A new randomness-generating mechanism in forced relaxation oscillations

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

This note points out that in a wide class of forced relaxation oscillators the hyperbolic behavior, which has up to now been known to exist only on small set, dominates in the Lebesgue sense in a wide class of relaxation oscillators. This note introduces the simplest physically realistic smooth system where the strange attractor is expected to exist for most (in the Lebesgue sense) parameter values. This phenomenon went unobserved for over half a century since the first work on forced relaxation oscillations by Cartwright, Littlewood and Levinson.

Original languageEnglish (US)
Pages (from-to)230-236
Number of pages7
JournalPhysica D: Nonlinear Phenomena
Volume114
Issue number3-4
DOIs
StatePublished - Jan 1 1998

Fingerprint

relaxation oscillators
strange attractors
oscillations

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

Cite this

@article{69e045273c06452584e032ec1aa16db4,
title = "A new randomness-generating mechanism in forced relaxation oscillations",
abstract = "This note points out that in a wide class of forced relaxation oscillators the hyperbolic behavior, which has up to now been known to exist only on small set, dominates in the Lebesgue sense in a wide class of relaxation oscillators. This note introduces the simplest physically realistic smooth system where the strange attractor is expected to exist for most (in the Lebesgue sense) parameter values. This phenomenon went unobserved for over half a century since the first work on forced relaxation oscillations by Cartwright, Littlewood and Levinson.",
author = "Mark Levi",
year = "1998",
month = "1",
day = "1",
doi = "10.1016/S0167-2789(97)00221-2",
language = "English (US)",
volume = "114",
pages = "230--236",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "3-4",

}

A new randomness-generating mechanism in forced relaxation oscillations. / Levi, Mark.

In: Physica D: Nonlinear Phenomena, Vol. 114, No. 3-4, 01.01.1998, p. 230-236.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A new randomness-generating mechanism in forced relaxation oscillations

AU - Levi, Mark

PY - 1998/1/1

Y1 - 1998/1/1

N2 - This note points out that in a wide class of forced relaxation oscillators the hyperbolic behavior, which has up to now been known to exist only on small set, dominates in the Lebesgue sense in a wide class of relaxation oscillators. This note introduces the simplest physically realistic smooth system where the strange attractor is expected to exist for most (in the Lebesgue sense) parameter values. This phenomenon went unobserved for over half a century since the first work on forced relaxation oscillations by Cartwright, Littlewood and Levinson.

AB - This note points out that in a wide class of forced relaxation oscillators the hyperbolic behavior, which has up to now been known to exist only on small set, dominates in the Lebesgue sense in a wide class of relaxation oscillators. This note introduces the simplest physically realistic smooth system where the strange attractor is expected to exist for most (in the Lebesgue sense) parameter values. This phenomenon went unobserved for over half a century since the first work on forced relaxation oscillations by Cartwright, Littlewood and Levinson.

UR - http://www.scopus.com/inward/record.url?scp=20444466427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=20444466427&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(97)00221-2

DO - 10.1016/S0167-2789(97)00221-2

M3 - Article

AN - SCOPUS:20444466427

VL - 114

SP - 230

EP - 236

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 3-4

ER -