Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis

Si Mohamed Sah; Bernold Fiedler; B. Shayak; Richard H. Rand

doi:10.1007/s11071-020-06012-8

Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis

Si Mohamed Sah^*
, Bernold Fiedler
, B. Shayak
, Richard H. Rand

^*Corresponding author for this work

Free University of Berlin
Cornell University

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

Abstract

The delayed Duffing equation x¨(t)+x(t−T)+x3(t)=0 is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions, for fixed delays such that T2<32π2. In contrast to several previous works which involved approximate solutions, the treatment here is exact.

Original language	English
Journal	Nonlinear Dynamics
Volume	103
Pages (from-to)	503–515
ISSN	0924-090X
DOIs	https://doi.org/10.1007/s11071-020-06012-8
Publication status	Published - 2021

Keywords

Delayed Duffing oscillator
Limit cycle
Exact analysis
Jacobi elliptic function

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10.1007/s11071-020-06012-8

https://arxiv.org/pdf/1908.06533

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title = "Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis",

abstract = "The delayed Duffing equation x¨(t)+x(t−T)+x3(t)=0 is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions, for fixed delays such that T2<32π2. In contrast to several previous works which involved approximate solutions, the treatment here is exact. ",

keywords = "Delayed Duffing oscillator, Limit cycle, Exact analysis, Jacobi elliptic function",

author = "Sah, \{Si Mohamed\} and Bernold Fiedler and B. Shayak and Rand, \{Richard H.\}",

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journal = "Nonlinear Dynamics",

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T1 - Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis

AU - Sah, Si Mohamed

AU - Fiedler, Bernold

AU - Shayak, B.

AU - Rand, Richard H.

PY - 2021

Y1 - 2021

N2 - The delayed Duffing equation x¨(t)+x(t−T)+x3(t)=0 is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions, for fixed delays such that T2<32π2. In contrast to several previous works which involved approximate solutions, the treatment here is exact.

AB - The delayed Duffing equation x¨(t)+x(t−T)+x3(t)=0 is shown to possess an infinite and unbounded sequence of rapidly oscillating, asymptotically stable periodic solutions, for fixed delays such that T2<32π2. In contrast to several previous works which involved approximate solutions, the treatment here is exact.

KW - Delayed Duffing oscillator

KW - Limit cycle

KW - Exact analysis

KW - Jacobi elliptic function

U2 - 10.1007/s11071-020-06012-8

DO - 10.1007/s11071-020-06012-8

M3 - Journal article

SN - 0924-090X

VL - 103

SP - 503

EP - 515

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

ER -

Unbounded sequences of stable limit cycles in the delayed Duffing equation: an exact analysis

Abstract

Keywords

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