Horseshoes of periodically kicked van der Pol oscillators

Brian Ryals, Lai-Sang Young

Research output: Contribution to journalArticle

Abstract

This paper contains a numerical study of the periodically forced van der Pol system. Our aim is to determine the extent to which chaotic behavior occurs in this system as well as the nature of the chaos. Unlike previous studies, which used continuous forcing, we work with instantaneous kicks, for which the geometry is simpler. Our study covers a range of parameters describing nonlinearity, kick sizes, kick periods. We show that horseshoes are abundant whenever the limit cycle is kicked to a specific region of the phase space offer a geometric explanation for the stretch-and-fold behavior which ensues.

Original languageEnglish (US)
Article number043140
JournalChaos
Volume22
Issue number4
DOIs
StatePublished - Oct 4 2012

Fingerprint

Van Der Pol Oscillator
Horseshoe
Chaos theory
oscillators
Geometry
Chaotic Behavior
Stretch
Limit Cycle
Forcing
Instantaneous
chaos
Numerical Study
Phase Space
Chaos
Fold
nonlinearity
Nonlinearity
Cover
cycles
geometry

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Horseshoes of periodically kicked van der Pol oscillators. / Ryals, Brian; Young, Lai-Sang.

In: Chaos, Vol. 22, No. 4, 043140, 04.10.2012.

Research output: Contribution to journalArticle

@article{fa55300bbd3f4e49ab84cecd4c40e59d,
title = "Horseshoes of periodically kicked van der Pol oscillators",
abstract = "This paper contains a numerical study of the periodically forced van der Pol system. Our aim is to determine the extent to which chaotic behavior occurs in this system as well as the nature of the chaos. Unlike previous studies, which used continuous forcing, we work with instantaneous kicks, for which the geometry is simpler. Our study covers a range of parameters describing nonlinearity, kick sizes, kick periods. We show that horseshoes are abundant whenever the limit cycle is kicked to a specific region of the phase space offer a geometric explanation for the stretch-and-fold behavior which ensues.",
author = "Brian Ryals and Lai-Sang Young",
year = "2012",
month = "10",
day = "4",
doi = "10.1063/1.4769361",
language = "English (US)",
volume = "22",
journal = "Chaos",
issn = "1054-1500",
publisher = "American Institute of Physics Publising LLC",
number = "4",

}

TY - JOUR

T1 - Horseshoes of periodically kicked van der Pol oscillators

AU - Ryals, Brian

AU - Young, Lai-Sang

PY - 2012/10/4

Y1 - 2012/10/4

N2 - This paper contains a numerical study of the periodically forced van der Pol system. Our aim is to determine the extent to which chaotic behavior occurs in this system as well as the nature of the chaos. Unlike previous studies, which used continuous forcing, we work with instantaneous kicks, for which the geometry is simpler. Our study covers a range of parameters describing nonlinearity, kick sizes, kick periods. We show that horseshoes are abundant whenever the limit cycle is kicked to a specific region of the phase space offer a geometric explanation for the stretch-and-fold behavior which ensues.

AB - This paper contains a numerical study of the periodically forced van der Pol system. Our aim is to determine the extent to which chaotic behavior occurs in this system as well as the nature of the chaos. Unlike previous studies, which used continuous forcing, we work with instantaneous kicks, for which the geometry is simpler. Our study covers a range of parameters describing nonlinearity, kick sizes, kick periods. We show that horseshoes are abundant whenever the limit cycle is kicked to a specific region of the phase space offer a geometric explanation for the stretch-and-fold behavior which ensues.

UR - http://www.scopus.com/inward/record.url?scp=84871859738&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871859738&partnerID=8YFLogxK

U2 - 10.1063/1.4769361

DO - 10.1063/1.4769361

M3 - Article

C2 - 23278075

AN - SCOPUS:84871859738

VL - 22

JO - Chaos

JF - Chaos

SN - 1054-1500

IS - 4

M1 - 043140

ER -