Persistence of invariant tori in systems of coupled oscillators I: Regular and singular problems

Masaji Watanabe; Hans G. Othmer; Klaus Schmitt

Persistence of invariant tori in systems of coupled oscillators I: Regular and singular problems

Masaji Watanabe, Hans G. Othmer, Klaus Schmitt

School of Mathematics

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

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Abstract

In this paper we study a class of differential equations that arises in the study of indirectly- or capacitively-coupled oscillators. We prove that the invariant tori which exist in the uncoupled system persist under coupling, we establish the asymptotic behavior of the flow in a neighborhood of these tori, and we study the flow on the invariant tori.

Original language	English (US)
Pages (from-to)	331-368
Number of pages	38
Journal	Differential and Integral Equations
Volume	4
Issue number	2
State	Published - Mar 1991

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title = "Persistence of invariant tori in systems of coupled oscillators I: Regular and singular problems",

abstract = "In this paper we study a class of differential equations that arises in the study of indirectly- or capacitively-coupled oscillators. We prove that the invariant tori which exist in the uncoupled system persist under coupling, we establish the asymptotic behavior of the flow in a neighborhood of these tori, and we study the flow on the invariant tori.",

author = "Masaji Watanabe and Othmer, {Hans G.} and Klaus Schmitt",

year = "1991",

month = mar,

language = "English (US)",

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pages = "331--368",

journal = "Differential and Integral Equations",

issn = "0893-4983",

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T1 - Persistence of invariant tori in systems of coupled oscillators I

T2 - Regular and singular problems

AU - Watanabe, Masaji

AU - Othmer, Hans G.

AU - Schmitt, Klaus

PY - 1991/3

Y1 - 1991/3

N2 - In this paper we study a class of differential equations that arises in the study of indirectly- or capacitively-coupled oscillators. We prove that the invariant tori which exist in the uncoupled system persist under coupling, we establish the asymptotic behavior of the flow in a neighborhood of these tori, and we study the flow on the invariant tori.

AB - In this paper we study a class of differential equations that arises in the study of indirectly- or capacitively-coupled oscillators. We prove that the invariant tori which exist in the uncoupled system persist under coupling, we establish the asymptotic behavior of the flow in a neighborhood of these tori, and we study the flow on the invariant tori.

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M3 - Article

AN - SCOPUS:84972502555

SN - 0893-4983

VL - 4

SP - 331

EP - 368

JO - Differential and Integral Equations

JF - Differential and Integral Equations

IS - 2

ER -

Persistence of invariant tori in systems of coupled oscillators I: Regular and singular problems

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