Mathematics – Dynamical Systems
Scientific paper
2011-11-18
Mathematics
Dynamical Systems
90 pages, 32 figures
Scientific paper
Periodic normal forms for the codim 2 bifurcations of limit cycles up to a 3-dimensional center manifold in generic autonomous ODEs and computational formulas for their coefficients are derived. The formulas are independent of the dimension of the phase space and involve solutions of certain boundary-value problems on the interval [0, T ], where T is the period of the critical cycle, as well as multilinear functions from the Taylor expansion of the right-hand sides near the cycle. The formulas allow us to distinguish between various bifurcation scenarios near codim 2 bifurcations. Our formulation makes it possible to use robust numerical boundary-value algorithms based on orthogonal collocation, rather than shooting techniques, which greatly expands its applicability. The actual implementation is described in detail with numerical examples.
Govaerts Willy
Kuznetsov Yuri A.
Rossa Fabio Della
Witte Virginie de
No associations
LandOfFree
Numerical Periodic Normalization for Codim 2 Bifurcations of Limit Cycles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Numerical Periodic Normalization for Codim 2 Bifurcations of Limit Cycles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical Periodic Normalization for Codim 2 Bifurcations of Limit Cycles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-550009