Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain

Bassem Ben Hamed; Ameni Gargouri; Lubomir Gavrilov

doi:10.1016/j.bulsci.2019.102796

Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain

Bassem Ben Hamed
, Ameni Gargouri
, Lubomir Gavrilov

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

1 Scopus citations

Abstract

We consider arbitrary one-parameter cubic deformations of the Duffing oscillator x^″=x−x³. In the case when the first Melnikov function M₁ vanishes, but M₂≠0 we compute the general form of M₂ and study its zeros in a suitable complex domain.

Original language	English
Article number	102796
Journal	Bulletin des Sciences Mathematiques
Volume	157
DOIs	https://doi.org/10.1016/j.bulsci.2019.102796
State	Published - Dec 2019
Externally published	Yes

Keywords

Duffing oscillator
Limit cycles
Zeros of elliptic integrals

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10.1016/j.bulsci.2019.102796

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title = "Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain",

abstract = "We consider arbitrary one-parameter cubic deformations of the Duffing oscillator x″=x−x3. In the case when the first Melnikov function M1 vanishes, but M2≠0 we compute the general form of M2 and study its zeros in a suitable complex domain.",

keywords = "Duffing oscillator, Limit cycles, Zeros of elliptic integrals",

author = "Hamed, \{Bassem Ben\} and Ameni Gargouri and Lubomir Gavrilov",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Masson SAS",

year = "2019",

month = dec,

doi = "10.1016/j.bulsci.2019.102796",

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T1 - Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain

AU - Hamed, Bassem Ben

AU - Gargouri, Ameni

AU - Gavrilov, Lubomir

PY - 2019/12

Y1 - 2019/12

N2 - We consider arbitrary one-parameter cubic deformations of the Duffing oscillator x″=x−x3. In the case when the first Melnikov function M1 vanishes, but M2≠0 we compute the general form of M2 and study its zeros in a suitable complex domain.

AB - We consider arbitrary one-parameter cubic deformations of the Duffing oscillator x″=x−x3. In the case when the first Melnikov function M1 vanishes, but M2≠0 we compute the general form of M2 and study its zeros in a suitable complex domain.

KW - Duffing oscillator

KW - Limit cycles

KW - Zeros of elliptic integrals

UR - https://www.scopus.com/pages/publications/85072740798

U2 - 10.1016/j.bulsci.2019.102796

DO - 10.1016/j.bulsci.2019.102796

M3 - Article

AN - SCOPUS:85072740798

SN - 0007-4497

VL - 157

JO - Bulletin des Sciences Mathematiques

JF - Bulletin des Sciences Mathematiques

M1 - 102796

ER -

Cubic perturbations of symmetric elliptic Hamiltonians of degree four in a complex domain

Abstract

Keywords

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