Fractional-order PWC systems without zero Lyapunov exponents

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1061-1078
Journal / PublicationNonlinear Dynamics
Volume92
Issue number3
Online published8 Feb 2018
Publication statusPublished - May 2018

Abstract

In this paper, it is shown numerically that a class of fractional-order piece-wise continuous systems, which depend on a single real bifurcation parameter, have no zero Lyapunov exponents but can be chaotic or hyperchaotic with hidden attractors. Although not analytically proved, this conjecture is verified on several systems including a fractional-order piece-wise continuous hyperchaotic system, a piece-wise continuous chaotic Chen system, a piece-wise continuous variant of the chaotic Shimizu-Morioka system and a piece-wise continuous chaotic Sprott system. These systems are continuously approximated based on results of differential inclusions and selection theory, and numerically integrated with the Adams-Bashforth-Moulton method for fractional-order differential equations. It is believed that the obtained results are valid for many, if not most, fractional-order PWC systems.

Research Area(s)

  • Chaotic system, Continuous approximation, Fractional-order piece-wise continuous system, Hyperchaotic system, Lyapunov exponent

Citation Format(s)

Fractional-order PWC systems without zero Lyapunov exponents. / Danca, Marius-F.; Fečkan, Michal; Kuznetsov, Nikolay V. et al.

In: Nonlinear Dynamics, Vol. 92, No. 3, 05.2018, p. 1061-1078.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review