LotkaVolterra

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

Diagram

Information

This information is part of the Business Simulation Library (BSL).

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:

Formula.svg

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 amount of B

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 amount of A fractional rate of groth for predator population per prey

See also

ComplexInteraction

Parameters (8)

alpha

Value: unspecified

Type: Rate (1/s)

Description: Fractional growth rate of prey population (A)

beta

Value: unspecified

Type: Rate (1/s)

Description: Fractional rate of decline for prey population (A) per predator

gamma

Value: unspecified

Type: Rate (1/s)

Description: Fractional rate of decline for predator population (B)

delta

Value: unspecified

Type: Rate (1/s)

Description: Fractional rate of growth for predator population (B) per prey

hasConstantAlpha

Value: false

Type: Boolean

Description: = true, if the constant parameter value is to be used instead of the input connector

hasConstantBeta

Value: false

Type: Boolean

Description: = true, if the constant parameter value is to be used instead of the input connector

hasConstantGamma

Value: false

Type: Boolean

Description: = true, if the constant parameter value is to be used instead of the input connector

hasConstantDelta

Value: false

Type: Boolean

Description: = true, if the constant parameter value is to be used instead of the input connector

Connectors (12)

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: Inputs for predator-prey model

u_alpha

Type: RealOutput

u_beta

Type: RealOutput

u_gamma

Type: RealOutput

u_delta

Type: RealOutput

dataBus

Type: DataBus

Components (8)

complexInteraction

Type: ComplexInteraction

zeroRate

Type: ConstantConverterRate

Description: Zero rate input

fractionalGrowthRatePredator

Type: Gain

Description: Convert rate of delince to growth rate

couplingFactorForPrey

Type: Gain

Description: Convert rate of delince to growth rate

parAlpha

Type: ConstantConverterRate

Description: Constant alpha (optional)

parBeta

Type: ConstantConverterRate

Description: Constant beta (optional)

parGamma

Type: ConstantConverterRate

Description: Constant gamma (optional)

parDelta

Type: ConstantConverterRate

Description: Constant delta (optional)

Used in Examples (1)

LotkaVolterraSystems

BusinessSimulation.Examples

Predator-prey dynamics

Revisions

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

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