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Cafagna, Donato; Grassi, Giuseppe

Bifurcation and chaos in the fractional-order Chen system via a time-domain approach. (English) Zbl 1158.34300

Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 7, 1845-1863 (2008).
Summary: This tutorial investigates bifurcation and chaos in the fractional-order Chen system from the time-domain point of view. The objective is achieved using the Adomian decomposition method, which allows the solution of the fractional differential equations to be written in closed form. By taking advantage of the capabilities given by the decomposition method, the paper illustrates two remarkable findings: (i) chaos exists in the fractional Chen system with order as low as 0.24, which represents the smallest value ever reported in literature for any chaotic system studied so far; (ii) it is feasible to show the occurrence of pitchfork bifurcations and period-doubling routes to chaos in the fractional Chen system, by virtue of a systematic time-domain analysis of its dynamics.

Cited in 27 Documents

MSC:

34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
37Gxx Local and nonlocal bifurcation theory for dynamical systems
26A33 Fractional derivatives and integrals

Keywords:

fractional calculus; Chen system; chaotic dynamics; bifurcation analysis; test for chaos

Software:

Sprott's Software
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\textit{D. Cafagna} and \textit{G. Grassi}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 18, No. 7, 1845--1863 (2008; Zbl 1158.34300)
Full Text: DOI

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