System Dynamics

PredatorPrey Block

The Lotka-Volterra equations describing the dynamics of biological systems in which two species interact.

Description

The Predator-Prey model (also known as the Lotka-Volterra equations) describes the interaction between two species in an ecosystem: one is the predator and the other is the prey. It is a fundamental model in population biology that demonstrates natural oscillations.

Mathematical Model

\begin{aligned} \frac{dx}{dt} &= \alpha x - \beta xy \\ \frac{dy}{dt} &= \delta xy - \gamma y \end{aligned}

The model is defined by two coupled first-order nonlinear differential equations:

$$\frac{dx}{dt} = \alpha x - \beta xy$$ $$\frac{dy}{dt} = \delta xy - \gamma y$$

Where:

$x$: Population of prey (e.g., rabbits)
$y$: Population of predators (e.g., foxes)
$\alpha$: Prey birth rate
$\beta$: Rate at which predators eat prey
$\delta$: Predator growth rate per prey eaten
$\gamma$: Predator death rate

Parameters

alpha ($\alpha$)

The birth rate of the prey.

Default: 1.1

beta ($\beta$)

The rate at which predators encounter and consume prey.

Default: 0.4

delta ($\delta$)

How efficiently predator consumption translates into new predators.

Default: 0.1

gamma ($\gamma$)

The natural death rate of the predators.

Default: 0.4

initial_prey

Type: number (Default: 10)

Initial Prey parameter description placeholder.

initial_predator

Type: number (Default: 5)

Initial Predator parameter description placeholder.

Ports

prey (Output)

Current population of the prey species.

predator (Output)

Current population of the predator species.

Examples

Zie de ingebouwde voorbeelden in de handleiding voor een demonstratie van dit blok.

Remarks

Configuratie: Configureer dit blok via de parameters in het paneel.