Routes to chaos in continuous mechanical systems. Part 3: The Lyapunov exponents, hyper, hyper-hyper and spatial-temporal chaos

J. Awrejcewicz, A. V. Krysko, I. V. Papkova, V. A. Krysko

Результат исследований: Материалы для журналаСтатьярецензирование

39 Цитирования (Scopus)

Аннотация

Third part of the paper is devoted to analysis of the hyper, hyper-hyper and spatial-temporal chaos of continuous mechanical systems using the Lyapunov exponents. The constructed algorithms for the Lyapunov exponents' computation allowed detecting and analysing novel phase transitions from chaos through hyper chaos to hyper-hyper chaos. In addition, a novel characteristic "maximal deflection versus excitation amplitude" has been introduced to study stability properties of the investigated continuous systems. It should be emphasized that the latter characteristic yields results in full agreements with those obtained via the Lyapunov exponents' spectrum estimation. The introduced methods and tools of analysis allowed detecting the Sharkovskii windows of periodicity in all continuous mechanical systems investigated in this paper. Finally, the approach to study the space-temporal chaos exhibited by shell structural-members is also proposed.

Язык оригиналаАнглийский
Страницы (с-по)721-736
Число страниц16
ЖурналChaos, Solitons and Fractals
Том45
Номер выпуска6
DOI
СостояниеОпубликовано - 1 июн 2012
Опубликовано для внешнего пользованияДа

ASJC Scopus subject areas

  • Mathematics(all)

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