Random coupling of chaotic maps leads to spatiotemporal synchronization

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 1, 2002, Pages

  Sinha, Sudeshna ^a  

^a INSTITUTE OF MATHEMATICAL SCIENCES   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; HIGH ENERGY PHYSICS; MAPS; MATHEMATICAL MODELS; PROBABILITY; VECTORS;

BROWNIAN PARTICLES; CHAOTIC MAPS; RATCHET MECHANISM; RATCHET MODELS;

CHAOS THEORY;

EID: 37649032019     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.016209     Document Type: Article

References (19)

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10. Only the strong coupling range (Formula presented) is displayed in Figs. 11 and 22. The weak coupling range (Formula presented) (not shown) is strongly irregular for both (Formula presented) and (Formula presented)
11. The range of stability also depends on the specific coupling form. For instance, if one considered the future-coupled case, where the coupling occurs through (Formula presented), then an additional factor of (Formula presented) multiplies the second term in Eq. (4). The validity of the approximation in Eq. (3) also depends on the coupling form. Again for the future-coupled case the approximation is much worse as the term ignored is weighted by an additional factor of (Formula presented) which is greater than 1 for chaotic maps. In fact, for the future-coupled case numerical evidence of spatial synchronization is obtained for chaotic logistic maps with (Formula presented) only when (Formula presented) e.g., around (Formula presented) But even for (Formula presented) where exact synchronization is not obtained, the roughness of the spatial profile is much less than that for regular nearest neighbor coupling. So the random coupling does have a regularizing effect there as well, though not as complete as in the examples in this work.
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