Fractional-order PWC systems without zero Lyapunov exponents

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

In: Nonlinear Dynamics, Vol. 92, No. 3, 01.05.2018, p. 1061-1078.

Research output: Contribution to journal › Article › peer-review

Author

Danca, Marius F. ; Fečkan, Michal ; Kuznetsov, Nikolay V. ; Chen, Guanrong. / Fractional-order PWC systems without zero Lyapunov exponents. In: Nonlinear Dynamics. 2018 ; Vol. 92, No. 3. pp. 1061-1078.

BibTeX

@article{9c05b2e03a2146b89ccf5095c58962f8,

title = "Fractional-order PWC systems without zero Lyapunov exponents",

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.",

keywords = "Chaotic system, Continuous approximation, Fractional-order piece-wise continuous system, Hyperchaotic system, Lyapunov exponent",

author = "Danca, {Marius F.} and Michal Fe{\v c}kan and Kuznetsov, {Nikolay V.} and Guanrong Chen",

year = "2018",

month = may,

day = "1",

doi = "10.1007/s11071-018-4108-2",

language = "English",

volume = "92",

pages = "1061--1078",

journal = "Nonlinear Dynamics",

issn = "0924-090X",

publisher = "Springer Nature",

number = "3",

}

RIS

TY - JOUR

T1 - Fractional-order PWC systems without zero Lyapunov exponents

AU - Danca, Marius F.

AU - Fečkan, Michal

AU - Kuznetsov, Nikolay V.

AU - Chen, Guanrong

PY - 2018/5/1

Y1 - 2018/5/1

N2 - 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.

AB - 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.

KW - Chaotic system

KW - Continuous approximation

KW - Fractional-order piece-wise continuous system

KW - Hyperchaotic system

KW - Lyapunov exponent

UR - http://www.scopus.com/inward/record.url?scp=85041494019&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/fractionalorder-pwc-systems-without-zero-lyapunov-exponents

U2 - 10.1007/s11071-018-4108-2

DO - 10.1007/s11071-018-4108-2

M3 - Article

AN - SCOPUS:85041494019

VL - 92

SP - 1061

EP - 1078

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 3

ER -

ID: 35268554