modelLotkaVolterra

The Lotka-Volterra equations to model predator-prey-dynamics

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

Information

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These are the classical Lotka-Volterra equations describing predator-prey-dynamics in an idealized way [17]. The dynamics for the prey population (portA) and the predator population (portB) are given by the following 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.

Coefficient	Unit	Description
`alpha`	1 per second	fractional growth rate for prey population
`beta`	1 per second per base unit of B (`TypeB`)	fractional rate of decline for prey population per predator
`gamma`	1 per second	fractional rate of decline for predator population
`delta`	1 per second per base unit of A (`TypeB`)	fractional rate of groth for predator population per prey

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
Rate	alpha	unspecified	Fractional growth rate of prey population (A)
Rate	beta	unspecified	Fractional rate of decline for prey population (A) per predator
Rate	gamma	unspecified	Fractional rate of decline for predator population (B)
Rate	delta	unspecified	Fractional rate of growth for predator population (B) per prey
Structural Parameters
Boolean	hasConstantAlpha	false	= true, if the constant parameter value is to be used instead of the input connector
Boolean	hasConstantBeta	false	= true, if the constant parameter value is to be used instead of the input connector
Boolean	hasConstantGamma	false	= true, if the constant parameter value is to be used instead of the input connector
Boolean	hasConstantDelta	false	= true, if the constant parameter value is to be used instead of the input connector

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	Inputs for predator-prey model

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

Revisions

InputConnector defined as encapsulated expandable connector in v2.1.0.

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

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