ComplexInteraction

Combined linear and nonlinear interaction

Diagram

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 (2)

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

refA

Value: 1

Type: TypeA

Description: Reference value, i.e., divisor, for the couplings b_A, b_AB

refB

Value: 1

Type: TypeB

Description: Refrence value, i.e., divisor, for the couplings a_B, a_AB

Connectors (16)

	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 Description: Expandable connector for continuous input
	a_0	Type: RealOutput Description: Growth rate for A (independent)
	a_A	Type: RealOutput Description: Fractional rate of growth for A (self-coupling A)
	a_B	Type: RealOutput Description: Rate of growth for A per unit of B (coupling of B to A)
	a_AB	Type: RealOutput Description: Fractional rate of growth for A per unit of B (nonlinear coupling)
	b_0	Type: RealOutput Description: Growth rate for B (independent)
	b_B	Type: RealOutput Description: Fractional growth rate for B (self-coupling)
	b_A	Type: RealOutput Description: Rate of growth for B per unit of A (coupling of A to B)
	b_AB	Type: RealOutput Description: Fractional growth rate for B per unit of A (nonlinear coupling)
	dataBus	Type: DataBus Description: Expandable connector for multiple data signals (input/output)

Components (4)

	linearInteraction	Type: LinearInteraction Description: Linear interaction between A and B
	nonlinearInteraction	Type: NonlinearInteraction Description: Nonlinear interaction between A and B
	netRate_B	Type: Add_2 Description: Sum of two inputs
	netRate_A	Type: Add_2 Description: Sum of two inputs