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

dx/dt = αx - βxy, dy/dt = δxy - γy

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

Ports

prey (Output)

Current population of the prey species.

predator (Output)

Current population of the predator species.

See Also

• LogisticGrowth: For population growth with carrying capacity.
• SIR: For disease transmission dynamics.
• Stock: The internal state of populations is modeled using Stocks.