Experimental investigation of high-quality synchronization of coupled oscillators.

We describe two experiments in which we investigate the synchronization of coupled periodic oscillators. Each experimental system consists of two identical coupled electronic periodic oscillators that display bursts of desynchronization events similar to those observed previously in coupled chaotic systems. We measure the degree of synchronization as a function of coupling strength. In the first experiment, high-quality synchronization is achieved for all coupling strengths above a critical value. In the second experiment, no high-quality synchronization is observed. We compare our results to the predictions of the several proposed criteria for synchronization. We find that none of the criteria accurately predict the range of coupling strengths over which high-quality synchronization is observed. (c) 2000 American Institute of Physics.

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

[2]  Michael Menzinger,et al.  On the local stability of limit cycles. , 1999, Chaos.

[3]  Experimental Verification of Noise Induced Attractor Deformation. , 1999 .

[4]  Rahul Konnur.  Attractor Bubbling, Control, and Desynchronization of Chaotic Systems , 1997 .

[5]  Anne E. Trefethen,et al.  Hydrodynamic Stability Without Eigenvalues , 1993, Science.

[6]  Jürgen Parisi,et al.  Nonlinear Physics of Complex Systems , 1996 .

[7]  Kestutis Pyragas.  Predictable chaos in slightly perturbed unpredictable chaotic systems , 1993 .

[8]  Hirokazu Fujisaka,et al.  Statistical Dynamics Generated by Fluctuations of Local Lyapunov Exponents , 1983 .

[9]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[10]  James A. Yorke,et al.  Effect of Noise on Nonhyperbolic Chaotic Attractors , 1998 .

[11]  I. Stewart,et al.  From attractor to chaotic saddle: a tale of transverse instability , 1996 .

[12]  N. Rulkov,et al.  Robustness of Synchronized Chaotic Oscillations , 1997 .

[13]  Gebhardt,et al.  Chaos transition despite linear stability. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  T. Kapitaniak,et al.  MONOTONE SYNCHRONIZATION OF CHAOS , 1996 .

[15]  T. Carroll,et al.  Synchronization and Imposed Bifurcations in the Presence of Large Parameter Mismatch , 1998 .

[16]  Gauthier,et al.  Intermittent Loss of Synchronization in Coupled Chaotic Oscillators: Toward a New Criterion for High-Quality Synchronization. , 1996, Physical review letters.

[17]  Peng,et al.  Synchronizing hyperchaos with a scalar transmitted signal. , 1996, Physical review letters.

[18]  F. Kärtner,et al.  Turbulence in mode-locked lasers , 1999 .

[19]  Nikolai F. Rulkov,et al.  Designing a Coupling That Guarantees Synchronization between Identical Chaotic Systems , 1997 .

[20]  H. Kantz,et al.  Homoclinic tangencies and non-normal Jacobians—effects of noise in nonhyperbolic chaotic systems , 1997 .