English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Explicit computational formulas for coefficients of the periodic normal formsof the three most complex codim 2 bifurcations of limit cycles with dimensionof the center manifold equal to 4 or to 5 in generic autonomous ODEs arederived. The resulting formulas are independent of the dimension of the phasespace and involve solutions of certain boundary-value problems as well asmultilinear functions from the Taylor expansion of the ODE right-hand side nearthe cycle. The formulas allow one to distinguish between the complicatedbifurcation scenarios which can happen near these codim 2 bifurcations of limitcycles, where 3-tori and 4-tori can be present. We apply our techniques to thestudy of a known laser model, a novel model from population biology, and onefor mechanical vibrations; these models exhibit Limit Point--Neimark-Sacker,Period-Doubling--Neimark-Sacker and double Neimark-Sacker bifurcations.Lyapunov exponents are computed to numerically confirm the results of thenormal form analysis, in particular with respect to the existence of stableinvariant tori of various dimensions and chaos.

Numerical periodic normalization for codim 2 bifurcations of limit cycles with center manifold of dimension higher than 3