I am working with a 3D continuous dynamical system. I have plotted the bifurcation diagram and found that period-doubling bifurcation occurs at a certain parameter value. However, I also want to prove it analytically but haven't found any analytical method to do so. Is there any analytical method to prove the existence of period-doubling bifurcation of a 3D continuous system?
$\begingroup$
$\endgroup$
1
-
1$\begingroup$ I took out the [periods] tag, since that usually refers to en.wikipedia.org/wiki/Period_(algebraic_geometry) $\endgroup$– David Roberts ♦Commented Mar 14 at 6:29
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
It would be quite hard to give a purely analytical proof for continuous systems, since period doubling analysis (which is typically via Lyapunov-Schmidt bifurcation theory) will need to be carried on the the Poincare (discrete-time) map of the continuous system, and getting a good analytical handle on Poincare Maps is hard. The closest I could find was:
Period doubling in the Rössler system—a computer assisted proof D Wilczak, P Zgliczyński - Foundations of Computational Mathematics, 2009.
As the title says, its not 100% analytical but it is rigorous.
answered Mar 15 at 17:37