Dynamics of a ring of pulse-coupled oscillators: Group theoretic approach

被引:68
作者
Bressloff, PC
Coombes, S
deSouza, B
机构
[1] Nonlinear and Complex Systems Group, Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, Leicestershire
关键词
D O I
10.1103/PhysRevLett.79.2791
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We use group-theoretic methods to analyze phase-locking in a ring of identical integrate-and-fire oscillators with distributed delays. It is shown how certain phase-locked solutions emerge through symmetry breaking bifurcations as some characteristic delay of the system is varied. The reduction to a phase-coupled model in the weak coupling regime is discussed.
引用
收藏
页码:2791 / 2794
页数:4
相关论文
共 19 条
[1]  
ARONSON DG, 1991, NONLINEARITY, V4, P902
[2]   THE DYNAMICS OF N-WEAKLY COUPLED IDENTICAL OSCILLATORS [J].
ASHWIN, P ;
SWIFT, JW .
JOURNAL OF NONLINEAR SCIENCE, 1992, 2 (01) :69-108
[3]   PULSE-COUPLED RELAXATION-OSCILLATORS - FROM BIOLOGICAL SYNCHRONIZATION TO SELF-ORGANIZED CRITICALITY [J].
BOTTANI, S .
PHYSICAL REVIEW LETTERS, 1995, 74 (21) :4189-4192
[4]   Synchrony in an array of integrate-and-fire neurons with dendritic structure [J].
Bressloff, PC ;
Coombes, S .
PHYSICAL REVIEW LETTERS, 1997, 78 (24) :4665-4668
[5]  
BRESSLOFF PC, UNPUB
[6]   COUPLED NONLINEAR OSCILLATORS AND THE SYMMETRIES OF ANIMAL GAITS [J].
COLLINS, JJ ;
STEWART, IN .
JOURNAL OF NONLINEAR SCIENCE, 1993, 3 (03) :349-392
[7]   Desynchronization of pulse-coupled integrate-and-fire neurons [J].
Coombes, S ;
Lord, GJ .
PHYSICAL REVIEW E, 1997, 55 (03) :R2104-R2107
[8]   FREQUENCY PLATEAUS IN A CHAIN OF WEAKLY COUPLED OSCILLATORS .1. [J].
ERMENTROUT, GB ;
KOPELL, N .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1984, 15 (02) :215-237
[9]   THE BEHAVIOR OF RINGS OF COUPLED OSCILLATORS [J].
ERMENTROUT, GB .
JOURNAL OF MATHEMATICAL BIOLOGY, 1985, 23 (01) :55-74
[10]   SYNCHRONIZATION INDUCED BY TEMPORAL DELAYS IN PULSE-COUPLED OSCILLATORS [J].
ERNST, U ;
PAWELZIK, K ;
GEISEL, T .
PHYSICAL REVIEW LETTERS, 1995, 74 (09) :1570-1573