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- W4300796925 abstract "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." @default.
- W4300796925 created "2022-10-04" @default.
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- W4300796925 date "2011-11-18" @default.
- W4300796925 modified "2023-09-30" @default.
- W4300796925 title "Numerical Periodic Normalization for Codim 2 Bifurcations of Limit Cycles" @default.
- W4300796925 doi "https://doi.org/10.48550/arxiv.1111.4445" @default.
- W4300796925 hasPublicationYear "2011" @default.
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