Volume 103, Number 5, September 2013
|Number of page(s)||6|
|Published online||01 October 2013|
Global generalized synchronization in networks of different time-delay systems
1 Potsdam Institute for Climate Impact Research - 14473 Potsdam, Germany, EU
2 Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University - Tiruchirapalli 620 024, India
3 Institute of Physics, Humboldt University - 12489 Berlin, Germany, EU
4 Institute for Complex Systems and Mathematical Biology, University of Aberdeen - Aberdeen AB24 3UE, UK, EU
Received: 1 April 2013
Accepted: 4 September 2013
We show that global generalized synchronization (GS) exists in structurally different time-delay systems, even with different orders, with quite different fractal (Kaplan-Yorke) dimensions, which emerges via partial GS in symmetrically coupled regular networks. We find that there exists a smooth transformation in such systems, which maps them to a common GS manifold as corroborated by their maximal transverse Lyapunov exponent. In addition, an analytical stability condition using the Krasvoskii-Lyapunov theory is deduced. This phenomenon of GS in strongly distinct systems opens a new way for an effective control of pathological synchronous activity by means of extremely small perturbations to appropriate variables in the synchronization manifold.
PACS: 05.45.Xt – Synchronization; coupled oscillators / 05.45.Pq – Numerical simulations of chaotic systems / 05.45.-a – Nonlinear dynamics and chaos
© EPLA, 2013
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