Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems

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Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems. / Leonov, G. A.; Mokaev, R. N.; Kuznetsov, N. V.; Mokaev, T. N.

In: International Journal of Bifurcation and Chaos, Vol. 30, No. 8, 2050124, 30.06.2020.

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

BibTeX

@article{a2c9bbf9c8f34d219088ed380065725e,

title = "Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems",

abstract = "In this article using an analytical method called Fishing principle we obtain the region of parameters, where the existence of a homoclinic orbit to a zero saddle equilibrium in the Lorenz-like system is proved. For a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the obtained region of parameters is organized, which leads to the discovery of new bifurcation scenarios.",

keywords = "homoclinic bifurcation, homoclinic orbit, Lorenz attractor, Lorenz system, Lorenz-like system, strange attractor, EXISTENCE, TRAJECTORIES, CASCADE, LYAPUNOV DIMENSION, SHIMIZU-MORIOKA, CHEN, HIDDEN ATTRACTOR, ORBITS, STRANGE ATTRACTOR, BIRTH",

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

note = "Funding Information: This work was supported by the Russian Science Foundation (project 19-41-02002). We dedicate this work to the memory of our scientific father — Gen-nady A. Leonov, with whom we had started it in 2018 and finished after his sudden passing away [Kuznetsov et al., 2018b]. Publisher Copyright: {\textcopyright} 2020 World Scientific Publishing Company. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = jun,

day = "30",

doi = "10.1142/S0218127420501242",

language = "English",

volume = "30",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

number = "8",

}

RIS

TY - JOUR

T1 - Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems

AU - Leonov, G. A.

AU - Mokaev, R. N.

AU - Kuznetsov, N. V.

AU - Mokaev, T. N.

N1 - Funding Information: This work was supported by the Russian Science Foundation (project 19-41-02002). We dedicate this work to the memory of our scientific father — Gen-nady A. Leonov, with whom we had started it in 2018 and finished after his sudden passing away [Kuznetsov et al., 2018b]. Publisher Copyright: © 2020 World Scientific Publishing Company. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/6/30

Y1 - 2020/6/30

N2 - In this article using an analytical method called Fishing principle we obtain the region of parameters, where the existence of a homoclinic orbit to a zero saddle equilibrium in the Lorenz-like system is proved. For a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the obtained region of parameters is organized, which leads to the discovery of new bifurcation scenarios.

AB - In this article using an analytical method called Fishing principle we obtain the region of parameters, where the existence of a homoclinic orbit to a zero saddle equilibrium in the Lorenz-like system is proved. For a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the obtained region of parameters is organized, which leads to the discovery of new bifurcation scenarios.

KW - homoclinic bifurcation

KW - homoclinic orbit

KW - Lorenz attractor

KW - Lorenz system

KW - Lorenz-like system

KW - strange attractor

KW - EXISTENCE

KW - TRAJECTORIES

KW - CASCADE

KW - LYAPUNOV DIMENSION

KW - SHIMIZU-MORIOKA

KW - CHEN

KW - HIDDEN ATTRACTOR

KW - ORBITS

KW - STRANGE ATTRACTOR

KW - BIRTH

UR - http://www.scopus.com/inward/record.url?scp=85089291749&partnerID=8YFLogxK

U2 - 10.1142/S0218127420501242

DO - 10.1142/S0218127420501242

M3 - Article

AN - SCOPUS:85089291749

VL - 30

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 8

M1 - 2050124

ER -

ID: 71009550