Generalized synchronization in time-delayed systems.

We investigate the generalized synchronization between two unidirectionally linearly and nonlinearly coupled chaotic nonidentical Ikeda models and find existence conditions of the generalized synchronization. Also we study the chaos synchronization between nonidentical Ikeda models with variable feedback-delay times and find the existence and sufficient stability conditions for the retarded synchronization manifold with the coupling-delay lag time. Generalization of the approach to the wide class of nonlinear chaotic systems is also presented.

[1]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[2]  Pérez,et al.  Extracting messages masked by chaos. , 1995, Physical review letters.

[3]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[4]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[5]  W. Ditto,et al.  Introduction: Control and synchronization of chaos. , 1997, Chaos.

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

[7]  J. Kurths,et al.  Phase synchronization of chaotic oscillations in terms of periodic orbits. , 1997, Chaos.

[8]  Kevin M. Short,et al.  UNMASKING A HYPERCHAOTIC COMMUNICATION SCHEME , 1998 .

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

[10]  Y. Lai,et al.  Observability of lag synchronization of coupled chaotic oscillators. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  C Zhou,et al.  Extracting messages masked by chaotic signals of time-delay systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[12]  K A Shore,et al.  Demonstration of optical synchronization of chaotic external-cavity laser diodes. , 1999, Optics letters.

[13]  Ingo Fischer,et al.  Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication , 2000 .

[14]  J Ohtsubo,et al.  Experimental synchronization of chaotic oscillations in external-cavity semiconductor lasers. , 2000, Optics letters.

[15]  Shore,et al.  Experimental verification of the synchronization condition for chaotic external cavity diode lasers , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[17]  D. L. Valladares,et al.  Characterization of intermittent lag synchronization , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Y. Lai,et al.  Experimental observation of generalized time-lagged chaotic synchronization. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Stefano Boccaletti,et al.  Effect of a Variable Delay in delayed Dynamical Systems , 2001, Int. J. Bifurc. Chaos.

[20]  Hongwei Chen,et al.  Synchronization of optical-feedback-induced chaos in semiconductor lasers by optical injection , 2001 .

[21]  D. Zanette,et al.  Anticipated synchronization in coupled chaotic maps with delays , 2001, nlin/0104061.

[22]  L. Shampine,et al.  Solving DDEs in MATLAB , 2001 .

[23]  H U Voss,et al.  Dynamic long-term anticipation of chaotic states. , 2001, Physical review letters.

[24]  John R. Terry,et al.  Chaotic communication using generalized synchronization , 2001 .

[25]  E. M. Shahverdiev,et al.  Experimental demonstration of anticipating synchronization in chaotic semiconductor lasers with optical feedback. , 2001, Physical review letters.

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

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

[28]  K. Shore,et al.  Inverse anticipating chaos synchronization. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  K A Shore,et al.  Parameter mismatches and perfect anticipating synchronization in bidirectionally coupled external cavity laser diodes. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  P. Colet,et al.  Criteria for synchronization of coupled chaotic external-cavity semiconductor lasers , 2002, IEEE Photonics Technology Letters.

[31]  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.

[32]  K. A. Shore,et al.  Dual-time and cascaded anticipation of chaos synchronization , 2002, SPIE OPTO.

[33]  E. M. Shahverdiev,et al.  Lag synchronization in time-delayed systems , 2002 .

[34]  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.

[35]  Meng Zhan,et al.  Complete synchronization and generalized synchronization of one-way coupled time-delay systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Young-Jai Park,et al.  Synchronization of delayed systems in the presence of delay time modulation , 2003, nlin/0305053.