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Lyapunov spectrum of a lattice of chaotic systems with local and non-local couplings

Author

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  • Santos, A.M. dos
  • Woellner, C.F.
  • Lopes, S.R.
  • Batista, A.M.
  • Viana, R.L.

Abstract

We consider a one-dimensional chaotic piecewise linear map lattice with periodic boundary conditions and two types of interactions: (i) local couplings between nearest and next-to-the-nearest neighbors; and (ii) non-local couplings randomly chosen along the lattice according to a specified probability. The chaoticity of the lattice is described by means of its Lyapunov spectrum, which furnishes also information about the system global attractor in a high-dimensional phase space. We study in particular the dependence of this spectrum with the coupling parameters, as well as make comparisons with limiting cases, for which the Lyapunov spectrum is known.

Suggested Citation

  • Santos, A.M. dos & Woellner, C.F. & Lopes, S.R. & Batista, A.M. & Viana, R.L., 2007. "Lyapunov spectrum of a lattice of chaotic systems with local and non-local couplings," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 702-710.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:702-710
    DOI: 10.1016/j.chaos.2005.11.055
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    Cited by:

    1. Polynikis, A. & di Bernardo, M. & Hogan, S.J., 2009. "Synchronizability of coupled PWL maps," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1353-1367.
    2. Ngueuteu Mbouna, S.G. & Banerjee, Tanmoy & Yamapi, René & Woafo, Paul, 2022. "Diverse chimera and symmetry-breaking patterns induced by fractional derivation effect in a network of Stuart-Landau oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Gancio, Juan & Rubido, Nicolás, 2022. "Critical parameters of the synchronisation's stability for coupled maps in regular graphs," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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