Lotka-Voltera Model for Predator-Prey Interactions

The Lotka-Voltera model is a mathematical model that describe the interaction between two animal species, such as foxes and rabbits, one of which preys upon the other. The Lotke-Volterra model consists of the two differential equations shown below. The variables X and Y correspond to the densities of the prey and predator populations, respectively.

dX/dt = rX - aXY

dY/dt = bXY - mY

The model also contains the following parameters:

• r = intrinsic rate of increase of the prey population
• a = predation rate coefficient
• b = reproduction rate of predators per one prey eaten
• m = predator mortality rate

To graph solutions to the Lotke-Volterra model, enter values for the parameters and initial values for X and Y in the boxes below. Then click Graph solutions.

r: a: b: m: Initial value for X: Initial value for Y: Maximum time value for solutions:

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