Visualizing a Continuous Model of Mutualism 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 for two species who benefit mutualistically from each other. The equations are of the form:

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

The user inputs positive values of the parameters a, b, c, d, α_{1}, and α_{2}. Also, grid 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.

a =

b =

c =

d =

α_{1} =

α_{2} =

M (0) =

N (0) =

0 ≤ t ≤

≤ M ≤

≤ N ≤

References:

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