Invisible grazings and dangerous bifurcations in impacting systems

The problem of narrow-band chaos

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37 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 languageEnglish
Article number037201
Number of pages4
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume79
Issue number3
DOIs
Publication statusPublished - 17 Mar 2009

Keywords

  • bifurcation
  • chaos
  • impact (mechanical)
  • nonlinear dynamical systems
  • oscillators
  • oscillator

Cite this

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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}",
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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

VL - 79

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

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

SN - 1539-3755

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