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

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Andreyev Y. V. Global synchronization in lattices of chaotic maps with limited number of connections. Izvestiya VUZ. Applied Nonlinear Dynamics, 1999, vol. 7, iss. 1, pp. 12-28. DOI: 10.18500/0869-6632-1999-7-1-12-28

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
621.391.2: 519.72: 530.182
DOI: 
10.18500/0869-6632-1999-7-1-12-28

Global synchronization in lattices of chaotic maps with limited number of connections

Autors: 
Andreyev Yury Vladimirovich, Moscow Institute of Physics and Technology
Abstract: 

Stability of the global synchronous mode of chaotic map lattices is investigated by means of direct calculation of the stability conditions, and by means of numerical simulation. The lattices with local connections are shown to have a limit value of the Lyapunov exponent of the lattice maps, above which the global synchronous mode loses stability. The synchronous mode in large lattices is found impossible due to the local nature, i.e., «short range» of the connections. We propose some approaches to modification of the dynamic system structure that can provide stability of the synchronous mode, such as tuning the dynamic mode of the lattice maps, extension of the local neighborhood, use of nonlocal static and dynamic connections, and introduction of an external control node (a pacemaker). In the model with the pacemaker, a spatial synchronous lattice mode is revealed, different from the pacemaker mode («generalized» synchronization).

Key words: 
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Received: 
08.12.1998
Accepted: 
19.03.1999
Published: 
28.05.1999
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