International Journal of Bifurcation and Chaos, Vol. 9 No. 12 (1999) 2165-2172
© World Scientific Publishing Company
Conditions for Global Synchronization in Lattices of Chaotic Elements with Local Connections
Yuri V. Andreyev and Alexander S. Dmitriev
Institute of Radio Engineering and Electronics of the Russian Academy of Sciences,
Moscow, 103907, Russia. Email: email@example.com
International Journal of Bifurcations and Chaos, 1999, vol. 9, No. 12, pp. 2165-2172.
Received July 30, 1998.
We investigate phenomena on the edge of spatially homogeneous chaotic mode and spatiotemporal chaos in a lattice of chaotic 1-D maps with local connections. We show that spatially homogeneous chaotic mode cannot exist in a lattice with local connections if the Lyapunov exponent of the isolated chaotic map is greater than some critical positive value. We propose a few schemes that make spatial synchronization possible in large lattices. If the idea of only local connections is abandoned, the number of connections necessary for synchronization dramatically decreases to three per node. We also propose a model of a lattice with an external pacemaker, where we find a spatially homogeneous mode synchronous with the pacemaker, as well as different from the pacemaker mode.
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