This volume consists of proceedings of the one-day conference on "Coupled Oscillating Neurons" held at King's College, London on December 13th, 1990. The subject is currently of increasing interest to neurophysiologists, neural network researchers, applied mathematicians and physicists. The papers attempt to cover the major areas of the subject, as the titles indicate. It is hoped that the appearance of the papers (some of which have been updated since their original presentation) indicates why the subject is becoming of great excitement. A better understanding of coupled oscillating neurons may well hold the key to a clearer appreciation of the manner in which neural networks composed of such elements can control complex behaviour from the heart to consciousness. December 1991 J.G. Taylor King's College, London C.L.T. Mannion CONTENTS Contributors....... ..................... .......... .......................... .................... ix Introduction to Nonlinear Oscillators I. Stewart ....................................................................................... . Identical Oscillator Networks with Symmetry P.B. Ashwin .................................................................................... 21 Bifurcating Neurones AV. Holden, J. Hyde, M.A Muhamad, H.G. Zhang....................... 41 A Model for Low Threshold Oscillations in Neurons J.L. Hindmarsh, R.M. Rose ............................................................ 81 Information Processing by Oscillating Neurons C.L. T. Mannion, J.G. Taylor ........................................................... 100 Gamma Oscillations, Association and Consciousness R.M.J. Cotterill, C. Nielsen ............................................................. 117 Modelling of Cardiac Rhythm: From Single Celis to Massive Networks D. Noble, J. C. Denyer, H.F. Brown, R. Winslow, A Kimball .......... 1 32 CONTRIBUTORS Ashwin, P.B. Mathematics Institute, University of Warwick, Coventry, CV4 7 AL, UK Brown, H.F.

This volume contains the papers from the first British Neural Network Society meeting held at Queen Elizabeth Hall, King's College, London on 18--20 April 1990. The meeting was sponsored by the London Mathemati cal Society. The papers include introductory tutorial lectures, invited, and contributed papers. The invited contributions were given by experts from the United States, Finland, Denmark, Germany and the United Kingdom. The majority of the contributed papers came from workers in the United Kingdom. The first day was devoted to tutorials. Professor Stephen Grossberg was a guest speaker on the first day giving a thorough introduction to his Adaptive Resonance Theory of neural networks. Subsequent tutorials on the first day covered dynamical systems and neural networks, realistic neural modelling, pattern recognition using neural networks, and a review of hardware for neural network simulations. The contributed papers, given on the second day, demonstrated the breadth of interests of workers in the field. They covered topics in pattern recognition, multi-layer feedforward neural networks, network dynamics, memory and learning. The ordering of the papers in this volume is as they were given at the meeting. On the final day talks were given by Professor Kohonen (on self organising maps), Professor Kurten (on the dynamics of random and structured nets) and Professor Cotterill (on modelling the visual cortex). Dr A. Mayes presented a paper on various models for amnesia. The editors have taken the opportunity to include a paper of their own which was not presented at the meeting."