Resonance in periodically forced processes

I. G. Kevrekidis; R. Aris; L. D. Schmidt

doi:10.1016/0009-2509(86)87174-3

Resonance in periodically forced processes

I. G. Kevrekidis, R. Aris, L. D. Schmidt

Chemical & Biological Engineering

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

15 Scopus citations

Abstract

The interaction of an external periodic forcing with the natural frequencies of chemically reacting systems gives rise to interesting qualitative dynamic behavior. This behavior is centered around the creation and breaking of resonances and invariant tori. We present a numerical study of the high forcing amplitude region of the excitation diagram and through this an explanation for the shapes of entrainment regions. The algorithms constructed for this purpose are also discussed.

Original language	English (US)
Pages (from-to)	905-911
Number of pages	7
Journal	Chemical Engineering Science
Volume	41
Issue number	4
DOIs	https://doi.org/10.1016/0009-2509(86)87174-3
State	Published - 1986

All Science Journal Classification (ASJC) codes

General Chemistry
General Chemical Engineering
Industrial and Manufacturing Engineering

Keywords

Bifurcation
Hopf bifurcation
entrainment
forced oscillations
invariant circles
quasiperiodic response
stroboscopic map

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10.1016/0009-2509(86)87174-3

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title = "Resonance in periodically forced processes",

abstract = "The interaction of an external periodic forcing with the natural frequencies of chemically reacting systems gives rise to interesting qualitative dynamic behavior. This behavior is centered around the creation and breaking of resonances and invariant tori. We present a numerical study of the high forcing amplitude region of the excitation diagram and through this an explanation for the shapes of entrainment regions. The algorithms constructed for this purpose are also discussed.",

keywords = "Bifurcation, Hopf bifurcation, entrainment, forced oscillations, invariant circles, quasiperiodic response, stroboscopic map",

author = "Kevrekidis, {I. G.} and R. Aris and Schmidt, {L. D.}",

note = "Funding Information: This work was partially supported through NSF Grant Number CPE8313497. During this work I. G. Kevrekidis was a Dissertation Fellow of the Graduate School of the University of Minnesota. A grant of computer time from the University of Minnesota Computer Center is gratefully acknowledged.",

year = "1986",

doi = "10.1016/0009-2509(86)87174-3",

language = "English (US)",

volume = "41",

pages = "905--911",

journal = "Chemical Engineering Science",

issn = "0009-2509",

publisher = "Elsevier B.V.",

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TY - JOUR

T1 - Resonance in periodically forced processes

AU - Kevrekidis, I. G.

AU - Aris, R.

AU - Schmidt, L. D.

N1 - Funding Information: This work was partially supported through NSF Grant Number CPE8313497. During this work I. G. Kevrekidis was a Dissertation Fellow of the Graduate School of the University of Minnesota. A grant of computer time from the University of Minnesota Computer Center is gratefully acknowledged.

PY - 1986

Y1 - 1986

N2 - The interaction of an external periodic forcing with the natural frequencies of chemically reacting systems gives rise to interesting qualitative dynamic behavior. This behavior is centered around the creation and breaking of resonances and invariant tori. We present a numerical study of the high forcing amplitude region of the excitation diagram and through this an explanation for the shapes of entrainment regions. The algorithms constructed for this purpose are also discussed.

AB - The interaction of an external periodic forcing with the natural frequencies of chemically reacting systems gives rise to interesting qualitative dynamic behavior. This behavior is centered around the creation and breaking of resonances and invariant tori. We present a numerical study of the high forcing amplitude region of the excitation diagram and through this an explanation for the shapes of entrainment regions. The algorithms constructed for this purpose are also discussed.

KW - Bifurcation

KW - Hopf bifurcation

KW - entrainment

KW - forced oscillations

KW - invariant circles

KW - quasiperiodic response

KW - stroboscopic map

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U2 - 10.1016/0009-2509(86)87174-3

DO - 10.1016/0009-2509(86)87174-3

M3 - Article

AN - SCOPUS:0022913882

SN - 0009-2509

VL - 41

SP - 905

EP - 911

JO - Chemical Engineering Science

JF - Chemical Engineering Science

IS - 4

ER -

Resonance in periodically forced processes

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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