive inputs indicate a flow from A to B).

Using a_0 = -1, b_0 = f (other coefficients set to zero), and hasFactor = true a broken transition can be modeled, with the proportionality factor f indicating units of B per unit of A.

The parameters polA and polB allow to give visual cues with regard to polarity in the diagram.

Parameters

Type	Name	Default	Description
String	polA (from Interaction)	"±"	Polarity portA
String	polB (from Interaction)	"±"	Polarity portB
Structural Parameters
Boolean	hasFactor (from Interaction)	false	= true, if coefficients are to be multiplied with input u
Boolean	hasRateOutput (from Interaction)	false	= true, if the rate is reported via real output connectors
Parameters for net flow to A
Rate	a_0		Growth rate for A (independent)
Rate	a_A		Fractional rate of growth for A (self-coupling A)
Rate	a_B		Rate of growth for A per unit of B (coupling of B to A)
Rate	a_AB		Fractional rate of growth for A per unit of B (nonlinear coupling)
Parameters for net flow to B
Rate	b_0		Growth rate for B (independent)
Rate	b_B		Fractional growth rate for B (self-coupling)
Rate	b_A		Rate of growth for B per unit of A (coupling of A to B)
Rate	b_AB		Fractional growth rate for B per unit of A (nonlinear coupling)

Connectors

Type	Name	Description
Connectors.FlowPort	portA (from Interaction)
Connectors.FlowPort	portB (from Interaction)
Connectors.RealInput	u (from Interaction)	Factor input

Components

Type	Name	Default	Description
ATypeConnectors.RealOutput	y_A (from Interaction)		Output of current rate of flow for port A
BTypeConnectors.RealOutput	y_B (from Interaction)		Output of current rate of flow for port B

Revisions

Introduced in v2.0.0.