Coupled maps on trees

Gade, Prashant M. ; Cerdeira, Hilda A. ; Ramaswamy, Ramakrishna (1995) Coupled maps on trees Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 52 (3). pp. 2478-2485. ISSN 1539-3755

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We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stability of these states and their domains of attraction. Since the number of sites that become synchronized is much higher compared to that on a regular lattice, control is easier to achieve. A general procedure is given to deduce the eigenvalue spectrum for these states. Perturbations of the synchronized state lead to different spatiotemporal structures. We find that a mean-field-like treatment is valid on this (effectively infinite dimensional) lattice.

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Source:Copyright of this article belongs to The American Physical Society.
ID Code:45346
Deposited On:28 Jun 2011 04:47
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