ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Kuptsov P. V., Kuznetsov S. P. Synchronization and collective behavior of a coupled map lattice with unidirectional coupling and periodic boundary conditions. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 3, pp. 3-22. DOI: 10.18500/0869-6632-2004-12-3-3-22

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
571.3
DOI: 
10.18500/0869-6632-2004-12-3-3-22

Synchronization and collective behavior of a coupled map lattice with unidirectional coupling and periodic boundary conditions

Autors: 
Kuptsov Pavel Vladimirovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Kuznetsov Sergey Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

Full synchronization is considered for a coupled map lattice with periodic boundary conditions. The lattice composed of the identical maps and the coupling is local and unidirectional, i.e., every map undergoes the action only form its right neighbor. If the lattice consists of the chaotic maps, then there is the limiting lattice length above which synchronization is always unstable for any type of coupling. This limiting value depends on the Liapunov exponent of the partial map. When the partial Liapunov exponent is negative, as for the periodic map, there always exists ап appropriate coupling for which the lattice of any length have stable synchronization. As an example the lattice of logistic maps with the inertial and dissipative coupling is considered. Stability of synchronization is discussed for the different types of individual dynamics of the partial map. Some other typical regimes of dynamics are revealed and discussed.

Key words: 
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Acknowledgments: 
The work was supported by the RFBR 03-02-16192.
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Received: 
16.10.2003
Accepted: 
24.05.2004
Published: 
23.12.2004
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