Download Coupled Oscillating Neurons by Ian Stewart (auth.), John Gerald Taylor BA, BSc, MA, PhD, PDF

By Ian Stewart (auth.), John Gerald Taylor BA, BSc, MA, PhD, FlnstP, C. L. T. Mannion BSc, PhD, MlnstP (eds.)

This quantity involves lawsuits of the one-day convention on "Coupled Oscillating Neurons" held at King's collage, London on December thirteenth, 1990. the topic is at the moment of accelerating curiosity to neurophysiologists, neural community researchers, utilized mathematicians and physicists. The papers try and disguise the foremost parts of the topic, because the titles point out. it's was hoping that the looks of the papers (some of that have been up-to-date seeing that their unique presentation) exhibits why the topic is turning into of serious pleasure. a greater realizing of coupled oscillating neurons may possibly carry the major to a clearer appreciation of the style during which neural networks composed of such parts can keep watch over complicated behaviour from the center to cognizance. December 1991 J.G. Taylor King's university, London C.L.T. Mannion CONTENTS Contributors....... ..................... .......... .......................... .................... ix advent to Nonlinear Oscillators I. Stewart ....................................................................................... . exact Oscillator Networks with Symmetry P.B. Ashwin .................................................................................... 21 Bifurcating Neurones AV. Holden, J. Hyde, M.A Muhamad, H.G. Zhang....................... forty-one A version for Low Threshold Oscillations in Neurons J.L. Hindmarsh, R.M. Rose ............................................................ eighty one details Processing through Oscillating Neurons C.L. T. Mannion, J.G. Taylor ........................................................... a hundred Gamma Oscillations, organization and recognition R.M.J. Cotterill, C. Nielsen ............................................................. 117 Modelling of Cardiac Rhythm: From unmarried Celis to giant Networks D. Noble, J. C. Denyer, H.F. Brown, R. Winslow, A Kimball .......... 1 32 members Ashwin, P.B. arithmetic Institute, college of Warwick, Coventry, CV4 7 AL, united kingdom Brown, H.F.

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Hopf bifurcation in the presence of symmetry. Arch. Rat. Mech. , 87:107-165, 1985. W. Swift. Hopf bifurcation with the symmetry of the square. Nonlinearity, 1:333-377,1988. [27] M. Hirsch, C. Pugh, and M. Shub. Invariant Manifolds, volume 583 of LNM. Springer, Berlin, 1977. A. Sanders and F. Verhulst. Averaging methods in nonlinear dynamical systems. App. Math. Sci. 59. Springer, New York, 1985. B. Ermentrout. The behavior of rings of coupled oscillators. J. Math. , 23:55-74, 1985. G. Aronson, M.

1 Experiments An electronic van der Pol oscillator The oscillator consists of a parallel inductor-capacitor-resistor (LCR) network, the circuit being shown in figure 4. 2 Electronic simulation of an S3 network of oscillators Three van der Pol oscillators were coupled through a low-pass filter made of a star configuration of resistors earthed through a capacitor at the central node, as shown in figure 5. This provides a network with approximate S3 symmetry 30 = Co 10nF I~) I(V) = symmetry 6 x IN4148 switch diodes Figure 4: (a) The circuit for one van der Pol oscillator.

Reprinted 1985 by Princeton University Press. S. W. Cumming. Three-frequency quasiperiodicity, phase locking and the onset of chaos. Physica D, 40:196-217, 1990. 39 [16] P. R. Beasley, and K. Wiesenfeld. Phase locking of Josephson junction series arrays. Phys Rev B, 38:8712-8719, 1988. [17] P. Hadley. Dynamics of Josephson junction arrays. PhD thesis, Dept of Applied Physics, Stanford University, 1989. [18] K. Wiesenfeld and P. Hadley. Attractor crowding in oscillator arrays. Preprint, Dept. , 1988.

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