Visualizing a Continuous Competing Species Model by Mike Martin

On this page, plots of direction fields and solution curves are generated for the phase plane associated with a system of two 1^{st}-order autonomous ordinary differential equations. Plots of the solution curves as functions of time are given below the phase plane, too. This page focuses on a particular form of differential equations which are most often used to model the population numbers of two competing species. The equations are of the form:

M(0) = M_{0} N(0) = N_{0}

The user inputs positive values of the parameters r_{1}, r_{2}, K_{1}, K_{2}, α_{12}, and α_{21}. Also, gird bounds, time bounds, and the initial conditions must be specified.

Enter in the value of the parameters and select the plotting bounds, then press the "Plot/Evaluate" button.

r_{1} =

r_{2} =

K_{1} =

K_{2} =

α_{12} =

α_{21} =

M (0) =

N (0) =

0 ≤ t ≤

≤ M ≤

≤ N ≤

References:

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