It is very easy to use Mathematica to make stream plots for differential equations.
Stream plots for a single equation
Consider the example
$latex
frac{dy}{dt} = (y-y^3)cos{(t)}.
$
Points on a solution curve to this equation will take the form $latex (t,y(t))$. Thus the slope will look like
$latex (frac{d}{dt}[t],frac{d}{dt}[y(t)]) = (1,frac{dy}{dt})$.
Using the differential equation, we see that
$latex
left((1,frac{dy}{dt}right) = left(1, (y-y^3)cos{(t)}right).
$
Thus this is what we want to plot. The Mathematica code for this is the following:
StreamPlot[{1,(y-y^3) Cos[t]}, {t,0,5},{y,-2,2}]
The output is this:
Notice the following:
- The command
{1,(y-y^3) Cos[t]}gives the slope to be plotted at each point. - The command
{t,0,5}gives the range of $latex t$ values. - The command
{y,-2,2}gives the range of $latex y$ values.
Notice also that it is easy to see the equilibrium solutions on the picture – how cool is that!
Stream plots for systems
For a system…
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