ComplexInteraction

Interaction with linear and nonlinear terms

Diagram

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 (12)

polA	Value: "±" Type: String Description: Polarity portA
polB	Value: "±" Type: String Description: Polarity portB
hasFactor	Value: false Type: Boolean Description: = true, if coefficients are to be multiplied with input u
hasRateOutput	Value: false Type: Boolean Description: = true, if the rate is reported via real output connectors
a_0	Value: Type: Rate (1/s) Description: Growth rate for A (independent)
a_A	Value: Type: Rate (1/s) Description: Fractional rate of growth for A (self-coupling A)
a_B	Value: Type: Rate (1/s) Description: Rate of growth for A per unit of B (coupling of B to A)
a_AB	Value: Type: Rate (1/s) Description: Fractional rate of growth for A per unit of B (nonlinear coupling)
b_0	Value: Type: Rate (1/s) Description: Growth rate for B (independent)
b_B	Value: Type: Rate (1/s) Description: Fractional growth rate for B (self-coupling)
b_A	Value: Type: Rate (1/s) Description: Rate of growth for B per unit of A (coupling of A to B)
b_AB	Value: Type: Rate (1/s) Description: Fractional growth rate for B per unit of A (nonlinear coupling)

Connectors (15)

	portA	Type: FlowPort Description: Used to represent stock and flow connections
	portB	Type: FlowPort Description: Used to represent stock and flow connections
	u	Type: RealInput Description: Factor input
	y_A	Type: RealOutput Description: Output of current rate of flow for port A
	y_B	Type: RealOutput Description: Output of current rate of flow for port B
	one	Type: RealOutput Description: Default factor
	y_a0	Type: RealOutput Description: Output signal
	dataIn	Type: InputConnector Description: Data bus for inputs
	y_aA	Type: RealOutput Description: Output signal
	y_aB	Type: RealOutput Description: Output signal
	y_aAB	Type: RealOutput Description: Output signal
	y_b0	Type: RealOutput Description: Output signal
	y_bA	Type: RealOutput Description: Output signal
	y_bB	Type: RealOutput Description: Output signal
	y_bAB	Type: RealOutput Description: Output signal

Components (3)

	complexInteraction	Type: ComplexInteraction Description: Combined linear and nonlinear interaction
	actualCoefficients	Type: ScalarMultiplication Description: Multiplication of a vector with a scalar
	constantCoefficients	Type: ConstantConverter Description: A list of constant values is turned into a constant vector of signals