Search results for "Lyapunov quantities"

showing 2 items of 2 documents

Lyapunov quantities and limit cycles in two-dimensional dynamical systems : analytical methods, symbolic computation and visualization

2011

mallintaminenLienard systemhidden oscillationslimit cyclesLyapunov exponentsdynamical systemssymbolic computationLyapunov quantitiesPoincare-Lyapunov constantscomputer visualizationtwo-dimensional dynamical systemsKolmogorov's problemmatemaattiset mallittietojenkäsittely
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Cycles in continuous and discrete dynamical systems : computations, computer-assisted proofs, and computer experiments

2009

The present work is devoted to calculation of periodic solutions and bifurcation research in quadratic systems, Lienard system, and non-unimodal one-dimensional discrete maps using modern computational capabilities and symbolic computing packages.In the first chapter the problem of Academician A.N. Kolmogorov on localization and modeling of cycles of quadratic systems is considered. For the investigation of small limit cycles (so-called local 16th Hilbert’s problem) the method of calculation of Lyapunov quantities (or Poincaré-Lyapunov constants) is used. To calculate symbolic expressions for the Lyapunov quantities the Lyapunov method to the case of non-analytical systems was generalized. …

Lyapunov quantitiesmallintaminenLienard systemPLLlimit cyclessymbolinen laskentabifurcationdynaamiset järjestelmätKolmogorov's problemdynamical systemsmatemaattiset mallitphase locked loopstietojenkäsittely
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