Slowly coupled oscillators: Phase dynamics and synchronization

SIAM Journal on Applied Mathematics

Volumn 63, Issue 6, 2003, Pages 1935-1953

  Izhikevich, Eugene M ^a   Hoppensteadt, Frank C ^b  

^a NEUROSCIENCES INSTITUTE   (United States)

^b ARIZONA STATE UNIVERSITY   (United States)

Author keywords

Andronov Hopf; Class 1 excitability; Malkin theorem; MATLAB; Phase model; Relaxation oscillators; Saddle node on invariant circle

Indexed keywords

ASYMPTOTIC STABILITY; BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; COUPLED CIRCUITS; INTEGRAL EQUATIONS; MATRIX ALGEBRA; RELAXATION OSCILLATORS; SYNCHRONIZATION; VECTORS;

COUPLED OSCILLATORS; EXCITABILITY; MALKIN THEOREM; MATLAB; PHASE DYNAMICS; PHASE MODEL; SADDLE NODE ON INVARIANT CIRCLE;

MATHEMATICAL MODELS;

EID: 1642421812     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139902400945     Document Type: Article

References (15)

1. P.C. Bressloff and S. Coombes (2000), Dynamics of strongly coupled spiking neurons, Neural Computation, 12, pp. 91-129.
2. G.B. Ermentrout (1994), Reduction of conductance-based models with slow synapses to neural nets, Neural Computation, 6, pp. 679-695.
3. G.B. Ermentrout (1996), Type I membranes, phase resetting curves, and synchrony, Neural Computation, 8, pp. 979-1001.
4. P. Frankel and T. Kiemel (1993), Relative phase behavior of two slowly coupled oscillators, SIAM J. Appl. Math., 53, pp. 1436-1446.
5. D. Hansel, G. Mato, and C. Meunier (1995), Synchrony in excitatory neural networks, Neural Computations, 7, pp. 307-335.
6. F.C. Hoppensteadt and E.M. Izhikevich (1997), Weakly Connected Neural Networks, Springer-Verlag, New York.
7. J.T. Isaac, R.A. Nicoll, and R.C. Malenka (1995), Evidence for silent synapses: Implications for the expression of LTP, Neuron, 15, pp. 427-34.
8. J.T. Isaac, M.C. Crair, R.A. Nicoll, and R.C. Malenka (1997), Silent synapses during development of thalamocortical inputs, Neuron, 18, pp. 269-280.
9. E.M. Izhikevich (2000), Phase equations for relaxation oscillators, SIAM J. Appl. Math., 60, pp. 1789-1804.
10. E.M. Izhikevich (1999), Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models, IEEE Trans. Neural Networks, 10, pp. 499-507.
11. Y. Kuramoto (1984), Chemical Oscillations, Waves, and Turbulence, Springer-Verlag, New York.
12. I.G. Malkin (1949), Methods of Poincare and Liapunov in Theory of Non-linear Oscillations, Gostexizdat, Moscow (in Russia).
13. I.G. Malkin (1956), Some Problems in Nonlinear Oscillation Theory, Gostexizdat, Moscow (in Russian).
14. J. Rinzel and P. Frankel (1992) Activity patterns of a slow synapse network predicted by explicitly averaging spike dynamics, Neural Computation, 4, pp. 534-545.
15. T.L. Williams and G. Bowtell (1997), The calculation of frequency-shift functions for chains of coupled oscillators, with application to a network model of the lamprey locomotor pattern generator, J. Comput. Neurosci., 4, pp. 47-55.