Invisible grazings and dangerous bifurcations in impacting systems: The problem of narrow-band chaos

Soumitro Banerjee; James Ing; Ekaterina Evgenievna Pavlovskaia; Marian Wiercigroch; Aravind R Reddy

doi:10.1103/PhysRevE.79.037201

Invisible grazings and dangerous bifurcations in impacting systems: The problem of narrow-band chaos

Soumitro Banerjee, James Ing, Ekaterina Evgenievna Pavlovskaia, Marian Wiercigroch, Aravind R Reddy

Indian Institute of Technology Kharagpur

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

60 Citations (Scopus)

Abstract

We discovered a narrow band of chaos close to the grazing condition for a simple soft impact oscillator. The phenomenon was observed experimentally for a range of system parameters. Through numerical stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits, created at "invisible" grazings, take part.

Original language	English
Article number	037201
Number of pages	4
Journal	Physical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume	79
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevE.79.037201
Publication status	Published - 17 Mar 2009

Keywords

bifurcation
chaos
impact (mechanical)
nonlinear dynamical systems
oscillators
oscillator

Access to Document

10.1103/PhysRevE.79.037201Licence: Unspecified

Cite this

@article{c213bef0a9a54cd2924efeb6020f23cb,

title = "Invisible grazings and dangerous bifurcations in impacting systems: The problem of narrow-band chaos",

abstract = "We discovered a narrow band of chaos close to the grazing condition for a simple soft impact oscillator. The phenomenon was observed experimentally for a range of system parameters. Through numerical stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits, created at {"}invisible{"} grazings, take part.",

keywords = "bifurcation, chaos, impact (mechanical), nonlinear dynamical systems, oscillators, oscillator",

author = "Soumitro Banerjee and James Ing and Pavlovskaia, {Ekaterina Evgenievna} and Marian Wiercigroch and Reddy, {Aravind R}",

year = "2009",

month = mar,

day = "17",

doi = "10.1103/PhysRevE.79.037201",

language = "English",

volume = "79",

journal = "Physical Review. E, Statistical, Nonlinear and Soft Matter Physics",

issn = "1539-3755",

publisher = "AMER PHYSICAL SOC",

number = "3",

}

TY - JOUR

T1 - Invisible grazings and dangerous bifurcations in impacting systems

T2 - The problem of narrow-band chaos

AU - Banerjee, Soumitro

AU - Ing, James

AU - Pavlovskaia, Ekaterina Evgenievna

AU - Wiercigroch, Marian

AU - Reddy, Aravind R

PY - 2009/3/17

Y1 - 2009/3/17

N2 - We discovered a narrow band of chaos close to the grazing condition for a simple soft impact oscillator. The phenomenon was observed experimentally for a range of system parameters. Through numerical stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits, created at "invisible" grazings, take part.

AB - We discovered a narrow band of chaos close to the grazing condition for a simple soft impact oscillator. The phenomenon was observed experimentally for a range of system parameters. Through numerical stability analysis, we argue that this abrupt onset to chaos is caused by a dangerous bifurcation in which two unstable period-3 orbits, created at "invisible" grazings, take part.

KW - bifurcation

KW - chaos

KW - impact (mechanical)

KW - nonlinear dynamical systems

KW - oscillators

KW - oscillator

U2 - 10.1103/PhysRevE.79.037201

DO - 10.1103/PhysRevE.79.037201

M3 - Article

SN - 1539-3755

VL - 79

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

IS - 3

M1 - 037201

ER -

Invisible grazings and dangerous bifurcations in impacting systems: The problem of narrow-band chaos

Abstract

Keywords

Access to Document

Fingerprint

Cite this