Chaos in a fractional order modified Duffing system

In this paper, the chaotic behaviors in a fractional order modified Duffing system are studied numerically by phase portraits, Poincaré maps and bifurcation diagrams. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in (0, 1], b...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2007-10, Vol.34 (2), p.262-291
Main Authors: Ge, Zheng-Ming, Ou, Chan-Yi
Format: Article
Language:English
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Summary:In this paper, the chaotic behaviors in a fractional order modified Duffing system are studied numerically by phase portraits, Poincaré maps and bifurcation diagrams. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in (0, 1], based on frequency domain arguments. The total system orders found for chaos to exist in such systems are 1.8, 1.9, 2.0 and 2.1.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2005.11.059