It is very easy to use Mathematica to make stream plots for differential equations.
Stream plots for a single equation
Consider the example
Points on a solution curve to this equation will take the form . Thus the slope will look like
.
Using the differential equation, we see that
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 ofvalues.
- The command
{y,-2,2}
gives the range ofvalues.
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 of the form
we can make a stream plot on the domain ,
using
StreamPlot[{f(x,y),g(x,y)},{x,a,b},{y,c,d}]
For example, the stream plot for the system
is generated using the code
StreamPlot[{x(1-x)+Sin[y], y^2+x/Exp[y]},{x,-2,2},{y,-3,3}]
The result is
Reblogged this on Mario A. G. Meza.