Physical interpretation and theory of existence of cluster structures in lattices of dynamical systems

Nikolai N. Verichev, Stanislav N. Verichev, Marian Wiercigroch

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The alternative theory of existence of clusterstructures in lattices of dynamicalsystems (oscillators) is proposed. This theory is based on representation of structures as a result of classical (full) synchronization of structural objects called cluster oscillators (C-oscillators). Different types of C-oscillators, whose number is defined by the geometrical properties of lattices (dimensions and forms) are introduced. The completeness of all types of C-oscillators for lattices of different dimensions is proven. This fact provides a full set of types of clusterstructures that can be realized in a given lattice. The solution is derived without the necessity to verify the existence of invariant (cluster) manifolds. The principles of coupling of C-oscillators into the clusterstructures and principles of transformations of such structures are described. Having interpreted the processes of structuring in terms of the classical synchronization of C-oscillators, one can solve the problem of fusion of lattices with pre-described properties at the engineering level.
Original languageEnglish
Pages (from-to)1082-1104
Number of pages23
JournalChaos, Solitons & Fractals
Volume34
Issue number4
Early online date21 Jul 2006
DOIs
Publication statusPublished - Nov 2007

Fingerprint

Dynamical system
Synchronization
Interpretation
Completeness
Fusion
Verify
Engineering
Invariant
Alternatives

Cite this

Physical interpretation and theory of existence of cluster structures in lattices of dynamical systems. / Verichev, Nikolai N.; Verichev, Stanislav N.; Wiercigroch, Marian.

In: Chaos, Solitons & Fractals, Vol. 34, No. 4, 11.2007, p. 1082-1104.

Research output: Contribution to journalArticle

@article{c3460ef438534a598c06269d326b16dc,
title = "Physical interpretation and theory of existence of cluster structures in lattices of dynamical systems",
abstract = "The alternative theory of existence of clusterstructures in lattices of dynamicalsystems (oscillators) is proposed. This theory is based on representation of structures as a result of classical (full) synchronization of structural objects called cluster oscillators (C-oscillators). Different types of C-oscillators, whose number is defined by the geometrical properties of lattices (dimensions and forms) are introduced. The completeness of all types of C-oscillators for lattices of different dimensions is proven. This fact provides a full set of types of clusterstructures that can be realized in a given lattice. The solution is derived without the necessity to verify the existence of invariant (cluster) manifolds. The principles of coupling of C-oscillators into the clusterstructures and principles of transformations of such structures are described. Having interpreted the processes of structuring in terms of the classical synchronization of C-oscillators, one can solve the problem of fusion of lattices with pre-described properties at the engineering level.",
author = "Verichev, {Nikolai N.} and Verichev, {Stanislav N.} and Marian Wiercigroch",
year = "2007",
month = "11",
doi = "10.1016/j.chaos.2006.05.062",
language = "English",
volume = "34",
pages = "1082--1104",
journal = "Chaos, Solitons & Fractals",
issn = "0960-0779",
publisher = "Elsevier Limited",
number = "4",

}

TY - JOUR

T1 - Physical interpretation and theory of existence of cluster structures in lattices of dynamical systems

AU - Verichev, Nikolai N.

AU - Verichev, Stanislav N.

AU - Wiercigroch, Marian

PY - 2007/11

Y1 - 2007/11

N2 - The alternative theory of existence of clusterstructures in lattices of dynamicalsystems (oscillators) is proposed. This theory is based on representation of structures as a result of classical (full) synchronization of structural objects called cluster oscillators (C-oscillators). Different types of C-oscillators, whose number is defined by the geometrical properties of lattices (dimensions and forms) are introduced. The completeness of all types of C-oscillators for lattices of different dimensions is proven. This fact provides a full set of types of clusterstructures that can be realized in a given lattice. The solution is derived without the necessity to verify the existence of invariant (cluster) manifolds. The principles of coupling of C-oscillators into the clusterstructures and principles of transformations of such structures are described. Having interpreted the processes of structuring in terms of the classical synchronization of C-oscillators, one can solve the problem of fusion of lattices with pre-described properties at the engineering level.

AB - The alternative theory of existence of clusterstructures in lattices of dynamicalsystems (oscillators) is proposed. This theory is based on representation of structures as a result of classical (full) synchronization of structural objects called cluster oscillators (C-oscillators). Different types of C-oscillators, whose number is defined by the geometrical properties of lattices (dimensions and forms) are introduced. The completeness of all types of C-oscillators for lattices of different dimensions is proven. This fact provides a full set of types of clusterstructures that can be realized in a given lattice. The solution is derived without the necessity to verify the existence of invariant (cluster) manifolds. The principles of coupling of C-oscillators into the clusterstructures and principles of transformations of such structures are described. Having interpreted the processes of structuring in terms of the classical synchronization of C-oscillators, one can solve the problem of fusion of lattices with pre-described properties at the engineering level.

U2 - 10.1016/j.chaos.2006.05.062

DO - 10.1016/j.chaos.2006.05.062

M3 - Article

VL - 34

SP - 1082

EP - 1104

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

SN - 0960-0779

IS - 4

ER -