xmapleworksheet , or the postscript version.
The eigenvalues are:
at (0,0,0,0), the following stability can be found:
xrkwas used, along with
xmaple, to discover the model's behavior. A bifurcation diagram is necessary to find the behavior of the point (0,0,0,0) for = 0 and c1 = 0. Please see the
xmapleworksheet or the postscript version of the main work for this results section. Additional work is on the graphics page. Warning! Lots of large graphics! May take a while to load!
x" = -ax' -bx
(where the right hand side of the equation is the sum of two forces: the restoring force bx and the linear frictional force ax'), except that the frictional term is nonlinear in the van der Pol model. The van der Pol equation is
x" + ( + x2)*x' + x = 0
where is constant.
The behavior of the x-y system (when plotted), with positive c1 and , acts much like the van der Pol forced oscillation model with < 0. (see case on graphics page)
xmaple worksheet on the van der
Pol oscillator, and the postscript version
Michelle Vadeboncoeur <email@example.com>