Existence of homoclinic orbits and heteroclinic cycle in a class of three-dimensional piecewise linear systems with three switching manifolds

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Existence of homoclinic orbits and heteroclinic cycle in a class of three-dimensional piecewise linear systems with three switching manifolds. / Zhu, Bin; Wei, Zhouchao; Escalante-González, R. J.; Kuznetsov, Nikolay V.

In: Chaos, Vol. 30, No. 12, 123143, 01.12.2020.

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

BibTeX

@article{638f051635e24c028bb70434499d61ca,

title = "Existence of homoclinic orbits and heteroclinic cycle in a class of three-dimensional piecewise linear systems with three switching manifolds",

abstract = "In this article, we construct a kind of three-dimensional piecewise linear (PWL) system with three switching manifolds and obtain four theorems with regard to the existence of a homoclinic orbit and a heteroclinic cycle in this class of PWL system. The first theorem studies the existence of a heteroclinic cycle connecting two saddle-foci. The existence of a homoclinic orbit connecting one saddle-focus is investigated in the second theorem, and the third theorem examines the existence of a homoclinic orbit connecting another saddle-focus. The last one proves the coexistence of the heteroclinic cycle and two homoclinic orbits for the same parameters. Numerical simulations are given as examples and the results are consistent with the predictions of theorems. ",

author = "Bin Zhu and Zhouchao Wei and Escalante-Gonz{\'a}lez, {R. J.} and Kuznetsov, {Nikolay V.}",

note = "Publisher Copyright: {\textcopyright} 2020 Author(s).",

year = "2020",

month = dec,

day = "1",

doi = "10.1063/5.0032702",

language = "English",

volume = "30",

journal = "Chaos",

issn = "1054-1500",

publisher = "American Institute of Physics",

number = "12",

}

RIS

TY - JOUR

T1 - Existence of homoclinic orbits and heteroclinic cycle in a class of three-dimensional piecewise linear systems with three switching manifolds

AU - Zhu, Bin

AU - Wei, Zhouchao

AU - Escalante-González, R. J.

AU - Kuznetsov, Nikolay V.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - In this article, we construct a kind of three-dimensional piecewise linear (PWL) system with three switching manifolds and obtain four theorems with regard to the existence of a homoclinic orbit and a heteroclinic cycle in this class of PWL system. The first theorem studies the existence of a heteroclinic cycle connecting two saddle-foci. The existence of a homoclinic orbit connecting one saddle-focus is investigated in the second theorem, and the third theorem examines the existence of a homoclinic orbit connecting another saddle-focus. The last one proves the coexistence of the heteroclinic cycle and two homoclinic orbits for the same parameters. Numerical simulations are given as examples and the results are consistent with the predictions of theorems.

AB - In this article, we construct a kind of three-dimensional piecewise linear (PWL) system with three switching manifolds and obtain four theorems with regard to the existence of a homoclinic orbit and a heteroclinic cycle in this class of PWL system. The first theorem studies the existence of a heteroclinic cycle connecting two saddle-foci. The existence of a homoclinic orbit connecting one saddle-focus is investigated in the second theorem, and the third theorem examines the existence of a homoclinic orbit connecting another saddle-focus. The last one proves the coexistence of the heteroclinic cycle and two homoclinic orbits for the same parameters. Numerical simulations are given as examples and the results are consistent with the predictions of theorems.

UR - http://www.scopus.com/inward/record.url?scp=85099260365&partnerID=8YFLogxK

U2 - 10.1063/5.0032702

DO - 10.1063/5.0032702

M3 - Article

C2 - 33380050

AN - SCOPUS:85099260365

VL - 30

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 12

M1 - 123143

ER -

ID: 85433890