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Abstract <p> We consider some special systems of integro-differential equations, the so-called integral networks of nonlinear oscillators. These networks are obtained from finite-dimensional fully connected networks when the number of interacting oscillators tends to infinity. We study both general properties of the introduced class of equations and the characteristic features of the dynamics of integral networks. Namely, we establish the fundamental possibility of the existence of so-called periodic regimes of multicluster synchronization in these networks. For any such regime, the set of oscillators decomposes into <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2657_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2657_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\ge 2\)</EquationSource> </InlineEquation>, nonintersecting classes. Within these classes, complete synchronization of oscillations is observed, and every two oscillators from different classes oscillate asynchronously. We also establish the realizability of the phenomenon of continuum buffering, that is, of the existence under certain conditions of a continuum family of isolated attractors. </p>

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Integral networks of nonlinear oscillators

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • S. D. Glyzin,
  • A. Yu. Kolesov

摘要

Abstract

We consider some special systems of integro-differential equations, the so-called integral networks of nonlinear oscillators. These networks are obtained from finite-dimensional fully connected networks when the number of interacting oscillators tends to infinity. We study both general properties of the introduced class of equations and the characteristic features of the dynamics of integral networks. Namely, we establish the fundamental possibility of the existence of so-called periodic regimes of multicluster synchronization in these networks. For any such regime, the set of oscillators decomposes into \(r\) , \(r\ge 2\) , nonintersecting classes. Within these classes, complete synchronization of oscillations is observed, and every two oscillators from different classes oscillate asynchronously. We also establish the realizability of the phenomenon of continuum buffering, that is, of the existence under certain conditions of a continuum family of isolated attractors.