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

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

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.

Suggested Citation

  • Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2007. "Physical interpretation and theory of existence of cluster structures in lattices of dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1082-1104.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:4:p:1082-1104
    DOI: 10.1016/j.chaos.2006.05.062
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    References listed on IDEAS

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    1. Belykh, V.N. & Belykh, I.V. & Nelvidin, K.V., 2002. "Spatiotemporal synchronization in lattices of locally coupled chaotic oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(4), pages 477-492.
    2. Rabinovich, M.I. & Varona, P. & Torres, J.J. & Huerta, R. & Abarbanel, H.D.I., 1999. "Slow dynamics and regularization phenomena in ensembles of chaotic neurons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 405-414.
    3. Yanchuk, Sergiy & Maistrenko, Yuri & Mosekilde, Erik, 2001. "Partial synchronization and clustering in a system of diffusively coupled chaotic oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(6), pages 491-508.
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    Cited by:

    1. Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2009. "Asymptotic theory of chaotic synchronization for dissipative-coupled dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 752-763.
    2. Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2009. "C-oscillators and stability of stationary cluster structures in lattices of diffusively coupled oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 686-701.

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    2. Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2009. "C-oscillators and stability of stationary cluster structures in lattices of diffusively coupled oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 686-701.

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