Pulse-coupled chemical oscillators with time delay.

Finger on the pulse: in a system of two pulse-coupled Belousov-Zhabotinsky oscillators, introducing a time delay or increasing the coupling strength brings about novel dynamic features (see picture, the two oscillators are shown in different colors), such as reversal of the roles of excitatory and inhibitory coupling or fast anti-phase oscillation. These features are not observed in diffusively coupled systems, and shed light on how such pulse coupling occurs at synapses.

[1]  F. W. Schneider,et al.  PATTERN RECOGNITION BY ELECTRICAL COUPLING OF EIGHT CHEMICAL REACTORS , 1999 .

[2]  M. Timme,et al.  Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling , 2005, cond-mat/0501384.

[3]  P. Jonas,et al.  Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks , 2007, Nature Reviews Neuroscience.

[4]  Michael F. Crowley,et al.  Electrically coupled Belousov-Zhabotinskii oscillators. 1. Experiments and simulations , 1986 .

[5]  M. Rosenblum,et al.  Controlling oscillator coherence by delayed feedback. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  P. Ruoff,et al.  Potentiometric and spectrophotometric studies of the silver bromide reaction in 1 M sulfuric acid and its relevance to silver ion perturbed bromate-driven oscillators , 1989 .

[7]  Irving R Epstein,et al.  Diffusively coupled chemical oscillators in a microfluidic assembly. , 2008, Angewandte Chemie.

[8]  Kenneth Showalter,et al.  Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos , 1996 .

[9]  Vladimir I. Nekorkin,et al.  Synchronization of time-delay coupled pulse oscillators , 2011 .

[10]  Wei Wu,et al.  Analysis of firing behaviors in networks of pulse-coupled oscillators with delayed excitatory coupling , 2010, Neural Networks.

[11]  T. Geisel,et al.  Delay-induced multistable synchronization of biological oscillators , 1998 .

[12]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[13]  I. Schreiber,et al.  Dynamical regimes of a pH-oscillator operated in two mass-coupled flow-through reactors. , 2011, Physical chemistry chemical physics : PCCP.

[14]  R. Holz,et al.  Control of dynamic states with time delay between two mutually flow rate coupled reactors , 1993 .

[15]  Klaus Lehnertz,et al.  Recurrent events of synchrony in complex networks of pulse-coupled oscillators , 2011 .

[16]  Cheng Ly,et al.  Analysis of Recurrent Networks of Pulse-Coupled Noisy Neural Oscillators , 2010, SIAM J. Appl. Dyn. Syst..

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

[18]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[19]  Z. Noszticzius NON-BROMIDE(1-) ION-CONTROLLED OSCILLATIONS IN THE BELOUSOV-ZHABOTINSKII REACTION OF MALONIC ACID , 1979 .

[20]  Bard Ermentrout,et al.  When inhibition not excitation synchronizes neural firing , 1994, Journal of Computational Neuroscience.

[21]  A. Selverston,et al.  Dynamical principles in neuroscience , 2006 .

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

[23]  R Huerta,et al.  Robustness and enhancement of neural synchronization by activity-dependent coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  John L Hudson,et al.  Emerging Coherence in a Population of Chemical Oscillators , 2002, Science.