Synchronization and beam forming in an array of repulsively coupled oscillators.

We study the dynamics of an array of Stuart-Landau oscillators with repulsive coupling. Autonomous network with global repulsive coupling settles on one from a continuum of synchronized regimes characterized by zero mean field. Driving this array by an external oscillatory signal produces a nonzero mean field that follows the driving signal even when the oscillators are not locked to the external signal. At sufficiently large amplitude the external signal synchronizes the oscillators and locks the phases of the array oscillations. Application of this system as a beam-forming element of a phase array antenna is considered. The phase dynamics of the oscillator array synchronization is used to reshape the phases of signals received from the phase array antenna and improve its beam pattern characteristics.

[1]  Kurt Wiesenfeld,et al.  Stability results for in-phase and splay-phase states of solid-state laser arrays , 1993 .

[2]  I. Aranson,et al.  The world of the complex Ginzburg-Landau equation , 2001, cond-mat/0106115.

[3]  Visarath In,et al.  Nonlinear antenna technology , 2002, Proc. IEEE.

[4]  Pan-Jun Kim,et al.  Pattern formation in a two-dimensional array of oscillators with phase-shifted coupling. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  A. A. Dvornikov,et al.  Mutual synchronization of a chain of resistance-coupled self-excited oscillators , 1984 .

[6]  S. Strogatz,et al.  Frequency locking in Josephson arrays: Connection with the Kuramoto model , 1998 .

[7]  Hidetsugu Sakaguchi,et al.  Cooperative Phenomena in Coupled Oscillator Systems under External Fields , 1988 .

[8]  L. Tsimring,et al.  Globally coupled noisy oscillators with inhomogeneous periodic forcing. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Y. Kuramoto,et al.  Phase transitions in active rotator systems , 1986 .

[10]  J. Acebrón,et al.  Asymptotic description of transients and synchronized states of globally coupled oscillators , 1998 .

[11]  Michael Gabbay,et al.  Phased array beamforming using nonlinear oscillators , 2004, SPIE Optics + Photonics.

[12]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[13]  Peter Lynch,et al.  The Dolph-Chebyshev Window: A Simple Optimal Filter , 1997 .

[14]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[15]  C.L. Dolph,et al.  A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level , 1946, Proceedings of the IRE.

[16]  Kurt Wiesenfeld,et al.  Manipulated Synchronization: Beam Steering in Phased Arrays , 2000, Int. J. Bifurc. Chaos.

[17]  S. Strogatz,et al.  Stability of incoherence in a population of coupled oscillators , 1991 .

[18]  Lev S Tsimring,et al.  Plasticity and learning in a network of coupled phase oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  R. G. Medhurst,et al.  Topics in the Theory of Random Noise , 1969 .

[20]  L S Tsimring,et al.  Repulsive synchronization in an array of phase oscillators. , 2005, Physical review letters.

[21]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[22]  Shigeru Shinomoto,et al.  Mutual Entrainment in Oscillator Lattices with Nonvariational Type Interaction , 1988 .

[23]  J. Crawford,et al.  Scaling and singularities in the entrainment of globally coupled oscillators. , 1995, Physical review letters.

[24]  S. Strogatz,et al.  Time Delay in the Kuramoto Model of Coupled Oscillators , 1998, chao-dyn/9807030.

[25]  Patrick S. Hagan,et al.  Spiral Waves in Reaction-Diffusion Equations , 1982 .