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Title: Chaotic vibrations of the duffing system with fractional damping

We examined the Duffing system with a fractional damping term. Calculating the basins of attraction, we demonstrate a broad spectrum of non-linear behaviour connected with sensitivity to the initial conditions and chaos. To quantify dynamical response of the system, we propose the statistical 0-1 test as well as the maximal Lyapunov exponent; the application of the latter encounter a few difficulties because of the memory effect due to the fractional derivative. The results are confirmed by bifurcation diagrams, phase portraits, and Poincaré sections.
Authors:
;  [1] ;  [2] ;  [3]
  1. Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, PL-20-618 Lublin (Poland)
  2. Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, 60131 Ancona (Italy)
  3. Institut für Festkörpermechanik, Technische Universität Dresden, 01062 Dresden (Germany)
Publication Date:
OSTI Identifier:
22251663
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; DAMPING; DIAGRAMS; LYAPUNOV METHOD; NONLINEAR PROBLEMS