Modified projective phase synchronization of chaotic complex nonlinear systems

This paper introduces the concept of Modified Projective Phase Synchronization (MPPS) for interacting chaotic systems with complex variables. The idea is that the number of effective state variables can be increased by treating the real and imaginary parts separately. On the basis of the Lyapunov stability theory, a scheme is designed to realize the new form of chaotic synchronization, and we demonstrate how chaotic complex systems in a master–slave configuration can be synchronized to a constant scaling matrix. The speed and accuracy of the synchronization are illustrated by means of computer simulation.

[1]  Celso Grebogi,et al.  Basin boundary metamorphoses: changes in accessible boundary orbits , 1987 .

[2]  H. Abarbanel,et al.  Robustness and stability of synchronized chaos: an illustrative model , 1997 .

[3]  E. Ott,et al.  Blowout bifurcations: the occurrence of riddled basins and on-off intermittency , 1994 .

[4]  Dmitry E. Postnov,et al.  SYNCHRONIZATION OF CHAOS , 1992 .

[5]  Gamal M. Mahmoud,et al.  Modified projective synchronization and control of complex Chen and Lü systems , 2011 .

[6]  Zbigniew Galias,et al.  Observations of phase Synchronization Phenomena in One-Dimensional Arrays of Coupled Chaotic Electronic Circuits , 2000, Int. J. Bifurc. Chaos.

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

[8]  I. Stewart,et al.  Bubbling of attractors and synchronisation of chaotic oscillators , 1994 .

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

[10]  Jinghua Xiao,et al.  Antiphase synchronization in coupled chaotic oscillators. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  G. Mahmoud,et al.  Lag synchronization of hyperchaotic complex nonlinear systems , 2012 .

[12]  Ying-Cheng Lai,et al.  ANTIPHASE SYNCHRONISM IN CHAOTIC SYSTEMS , 1998 .

[13]  Emad E. Mahmoud,et al.  Synchronization and control of hyperchaotic complex Lorenz system , 2010, Math. Comput. Simul..

[14]  Emad E. Mahmoud,et al.  Phase and antiphase synchronization of two identical hyperchaotic complex nonlinear systems , 2010 .

[15]  J. Pernier,et al.  Stimulus Specificity of Phase-Locked and Non-Phase-Locked 40 Hz Visual Responses in Human , 1996, The Journal of Neuroscience.

[16]  Emad E. Mahmoud,et al.  Adaptive anti-lag synchronization of two identical or non-identical hyperchaotic complex nonlinear systems with uncertain parameters , 2012, J. Frankl. Inst..

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

[18]  Carroll,et al.  Desynchronization by periodic orbits. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[20]  Guohui Li,et al.  Generalized projective synchronization between Lorenz system and Chen’s system , 2007 .

[21]  H. Haken,et al.  Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[22]  Sergey P. Kuznetsov,et al.  Coupled map lattices with complex order parameter , 2001 .

[23]  A. Balanov,et al.  Synchronization: From Simple to Complex , 2008 .

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

[25]  J. Milnor.  On the concept of attractor , 1985 .

[26]  Emad E. Mahmoud,et al.  Dynamics and synchronization of new hyperchaotic complex Lorenz system , 2012, Math. Comput. Model..

[27]  Emad E. Mahmoud,et al.  Modified Projective Lag Synchronization of Two nonidentical hyperchaotic Complex nonlinear Systems , 2011, Int. J. Bifurc. Chaos.

[28]  Emad E. Mahmoud,et al.  ANALYSIS OF HYPERCHAOTIC COMPLEX LORENZ SYSTEMS , 2008 .

[29]  J. L. Hudson,et al.  Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. , 2000, Chaos.

[30]  Tassos Bountis,et al.  Active Control and Global Synchronization of the Complex Chen and lÜ Systems , 2007, Int. J. Bifurc. Chaos.

[31]  Guohui Li.  Modified projective synchronization of chaotic system , 2007 .

[32]  Michael Peter Kennedy,et al.  The role of synchronization in digital communications using chaos. I . Fundamentals of digital communications , 1997 .

[33]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[34]  Emad E. Mahmoud,et al.  Passive control of n-dimensional chaotic complex nonlinear systems , 2013 .

[35]  Mark J. McGuinness,et al.  The complex Lorenz equations , 1982 .

[36]  Manfeng Hu,et al.  Adaptive feedback controller for projective synchronization , 2008 .

[37]  Celso Grebogi,et al.  Basin boundary metamorphoses: Changes in accessible boundary orbits☆ , 1987 .

[38]  Gamal M. Mahmoud,et al.  BASIC PROPERTIES AND CHAOTIC SYNCHRONIZATION OF COMPLEX LORENZ SYSTEM , 2007 .

[39]  Marco Monti,et al.  Phase Synchronization of Chaos in a plasma discharge tube , 2000, Int. J. Bifurc. Chaos.