Numerical Periodic Normalization for Codim 2 Bifurcations of Limit Cycles

Autor:	Della Rossa, Fabio, De Witte, Virginie, Govaerts, Willy, Kuznetsov, Yuri A.
Rok vydání:	2011
Předmět:	Mathematics - Dynamical Systems Mathematics - Classical Analysis and ODEs Mathematics - Numerical Analysis 34C20 37G15 37M20 65L07
Druh dokumentu:	Working Paper
Popis:	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. Comment: 90 pages, 32 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1111.4445 Zobrazit plný text záznamu View this record from Arxiv