Stability of spatio-temporal structures in a lattice model of pulse-coupled oscillators

We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By studying the intrinsic dynamics of each member of the population and their mutual interactions we observe the emergence of either spatio-temporal structures or synchronized regimes. We perform a linear stability analysis of these structures.

[1]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[2]  W. Gerstner,et al.  Time structure of the activity in neural network models. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Arenas,et al.  Synchronization in a lattice model of pulse-coupled oscillators. , 1995, Physical review letters.

[4]  B. M. Fulk MATH , 1992 .

[5]  Y. Kuramoto Collective synchronization of pulse-coupled oscillators and excitable units , 1991 .

[6]  L. F. Abbott,et al.  Self-Sustained Firing in Populations of Integrate-and-Fire Neurons , 1993, SIAM J. Appl. Math..

[7]  Arenas,et al.  Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators. , 1994, Physical review letters.

[8]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[9]  John J. Hopfield,et al.  Neurons, Dynamics and Computation , 1994 .

[10]  Ernst,et al.  Synchronization induced by temporal delays in pulse-coupled oscillators. , 1995, Physical review letters.

[11]  Bottani Pulse-coupled relaxation oscillators: From biological synchronization to self-organized criticality. , 1995, Physical review letters.

[12]  G. Bard Ermentrout,et al.  Synchronization in a pool of mutually coupled oscillators with random frequencies , 1985 .

[13]  C. T. Genís Entrainment in pacemakers characterized by a V-shaped PRC. , 1986 .

[14]  A. Winfree The geometry of biological time , 1991 .

[15]  Tang,et al.  Self-Organized Criticality in Nonconserved Systems. , 1995, Physical review letters.

[16]  James D. Kurfess,et al.  The Compton Gamma Ray Observatory , 1993 .

[17]  J. Rinzel,et al.  INTEGRATE-AND-FIRE MODELS OF NERVE MEMBRANE RESPONSE TO OSCILLATORY INPUT. , 1981 .

[18]  Abbott,et al.  Asynchronous states in networks of pulse-coupled oscillators. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Charles S. Peskin,et al.  Mathematical aspects of heart physiology , 1975 .

[20]  J. Hopfield,et al.  Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements. , 1995, Physical review letters.

[21]  Chen Threshold effects on synchronization of pulse-coupled oscillators. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[22]  C. J. P'erez,et al.  ON SELF-ORGANIZED CRITICALITY AND SYNCHRONIZATION IN LATTICE MODELS OF COUPLED DYNAMICAL SYSTEMS , 1996, cond-mat/9601102.