Linear observer based projective synchronization in delay Rössler system

Abstract A new type of linear observer based projective, projective anticipating and projective lag synchronization of time-delayed Rossler system is studied. Along with this, the approach arbitrarily scales a drive system attractor and hence a similar chaotic attractor of any desired scale can be realized with the help of a synchronizing scaling factor. A scalar synchronizing output is considered where the output equation includes both the delay and non-delay terms of the nonlinear function. The condition for synchronization is derived analytically and the values of the coupling parameters are obtained. Analytical results are verified through numerical investigation and the effect of modulated time delay in the method is discussed. An important aspect of this method is that it does not require the computation of conditional Lyapunov exponents for the verification of synchronization.

[1]  Chil-Min Kim,et al.  Routes to complete synchronization via phase synchronization in coupled nonidentical chaotic oscillators. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  O. Rössler.  An equation for continuous chaos , 1976 .

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

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

[5]  Shuguang Guan,et al.  Phase synchronization between two essentially different chaotic systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  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.

[7]  Santo Banerjee,et al.  Synchronization between two different time-delayed systems and image encryption , 2007 .

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

[9]  Alfredo C. Desages,et al.  Bifurcations and Hopf Degeneracies in Nonlinear Feedback Systems with Time Delay , 1996 .

[10]  Santo Banerjee,et al.  Multiplexing synchronization and its applications in cryptography , 2008 .

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

[12]  C. Masoller.  Anticipation in the synchronization of chaotic time-delay systems , 2001 .

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

[14]  G. Grassi,et al.  Theory and experimental realization of observer-based discrete-time hyperchaos synchronization , 2002 .

[15]  J. M. González-Miranda,et al.  Amplification and displacement of chaotic attractors by means of unidirectional chaotic driving , 1998 .

[16]  J. Kurths,et al.  Heartbeat synchronized with ventilation , 1998, Nature.

[17]  Ulrich Parlitz,et al.  Hyperchaotic dynamics and synchronization of external-cavity semiconductor lasers , 1998 .

[18]  Rong He,et al.  Time delayed chaotic systems and their synchronization , 1999 .

[19]  S. Bishop,et al.  Manipulating the scaling factor of projective synchronization in three-dimensional chaotic systems. , 2001, Chaos.

[20]  L. Wilkens,et al.  Synchronization of the Noisy Electrosensitive Cells in the Paddlefish , 1999 .

[21]  J. Kurths,et al.  Phase Synchronization of Chaotic Oscillators by External Driving , 1997 .

[22]  Zhenya He,et al.  A chaos-generator: analyses of complex dynamics of a cell equation in delayed cellular neural networks , 1998 .

[23]  P. Saha,et al.  Multiple delay Rössler system—Bifurcation and chaos control , 2008 .

[24]  Zhenyuan Xu,et al.  Projective synchronization in drive-response dynamical networks , 2007 .

[25]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[26]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[27]  S. Mascolo,et al.  Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal , 1997 .

[28]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[29]  D Xu,et al.  Control of projective synchronization in chaotic systems. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  Santo Banerjee,et al.  Synchronization between variable time-delayed systems and cryptography , 2007, 0802.0768.

[31]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

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

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

[34]  Kurths,et al.  Synchronization of chaotic structurally nonequivalent systems , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.