LotkaVolterraThe Lotka-Volterra equations to model predator-prey-dynamics |
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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:
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 |
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1 per second per amount of A | fractional rate of groth for predator population per prey |
See also
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)
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portA |
Type: FlowPort Description: Flow from/to Stock A |
|---|---|---|
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portB |
Type: FlowPort Description: Flow to/from Stock B |
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y_B |
Type: RealOutput_B Description: Rate for flow to and from B (positive value indicates inflow) |
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y1_B |
Type: RealOutput_B Description: Rate for flow to and from B (positive value indicates inflow) |
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y1_A |
Type: RealOutput_A Description: Rate for flow to and from A (positive value indicates inflow) |
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y_A |
Type: RealOutput_A Description: Rate for flow to and from A (positive value indicates inflow) |
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dataIn |
Type: InputConnector Description: Inputs for predator-prey model |
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u_alpha |
Type: RealOutput |
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u_beta |
Type: RealOutput |
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u_gamma |
Type: RealOutput |
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u_delta |
Type: RealOutput |
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dataBus |
Type: DataBus |
Components (8)
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complexInteraction |
Type: ComplexInteraction |
|---|---|---|
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zeroRate |
Type: ConstantConverterRate Description: Zero rate input |
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fractionalGrowthRatePredator |
Type: Gain Description: Convert rate of delince to growth rate |
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couplingFactorForPrey |
Type: Gain Description: Convert rate of delince to growth rate |
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parAlpha |
Type: ConstantConverterRate Description: Constant alpha (optional) |
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parBeta |
Type: ConstantConverterRate Description: Constant beta (optional) |
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parGamma |
Type: ConstantConverterRate Description: Constant gamma (optional) |
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parDelta |
Type: ConstantConverterRate Description: Constant delta (optional) |
Used in Examples (1)
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BusinessSimulation.Examples Predator-prey dynamics |
Revisions
InputConnectordefined asencapsulated expandable connectorin v2.1.0.- Values for optional parameters changed to
unspecifiedin v2.1.0.