Phase Portrait - Autonomous Systems - Maple Help

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Phase Portraits for Autonomous Systems


Plot an autonomous system of two ODEs, including the direction field, critical point(s), and phase portraits as desired.



To begin, enter the necessary information into the fields below:


  the bounds for the plot window


  Fx,y and Gx,y, the right-hand sides of the autonomous ODEs x.=Fx,y and y.=Gx,y


  one equilibrium (critical) point as a list a,b, and multiple such points in a sequence a,b,c,d


  bounds for t, the independent variable of the ODEs, and hence, the parameter along orbits (trajectories or paths)


Click the Enter Data button to obtain a direction field and all entered equilibrium (critical) points.


Click on the plot area and select the Click and Drag Manipulator ( ) from the Plot menu or plotting toolbar.  Then click anywhere in the direction field to create a phase portrait through that point.


The Erase Phase Portrait button erases all orbits and field arrows.  The Clear All button clears every field in the template.


Phase Portraits for Autonomous Systems

Plot Window


x,     y


Differential Equations


x.=Fx,y =

y.=Gx,y =


Equilibrium (Critical) Points






Commands Used

DEplot, dsolve[numeric], odeplot

See Also

dsolve[interactive], fsolve, ODE Analyzer Assistant, solve