### Abstract

Original language | English |
---|---|

Pages (from-to) | 1082-1104 |

Number of pages | 23 |

Journal | Chaos, Solitons & Fractals |

Volume | 34 |

Issue number | 4 |

Early online date | 21 Jul 2006 |

DOIs | |

Publication status | Published - Nov 2007 |

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### Cite this

*Chaos, Solitons & Fractals*,

*34*(4), 1082-1104. https://doi.org/10.1016/j.chaos.2006.05.062

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

Research output: Contribution to journal › Article

*Chaos, Solitons & Fractals*, vol. 34, no. 4, pp. 1082-1104. https://doi.org/10.1016/j.chaos.2006.05.062

}

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 -