Oscillator-phase coupling for different two-dimensional network connectivities.

We investigate the dynamics of large arrays of coupled phase oscillators driven by random intrinsic frequencies under a variety of coupling schemes, by computing the time-dependent cross-correlation function numerically for a two-dimensional array consisting of 128×128 oscillators as well as analytically for a simpler model. Our analysis shows that for overall equal interaction strength, a sparse-coupling scheme in which each oscillator is coupled to a small, randomly selected subset of its neighbors leads to a more rapid and robust phase locking than nearest-neighbor coupling or locally dense connection schemes.

[1]  D. Tilley.  Superradiance in arrays of superconducting weak links , 1970 .

[2]  D. Thouless,et al.  Ordering, metastability and phase transitions in two-dimensional systems , 1973 .

[3]  J. Kosterlitz,et al.  The critical properties of the two-dimensional xy model , 1974 .

[4]  W. Freeman.  Spatial properties of an EEG event in the olfactory bulb and cortex. , 1978, Electroencephalography and clinical neurophysiology.

[5]  P. Holmes,et al.  The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: A mathematical model , 1982, Journal of mathematical biology.

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

[7]  T. Wiesel,et al.  Relationships between horizontal interactions and functional architecture in cat striate cortex as revealed by cross-correlation analysis , 1986, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[8]  Shigeru Shinomoto,et al.  Local and Grobal Self-Entrainments in Oscillator Lattices , 1987 .

[9]  Loft,et al.  Numerical simulation of dynamics in the XY model. , 1987, Physical review. B, Condensed matter.

[10]  S. Strogatz,et al.  CORRIGENDUM: Collective synchronisation in lattices of non-linear oscillators with randomness , 1988 .

[11]  S. Rossignol,et al.  Neural Control of Rhythmic Movements in Vertebrates , 1988 .

[12]  R. A. Davidoff.  Neural Control of Rhythmic Movements in Vertebrates , 1988, Neurology.

[13]  G. Ermentrout,et al.  Coupled oscillators and the design of central pattern generators , 1988 .

[14]  H. Winful,et al.  Dynamics of phase-locked semiconductor laser arrays , 1988 .

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

[16]  Rodney Cotterill,et al.  Models of brain function , 1989 .

[17]  K. Satoh.  Computer Experiment on the Cooperative Behavior of a Network of Interacting Nonlinear Oscillators , 1989 .

[18]  W. Singer,et al.  Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[19]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[20]  S. Strogatz,et al.  Phase diagram for the collective behavior of limit-cycle oscillators. , 1990, Physical review letters.

[21]  G. Ermentrout,et al.  Oscillator death in systems of coupled neural oscillators , 1990 .

[22]  H Sompolinsky,et al.  Global processing of visual stimuli in a neural network of coupled oscillators. , 1990, Proceedings of the National Academy of Sciences of the United States of America.

[23]  W. Singer,et al.  Interhemispheric synchronization of oscillatory neuronal responses in cat visual cortex , 1991, Science.

[24]  Sompolinsky,et al.  Cooperative dynamics in visual processing. , 1991, Physical review. A, Atomic, molecular, and optical physics.

[25]  B. M. Fulk.  MATH , 1992 .