Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

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Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion. / Leonov, G. A.; Kuznetsov, N. V.; Mokaev, T. N.

In: European Physical Journal: Special Topics, Vol. 224, No. 8, 25.07.2015, p. 1421-1458.

Research output: Contribution to journal › Review article › peer-review

BibTeX

@article{9390db63f53a477a8e16e76c391e5f0a,

title = "Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion",

abstract = "In this paper, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky-Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.",

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

note = "Publisher Copyright: {\textcopyright} 2015, EDP Sciences and Springer.",

year = "2015",

month = jul,

day = "25",

doi = "10.1140/epjst/e2015-02470-3",

language = "English",

volume = "224",

pages = "1421--1458",

journal = "European Physical Journal: Special Topics",

issn = "1951-6355",

publisher = "Springer Nature",

number = "8",

}

RIS

TY - JOUR

T1 - Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

AU - Leonov, G. A.

AU - Kuznetsov, N. V.

AU - Mokaev, T. N.

PY - 2015/7/25

Y1 - 2015/7/25

N2 - In this paper, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky-Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.

AB - In this paper, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky-Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.

UR - http://www.scopus.com/inward/record.url?scp=84937868918&partnerID=8YFLogxK

U2 - 10.1140/epjst/e2015-02470-3

DO - 10.1140/epjst/e2015-02470-3

M3 - Review article

VL - 224

SP - 1421

EP - 1458

JO - European Physical Journal: Special Topics

JF - European Physical Journal: Special Topics

SN - 1951-6355

IS - 8

ER -

ID: 4005560