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



Here, represents the number of prey and 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 and 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.


Click on the image to start the applet.

Applet ‘Lotka-Volterra’.

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Page last modified on October 21, 2009, at 06:37 PM