summary:

This applet is an extension of the applet ODE 2D. In addition to the capability of drawing vector fields and solving initial value problems you can compute limit cycles of planar vector fields.

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theory

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help

drawing vector fields, initial value problems

Since this applet is an extension of the applet ODE 2D, you can find information on how to define a vector field, draw orbits and solve initial value problems here.

computing of limit cycles

In addition to the capabilities of the applet ODE 2D this applet allows the computation of limit cycles of planar vector fields. Exploring a vector field you may encounter a limit cycle. To compute this limit cycle accurately you have to switch to the tab Limit cycle. In the fields Period guess and Point guess you enter a guess for the period and a guess for a point of the limit cycle, respectively. Pressing Compute starts the computation. Success or failure of the computation is indicated in the label at the bottom of the applet. For more information, especially to see the intermediate steps of the computation, check the tab Output. If the computation succeeds, you can find there moreover the Floquet multipliers of the limit cycle. In the picture below you see a computed limit cycle of the Brusselator equation

x'=1+x(x*y-4)
y'=x*(3-x*y)

and the corresponding output in the tab Output.

screenshot

questions and comments

If you have any questions or comments or want to report a bug, please feel free to contact us.

Markus Unterweger, last modified: 05. January 2004