Generalized Synchronization in Autooscillatory Media

Generalized synchronization in Ginzburg-Landau equations with local coupling

“…It is of considerable interest to study the GS phenomenon in spatially distributed chaotic systems [11][12][13]. Previously, we have analyzed the process of GS establishment in unidirectionally coupled Ginzburg-Landau equations with a spatially homogeneous diffusion coupling [12,13].…”

“…It is of considerable interest to study the GS phenomenon in spatially distributed chaotic systems [11][12][13]. Previously, we have analyzed the process of GS establishment in unidirectionally coupled Ginzburg-Landau equations with a spatially homogeneous diffusion coupling [12,13]. However, it is also very important to study the synchronization and control of chaotic oscillations in coupled distributed systems in the case when an external signal acts upon the drive system at a certain finite number of points in space (local or point coupling) [14,15].…”

“…(3) where δ ( ξ ) is the Dirac delta function and ∆ X is the distance between spatial points at which the systems are coupled (note that ∆ X = 0 corresponds to the case of a spatially homogeneous dissipative spatial coupling studied previously [12,13]).…”

“…Previously, it was established [12,13] that a threshold value of the coupling parameter (ε GS ) for the appearance of GS in the case of a spatially homogeneous coupling weakly depends on the control parameters of the drive system. Analogous results were obtained for the local coupling between systems under consideration.…”