A hierarchy of coupled maps

Chaos

Volumn 12, Issue 3, 2002, Pages 719-731

  Balmforth, Neil J ^a   Provenzale, Antonello ^b,c   Sassi, Roberto ^a  

^a University of California Santa Cruz   (United States)

^b CNR   (Italy)

^c ISI FOUNDATION   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036710084     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1502929     Document Type: Article

References (10)

1. n). After the change of variables x = (4ζ-2)/(r-2) and a = r(r-2)/4, we return to the quadratic map. The transformation is continuous and invertible for r = (2,4).
2. K. Kaneko, "Overview of coupled map lattices," Chaos 2, 279 (1992).
3. K. Kaneko, "Clustering, coding, switching, hierarchical ordering, and control in network of chaotic elements," Physica D 41, 137 (1990).
4. N.J. Balmforth, A. Jacobson, and A. Provenzale, "Syncronized family dynamics in globally coupled maps," Chaos 9, 738 (1999).
5. T. Shibata and K. Kaneko, "Tonguelike bifurcation structures of the mean-field dynamics in a network of chaotic elements," J. Phys. D 124, 177 (1998).
6. The lack of tree synchronization is related to the purely bottom-up coupling of the system considered here. Adding a further top-down coupling from upper to lower levels may lead to tree synchronization of the system. However, we decided not to explore the even more complex dynamics of a fully coupled hierarchy.
7. S.C. Venkataramani, B.R. Hunt, and E. Ott, "Bubbling transition," Phys. Rev. E 54, 1346 (1996).
8. G. Benettin, L. Galgani, A. Giorgilli, and J.-M. Strelcyn, "Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them. Part I: Theory, and part II: Numerical application," Meccanica 15, 9 (1980).
9. K. Weisenfeld and P. Hadley, "Attractor crowding in oscillator arrays," Phys. Rev. Lett. 62, 1335 (1989).
10. F. Jacob, The Logic of Life: A History of Heredity (Princeton University Press, Princeton, 1993).