Special Cubic Perturbations of the Duffing Oscillator x′ ′= x- x3 Near the Eight-Loop

Lubomir Gavrilov; Ameni Gargouri; Bassem Ben Hamed

doi:10.1007/s00009-021-01868-5

Special Cubic Perturbations of the Duffing Oscillator x^{′ ′}= x- x³ Near the Eight-Loop

Lubomir Gavrilov
, Ameni Gargouri
, Bassem Ben Hamed

Mathematics

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

1 Scopus citations

Abstract

We find an upper bound for the number of limit cycles, bifurcating from the eight-loop of the Duffing oscillator x^{′ ′}= x- x³ under the special cubic perturbation x′′=x-x3+λ1y+λ2x2+λ3xy+λ4x2y.

Original language	English
Article number	229
Journal	Mediterranean Journal of Mathematics
Volume	18
Issue number	6
DOIs	https://doi.org/10.1007/s00009-021-01868-5
State	Published - Dec 2021

Keywords

Duffing oscillator
Limit cycles
Melnikov functions

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10.1007/s00009-021-01868-5

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title = "Special Cubic Perturbations of the Duffing Oscillator x′ ′= x- x3 Near the Eight-Loop",

abstract = "We find an upper bound for the number of limit cycles, bifurcating from the eight-loop of the Duffing oscillator x′ ′= x- x3 under the special cubic perturbation x′′=x-x3+λ1y+λ2x2+λ3xy+λ4x2y.",

keywords = "Duffing oscillator, Limit cycles, Melnikov functions",

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

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AU - Gargouri, Ameni

AU - Hamed, Bassem Ben

PY - 2021/12

Y1 - 2021/12

N2 - We find an upper bound for the number of limit cycles, bifurcating from the eight-loop of the Duffing oscillator x′ ′= x- x3 under the special cubic perturbation x′′=x-x3+λ1y+λ2x2+λ3xy+λ4x2y.

AB - We find an upper bound for the number of limit cycles, bifurcating from the eight-loop of the Duffing oscillator x′ ′= x- x3 under the special cubic perturbation x′′=x-x3+λ1y+λ2x2+λ3xy+λ4x2y.

KW - Duffing oscillator

KW - Limit cycles

KW - Melnikov functions

UR - https://www.scopus.com/pages/publications/85115075055

U2 - 10.1007/s00009-021-01868-5

DO - 10.1007/s00009-021-01868-5

M3 - Article

AN - SCOPUS:85115075055

SN - 1660-5446

VL - 18

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

IS - 6

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ER -

Special Cubic Perturbations of the Duffing Oscillator x^{′ ′}= x- x³ Near the Eight-Loop

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Keywords

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