Patterns of Exact Synchronization in Chains of Feedback Loops with Two Characteristic Time-Lags

Synchronization patterns in chains of N bi-directionally delayed coupled systems with delayed feedback are studied. Each system is hyperchaotic when decoupled from the chain. It is shown that chains with odd or even number of cites N display different spatial patterns of stable exact synchronization. When N is odd the only stable pattern of exact synchronization is between all of the units. When N is even, next to the nearest neighbors could become exactly synchronized, with the dynamics of the nearest neighbors related in a more complicated way. Sufficiently strong coupling leads to the nearest neighbor synchronization also for even N. No other patterns have been observed.

[1]  C. Mirasso,et al.  Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers. , 2001, Physical review letters.

[2]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[3]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[4]  Kirk Green,et al.  Bistability and torus break-up in a semiconductor laser with phase-conjugate feedback , 2002 .

[5]  Zhang,et al.  From low-dimensional synchronous chaos to high-dimensional desynchronous spatiotemporal chaos in coupled systems , 2000, Physical review letters.

[6]  Munakata,et al.  Clustering behavior of time-delayed nearest-neighbor coupled oscillators. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Kestutis Pyragas.  SYNCHRONIZATION OF COUPLED TIME-DELAY SYSTEMS : ANALYTICAL ESTIMATIONS , 1998 .

[8]  J. D. Farmer,et al.  Chaotic attractors of an infinite-dimensional dynamical system , 1982 .

[9]  Leon O. Chua,et al.  Conditions for impulsive Synchronization of Chaotic and hyperchaotic Systems , 2001, Int. J. Bifurc. Chaos.

[10]  K. Shore,et al.  Lag times and parameter mismatches in synchronization of unidirectionally coupled chaotic external cavity semiconductor lasers. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  N. Buric,et al.  Synchronization of hyperchaotic systems with delayed bidirectional coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Roy,et al.  Communication with chaotic lasers , 1998, Science.

[13]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[14]  Voss,et al.  Anticipating chaotic synchronization , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  K. Ikeda,et al.  Study of a high-dimensional chaotic attractor , 1986 .

[16]  K. Ikeda,et al.  High-dimensional chaotic behavior in systems with time-delayed feedback , 1987 .

[17]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[18]  K. Gopalsamy,et al.  Delay induced periodicity in a neural netlet of excitation and inhibition , 1996 .

[19]  Saverio Mascolo,et al.  SYNCHRONIZING HIGH DIMENSIONAL CHAOTIC SYSTEMS VIA EIGENVALUE PLACEMENT WITH APPLICATION TO CELLULAR NEURAL NETWORKS , 1999 .

[20]  C Masoller,et al.  Synchronization regimes of optical-feedback-induced chaos in unidirectionally coupled semiconductor lasers. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  N. Buric,et al.  Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  C. Masoller.  Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback. , 2001, Physical review letters.

[23]  Laurent Larger,et al.  Optical Cryptosystem Based on Synchronization of Hyperchaos Generated by a Delayed Feedback Tunable Laser Diode , 1998 .

[24]  Excitable and oscillatory dynamics in an in-homogeneous chain of excitable systems with delayed coupling , 2004 .

[25]  Ingo Fischer,et al.  Synchronization scenario of two distant mutually coupled semiconductor lasers , 2004 .

[26]  Pere Colet,et al.  Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delay feedback loop , 2003, SPIE OPTO.