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Phys. Rev. E 68, 045202(R) (2003) [4 pages]

Analytical results for coupled-map lattices with long-range interactions

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Celia Anteneodo1, Sandro E. de S. Pinto2, Antônio M. Batista3, and Ricardo L. Viana2
1Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
2Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, PR, Brazil
3Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Ponta Grossa, PR, Brazil

See Also: Erratum

Received 18 June 2003; published 23 October 2003

We obtain exact analytical results for lattices of maps with couplings that decay with distance as r-α. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements are piecewise linear maps, we get an algebraic expression for the Lyapunov spectrum. When the local dynamics is given by a nonlinear map, the Lyapunov spectrum for a completely synchronized state is analytically obtained. The critical line characterizing the synchronization transition is determined from the expression for the largest transversal Lyapunov exponent. In particular, it is shown that in the thermodynamical limit, such transition is only possible for sufficiently long-range interactions, namely, for α<αc=d, where d is the lattice dimension.

© 2003 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.68.045202
DOI:
10.1103/PhysRevE.68.045202
PACS:
05.45.Ra, 05.45.Xt

See Also

Erratum: Celia Anteneodo, Sandro E. de S. Pinto, Antônio M. Batista, and Ricardo L. Viana, Erratum: Analytical results for coupled-map lattices with long-range interactions [Phys. Rev. E 68, 045202(R) (2003)], Phys. Rev. E 69, 029904 (2004).

 
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