Qualitative Analysis

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The key is to find the Jacobian matrix for the vector field in this differential equation. We probably could extract the functions F and G directly from the right-hand sides of the differential equations, but it's not difficult to retype the functions at this point.

> F := x*(10-x-y);

> G := y*(20-4*x-y);

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The jacobian command, from the linalg package, can be used to have Maple determine the Jacobian matrix for a vector field.

> J := jacobian( [F,G], [x,y] );

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The analysis of each equilibrium point begins by zooming in on the direction field in the vicinity of an equilibrium solution. This can be achieved by simply changing the range of and values that are displayed by DEplot .

Equilibrium Point #1:

Equilibrium Point #2:

Equilibrium Point #3:

Equilibrium Point #4: