Stability and optimization of chaos synchronization through feedback coupling with delay

Abstract We perform the stability and optimization analysis for the (non)delayed synchronization of Duffing-like oscillators, using a retroactive scheme. Stability boundaries are derived through Floquet theory. Critical values for the feedback synchronization coefficient are found. The influence of the delay and of the onset time of the driving upon stability and synchronization time is also analyzed.

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

[2]  P Woafo,et al.  Transitions to chaos and synchronization in a nonlinear emitter–receiver system , 2000 .

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

[4]  K.Murali,et al.  Secure communication using a compound signal from generalized synchronizable chaotic systems , 1997, chao-dyn/9709025.

[5]  N J Corron.  Loss of synchronization in coupled oscillators with ubiquitous local stability. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[7]  J. J. Stoker.  Nonlinear Vibrations in Mechanical and Electrical Systems , 1950 .

[8]  M. Lakshmanan,et al.  Chaos in Nonlinear Oscillators: Controlling and Synchronization , 1996 .

[9]  André Longtin,et al.  Synchronization of delay-differential equations with application to private communication , 1998 .

[10]  Ricardo Femat,et al.  Synchronization of a class of strictly different chaotic oscillators , 1997 .

[11]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[12]  Ulrich Parlitz,et al.  Superstructure in the bifurcation set of the Duffing equation ẍ + dẋ + x + x3 = f cos(ωt) , 1985 .

[13]  Carroll,et al.  Driving systems with chaotic signals. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[14]  C. Hayashi,et al.  Nonlinear oscillations in physical systems , 1987 .

[15]  T. Kapitaniak,et al.  Synchronization of chaos using continuous control. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  S. Boccaletti,et al.  ADAPTIVE SYNCHRONIZATION OF CHAOS FOR SECURE COMMUNICATION , 1997 .

[17]  Malescio.  Synchronization of chaotic systems by continuous control. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[18]  Earl H. Dowell,et al.  On chaos and fractal behavior in a generalized Duffing's system , 1988 .