Izv. VUZov, Prikladnaya nelineinaya dinamika, 1999, vol. 7, no. 1, pp. 12-28.
Global Synchronization in Lattices of Chaotic Maps with Sparse Connections
Yuri V. Andreyev
Institute of Radio Engineering and Electronics of Russian Academy of Sciences
Mokhovaya st. 11, GSP-3, 103907 Moscow, Russia.
Izv. VUZov, Prikladnaya nelineinaya dinamika, 1999, vol.7, no.1, pp.12-28.
Received Dec. 8, 1998.
The stability conditions of the global synchronous mode in lattices of chaotic maps are investigated by means of direct calculation and by numerical simulation. Locally coupled lattices are shown to have a limit admissible value of the Lyapunov exponent of the lattice maps, above which the global synchronous mode loses stability. The synchronous mode is found to be impossible in large lattices due to local, "short-range" nature of connections. Approaches to modification of the dynamic system structure are proposed which help provide the stability of the synchronous mode, such as tuning the lattice map dynamic mode, increasing the local neighborhood, use of nonlocal static or dynamic connections, and introducing an external control node (a pacemaker). In the model with the pacemaker, a spatial synchronous mode of the lattice nodes is discovered, different from the pacemaker mode ("generalized" synchronization effect).