Phase Portraits for Autonomous Systems - Maple Programming Help

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
 – $F\left(x,y\right)$ and $G\left(x,y\right)$, the right-hand sides of the autonomous ODEs $\stackrel{.}{x}=F\left(x,y\right)$ and $\stackrel{.}{y}=G\left(x,y\right)$
 – one equilibrium (critical) point as a list $\left[a,b\right]$, and multiple such points in a sequence $\left[a,b\right],\left[c,d\right]$
 – 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   $\le x\le$,     $\le y\le$   Differential Equations   $\stackrel{.}{x}=F\left(x,y\right)$ = $\stackrel{.}{y}=G\left(x,y\right)$ =   Equilibrium (Critical) Points     Parameter        $\le t\le$                      

 Commands Used