Hidden Oscillations in Dynamical Systems. 16 Hilbert’s Problem, Aizerman’s and Kalman’s Conjectures, Hidden Attractors in Chua’s Circuits

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Hidden Oscillations in Dynamical Systems. 16 Hilbert’s Problem, Aizerman’s and Kalman’s Conjectures, Hidden Attractors in Chua’s Circuits. / Leonov, G. A.; Kuznetsov, N. V.

In: Journal of Mathematical Sciences, Vol. 201, No. 5, 01.09.2014, p. 645-662.

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

BibTeX

@article{e09eb4b64e39465cafc489921c1dc728,

title = "Hidden Oscillations in Dynamical Systems. 16 Hilbert{\textquoteright}s Problem, Aizerman{\textquoteright}s and Kalman{\textquoteright}s Conjectures, Hidden Attractors in Chua{\textquoteright}s Circuits",

abstract = "The present survey is devoted to efficient methods for localization of hidden oscillations in dynamical systems. Their application to Hilbert{\textquoteright}s sixteenth problem for quadratic systems, Aizerman{\textquoteright}s problem, and Kalman{\textquoteright}s problem on absolute stability of control systems, and to the localization of chaotic hidden attractors (the basin of attraction of which does not contain neighborhoods of equilibria) is considered. The synthesis of the describing function method with the applied bifurcation theory and numerical methods for computing hidden oscillations is described.",

author = "Leonov, {G. A.} and Kuznetsov, {N. V.}",

note = "Publisher Copyright: {\textcopyright} 2014, Springer Science+Business Media New York.",

year = "2014",

month = sep,

day = "1",

doi = "10.1007/s10958-014-2017-6",

language = "English",

volume = "201",

pages = "645--662",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Hidden Oscillations in Dynamical Systems. 16 Hilbert’s Problem, Aizerman’s and Kalman’s Conjectures, Hidden Attractors in Chua’s Circuits

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

PY - 2014/9/1

Y1 - 2014/9/1

N2 - The present survey is devoted to efficient methods for localization of hidden oscillations in dynamical systems. Their application to Hilbert’s sixteenth problem for quadratic systems, Aizerman’s problem, and Kalman’s problem on absolute stability of control systems, and to the localization of chaotic hidden attractors (the basin of attraction of which does not contain neighborhoods of equilibria) is considered. The synthesis of the describing function method with the applied bifurcation theory and numerical methods for computing hidden oscillations is described.

AB - The present survey is devoted to efficient methods for localization of hidden oscillations in dynamical systems. Their application to Hilbert’s sixteenth problem for quadratic systems, Aizerman’s problem, and Kalman’s problem on absolute stability of control systems, and to the localization of chaotic hidden attractors (the basin of attraction of which does not contain neighborhoods of equilibria) is considered. The synthesis of the describing function method with the applied bifurcation theory and numerical methods for computing hidden oscillations is described.

UR - http://www.scopus.com/inward/record.url?scp=85027925604&partnerID=8YFLogxK

U2 - 10.1007/s10958-014-2017-6

DO - 10.1007/s10958-014-2017-6

M3 - Article

VL - 201

SP - 645

EP - 662

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -

ID: 7030357