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

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

Chaos, Solitons & Fractals, 2007, vol. 34, issue 4, 1082-1104

Abstract: The alternative theory of existence of cluster structures in lattices of dynamical systems (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 cluster structures 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 cluster structures 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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:34:y:2007:i:4:p:1082-1104

DOI: 10.1016/j.chaos.2006.05.062

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