Synchronized firings in the networks of class 1 excitable neurons with excitatory and inhibitory connections and their dependences on the forms of interactions

Neural Computation

Volumn 17, Issue 6, 2005, Pages 1315-1338

  Kanamaru, Takashi ^a   Sekine, Masatoshi ^a  

^a TOKYO UNIVERSITY OF AGRICULTURE AND TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; CENTRAL NERVOUS SYSTEM; CORTICAL SYNCHRONIZATION; EXCITATORY POSTSYNAPTIC POTENTIAL; HUMAN; INTERNEURON; NERVE CELL; NERVE CELL INHIBITION; NERVE CELL NETWORK; NERVE TRACT; PHYSIOLOGY; SYNAPTIC TRANSMISSION; TIME;

ACTION POTENTIALS; ANIMALS; CENTRAL NERVOUS SYSTEM; CORTICAL SYNCHRONIZATION; EXCITATORY POSTSYNAPTIC POTENTIALS; HUMANS; INTERNEURONS; NERVE NET; NEURAL INHIBITION; NEURAL NETWORKS (COMPUTER); NEURAL PATHWAYS; NEURONS; SYNAPTIC TRANSMISSION; TIME FACTORS;

EID: 18444406285     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/0899766053630387     Document Type: Article

References (32)

1. Abbott, L. F., & van Vreeswijk, C. (1993) Asynchronous states in networks of pulse-coupled oscillators. Physical Review E, 48, 1483-1490.
2. Börgers, C., & Kopell, N. (2003). Synchronization in networks of excitatory and inhibitory neurons with sparse, random connectivity. Neural Computation, 15, 509-538.
3. Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience, 8, 183-208.
4. Buzsáki, G., Horváth, Z., Urioste, R., Hetke, J., & Wise, K. (1992). High-frequency network oscillation in the hippocampus. Science, 256, 1025-1027.
5. Ermentrout, B. (1996). Type I membranes, phase resetting curves, and synchrony. Neural Computation, 8, 979-1001.
6. Fisahn, A., Pike, F. G., Buhl, E. H., & Paulsen, O. (1998). Cholinergic induction of network oscillations at 40Hz in the hippocampus in vitro. Nature, 394, 186-189.
7. Gardiner, C. W. (1985). Handbook of stochastic methods. Berlin: Springer-Verlag.
8. Gerstner, W., & Kistler, W. (2002). Spiking neuron models. Cambridge: Cambridge University Press.
9. Golomb, D., & Ermentrout, G. B. (2001). Bistability in pulse propagation in networks of excitatory and inhibitory populations. Physical Review Letters, 86, 4179-4182.
10. Gray, C. M. (1994). Synchronous oscillations in neuronal systems: Mechanisms and functions. Journal of Computational Neuroscience, 1, 11-38.
11. Gray, C. M., & Singer, W. (1989). Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proceedings of the National Academy of Sciences of USA, 86, 1698-1702.
12. Guckenheimer, J., & Holmes, P. (1983). Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. New York: Springer.
13. Hansel, D., & Mato, G. (2003). Asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons. Neural Computation, 15, 1-56.
14. Hansel, D., Mato, G., & Meunier, C. (1995). Synchrony in excitatory neural networks. Neural Computation, 7, 307-337.
15. Hoppensteadt, F. C., & Izhikevich, E. M. (1997). Weakly connected neural networks. New York: Springer.
16. Izhikevich, E. M. (1999). Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models. IEEE Transactions on Neural Networks, 10, 499-507.
17. Kanamaru, T., & Sekine, M. (2003). Analysis of globally connected active rotators with excitatory and inhibitory connections using the Fokker-Planck equation. Physical Review E, 67, 031916.
18. Kanamaru, T., & Sekine, M. (2004). An analysis of globally connected active rotators with excitatory and inhibitory connections having different time constants using the nonlinear Fokker-Planck equations. IEEE Transactions on Neural Networks, 15, 1009-1017.
19. Kuramoto, Y. (1984). Chemical oscillations, waves, and turbulence. Berlin: Springer.
20. Kuramoto, Y. (1991). Collective synchronization of pulse-coupled oscillators and excitable units. Physica D, 50, 15-30.
21. Kurrer, C., & Schulten, K. (1995). Noise-induced synchronous neuronal oscillations. Physical Review E, 51, 6213-6218.
22. Mirollo, R. E., & Strogatz, S. H. (1990). Synchronization of pulse-coupled biological oscillators. SIAM Journal of Applied Mathematics, 50, 1645-1662.
23. Ott, E., (1993). Chaos in dynamical systems. Cambridge: Cambridge University Press.
24. Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. (1988). Numerical recipes in C. Cambridge: Cambridge University Press.
25. Sakaguchi, H., Shinomoto, S., & Kuramoto, Y. (1988). Phase transitions and their bifurcation analysis in a large population of active rotators with mean-field coupling. Progress of Theoretical Physics, 79, 600-607.
26. Sato, Y. D., & Shiino, M. (2002). Spiking neuron models with excitatory or inhibitory synaptic couplings and synchronization phenomena. Physical Review E, 66, 041903.
27. Shinomoto, S., & Kuramoto, Y. (1986). Phase transitions in active rotator systems. Progress of Theoretical Physics, 75, 1105-1110.
28. Tanabe, S., Shimokawa, T., Sato, S., & Pakdaman, K. (1999). Response of coupled noisy excitable systems to weak stimulation. Physical Review E, 60, 2182-2185.
29. Tsodyks, M., Mitkov, I., & Sompolinsky, H. (1993). Pattern of synchrony in inhomogeneous networks of oscillators with pulse interactions. Physical Review Letters, 71, 1280-1283.
30. van Vreeswijk, C. (1996). Partial synchronization in populations of pulse-coupled oscillators. Physical Review E, 54, 5522-5537.
31. van Vreeswijk, C., Abbott, L. F., & Ermentrout, G. B. (1994). When inhibition not excitation synchronizes neural firing. Journal of Computational Neuroscience, 1, 313-321.
32. van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274, 1724-1726.