Chaos control in the fractional order logistic map via impulses

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Chaos control in the fractional order logistic map via impulses. / Danca, Marius F.; Fečkan, Michal; Kuznetsov, Nikolay.

In: Nonlinear Dynamics, Vol. 98, No. 2, 01.10.2019, p. 1219-1230.

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

Author

Danca, Marius F. ; Fečkan, Michal ; Kuznetsov, Nikolay. / Chaos control in the fractional order logistic map via impulses. In: Nonlinear Dynamics. 2019 ; Vol. 98, No. 2. pp. 1219-1230.

BibTeX

@article{3342f907dc764c849f23c8976fd9be33,

title = "Chaos control in the fractional order logistic map via impulses",

abstract = "In this paper, the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta fractional difference.Every Δ steps, the state variable is instantly modified with the same impulse value, chosen from a bifurcation diagram versus impulse. It is shown that the solution of the impulsive control is bounded. The numerical results are verified via time series, histograms and the 0-1 test. Several examples are considered.",

keywords = "0-1 test, Caputo delta fractional difference, Discrete logistic map of fractional order, Impulsive chaos control, Lyapunov exponent of discrete maps of fractional order",

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

note = "Danca, M., Fe{\v c}kan, M. & Kuznetsov, N. Chaos control in the fractional order logistic map via impulses. Nonlinear Dyn 98, 1219–1230 (2019). https://doi.org/10.1007/s11071-019-05257-2",

year = "2019",

month = oct,

day = "1",

doi = "10.1007/s11071-019-05257-2",

language = "English",

volume = "98",

pages = "1219--1230",

journal = "Nonlinear Dynamics",

issn = "0924-090X",

publisher = "Springer Nature",

number = "2",

}

RIS

TY - JOUR

T1 - Chaos control in the fractional order logistic map via impulses

AU - Danca, Marius F.

AU - Fečkan, Michal

AU - Kuznetsov, Nikolay

N1 - Danca, M., Fečkan, M. & Kuznetsov, N. Chaos control in the fractional order logistic map via impulses. Nonlinear Dyn 98, 1219–1230 (2019). https://doi.org/10.1007/s11071-019-05257-2

PY - 2019/10/1

Y1 - 2019/10/1

N2 - In this paper, the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta fractional difference.Every Δ steps, the state variable is instantly modified with the same impulse value, chosen from a bifurcation diagram versus impulse. It is shown that the solution of the impulsive control is bounded. The numerical results are verified via time series, histograms and the 0-1 test. Several examples are considered.

AB - In this paper, the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta fractional difference.Every Δ steps, the state variable is instantly modified with the same impulse value, chosen from a bifurcation diagram versus impulse. It is shown that the solution of the impulsive control is bounded. The numerical results are verified via time series, histograms and the 0-1 test. Several examples are considered.

KW - 0-1 test

KW - Caputo delta fractional difference

KW - Discrete logistic map of fractional order

KW - Impulsive chaos control

KW - Lyapunov exponent of discrete maps of fractional order

UR - http://www.scopus.com/inward/record.url?scp=85073683951&partnerID=8YFLogxK

U2 - 10.1007/s11071-019-05257-2

DO - 10.1007/s11071-019-05257-2

M3 - Article

AN - SCOPUS:85073683951

VL - 98

SP - 1219

EP - 1230

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 2

ER -

ID: 52006258