.BusinessSimulation.Flows.Interaction.LinearInteraction

Information

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The LinearInteraction component allows to model the interaction between two stocks A (portA) and B (portB) as linear 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.

The coefficients can be given as parameters or as variables via the expandable connector dataIn.

Examples

A linear harmonic oscillator can be modeled as a special case of linear interactions where the rates for the mutual influences (e.g., fractionalGrowthRate_B_per_A and fractionalGrowthRate_A_per_B) are negative. In that case, positive stock A will decrease stock B and vice versa.

The Linear Interaction can be used to model Strogatz' famous model for the dynamics of a love affair (conspicuously between "Romeo" and "Juliet") as shown in →LoveHateDynamics [16].

Notes

• The type selectors OutputType_A and OutputType_B will be used to conveniently set the types, e.g., units, of the parameters a_0,a_B and b_0, b_A.


• The coupling coefficient a_B might have rather convoluted units, e.g., base units of A/(base units of B.s). For convenient modeling, a_B will be divided by refB, which allows to use displayUnit should unit conversion be required. Since TypeB by default is set to Unspecified in most cases nothing needs to be done.


• This will, conversely, also apply to b_A.

See also

NonlinearInteraction, ComplexInteraction

Contents

Name	Description
TypeA	Type selector for stock A (default = Unspecified)
TypeB	Type selector for stock B (default = Unspecified)
Input_Connector	Data bus for inputs

Revisions

• Input_Connector defined as encapsulated expandable connector in v2.1.0.


• Values for optional parameters changed to unspecified in v2.1.0.


• Adapted types and added divisors for compliance with unit checking and convenient unit conversions in v2.2.