Phase Portraits for Autonomous Systems - Maple Help

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Phase Portraits for Autonomous Systems

Description

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

Instructions

• 

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

 

 

Parameter 

      t                      

                   

Commands Used

DEplot, dsolve[numeric], odeplot

See Also

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

 


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