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ExamplesLotkaVolterra

Lotka-Volterra predator-prey model
ODEs are frequently used in biology to model population dynamics. The famous Lotka-Volterra model describes the evolution of two species, one of which preys (feeds) on the other, using the ODEs:

\dot{x}_1 = a x_1 - b x_1 x_2
\dot{x}_2 = c x_1 x_2 - d x_2.

Here, x_1 represents the number of prey and x_2 is the number of predators (in appropriate units so that they take continuous values in the interval [0,1]), and a, b, c, and d are parameters. The terms a x_1 and -d x_2 account for the reproduction rate of each species in the absence of interaction with the other and the nonlinear terms represent the effects of predation on the reduction of preys and the reproduction of the predators.
The simulation plots 10 sample trajectories in phase-space, which start from different initial conditions, for the same values of the parameters.

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Última modificación de la página el 21 June 2008 a las 12h48