modelComplexInteraction

Combined linear and nonlinear interaction

Extends from Icons.Interaction (Icon for interactional flow classes), Interfaces.Basics.GenericFlow (Flow Template with two FlowPorts), Interfaces.Basics.Interaction4SO (Output connectors for interaction elements reporting rates).

Information

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The ComplexInteraction component combines linear and nonlinear interaction between two stocks A (portA) and B (portB):

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_0`	base unit of flow to A (`OutputType_A`)	Rate of growth for stock A
`b_0`	base unit of flow to B (`OutputType_B`)	Rate of growth for stock B
`a_A`	1/s	fractional rate of growth for stock A (e.g., the self-coupling coefficient for A)
`b_B`	1/s	fractional rate of growth for stock B (e.g., the self-coupling coefficient for B)
`a_B`	base unit of flow to A (`OutputType_A`) per base unit of B (`TypeB`)	Rate of growth for stock A per stock B (e.g., the coupling-cofficient for B towards A)
`b_A`	base unit of flow to B (`OutputType_B`) per base unit of A (`TypeA`)	Rate of growth for stock B per stock A (e.g., the coupling-coefficient for A towards B)
`a_AB`	1 per second per base unit of B (`TypeB`)	Factor used to determine the net flow to A (e.g., nonlinear coupling factor for A)
`b_AB`	1 per second per base unit of A `TypeA`)	Factor used to determine the net flow to B (e.g., nonlinear coupling factor for B)

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

Examples

The classical Lotka-Volterra-Model of predator-prey-dynamics can be derived from this model using the following parameterization:

a_0 = 0, a_A = α, a_B = 0, a_AB = -β, b_0 = 0, b_B = -γ, b_A = 0, b_AB = δ

Notes

Within the components LinearInteraction and NonlinearInteraction the rates passed for a_B, a_AB, b_A, b_AB call for divison by a reference level of the connected stocks. In many cases, modelers can leave the type selectors TypeA, TypeB at their default value of Unspecified so that no conversion will take place.

Should unit conversion be needed, modeleres may wish to select appropriate type values and corresponding displayUnit settings to enter convenient reference levels refA, refB.

Parameters

Type	Name	Default	Description
TypeA	refA	1	Reference value, i.e., divisor, for the couplings b_A, b_AB
TypeB	refB	1	Refrence value, i.e., divisor, for the couplings a_B, a_AB

Connectors

Type	Name	Description
Connectors.FlowPort	portA (from GenericFlow)	Flow from/to Stock A
Connectors.FlowPort	portB (from GenericFlow)	Flow to/from Stock B
RealOutput_B	y_B (from Interaction4SO)	Rate for flow to and from B (positive value indicates inflow)
RealOutput_B	y1_B (from Interaction4SO)	Rate for flow to and from B (positive value indicates inflow)
RealOutput_A	y1_A (from Interaction4SO)	Rate for flow to and from A (positive value indicates inflow)
RealOutput_A	y_A (from Interaction4SO)	Rate for flow to and from A (positive value indicates inflow)
InputConnector	dataIn	Expandable connector for continuous input

Name	Description
TypeA	Type selector for stock A
TypeB	Type selector for stock B
InputConnector	Data bus for inputs

Revisions

InputConnector defined as encapsulated expandable connector in v2.1.0.

TypeA, TypeB and corresponding reference levels refA, refB introduced to support unit checking and unit conversions in v2.2.