Synchronization in two neurons: Results for a two-component dynamical model with time-delayed inhibition

Physica D: Nonlinear Phenomena

Volumn 114, Issue 1-2, 1998, Pages 147-171

  Renversez, Gilles ^a,b  

^a CNRS   (France)

^b AIX MARSEILLE UNIVERSITY   (France)

Author keywords

Inhibition; Neuronal modelling; Phase plane analysis; Synchronization; Time delayed coupling

Indexed keywords

APPROXIMATION THEORY; BIOLOGICAL MEMBRANES; COMPUTER SIMULATION; MODELS; PIECEWISE LINEAR TECHNIQUES; SYNCHRONIZATION;

INHIBITION; MEMBRANE CONDUCTANCE; NEURONS; PHASE PLANE ANALYSIS; TIME DELAYED COUPLING;

NEURAL NETWORKS;

EID: 0032027291     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00149-8     Document Type: Article

References (41)

1. L.F. Abbott and T.B. Kepler, Model neurons: From Hodgkin-Huxley to Hopfield, in: Statistical Mechanics of Neural Networks, ed. L. Garrido (Springer, Berlin, 1990).
2. A.P. Andersen, J.C. Eccles and Y. Loyning, Recurrent inhibition in the Hippocampus with identification of the inhibitory cell and its synapses, Nature 198 (1963) 540-542.
3. A.P. Andersen, J.C. Eccles and Y. Loyning, Pathway of postsynaptic inhibition in the Hippocampus, J. Neurophysiology 27 (1964) 608-619.
4. E. Av-Ron, H. Parnas and L.A. Segel, A minimal biophysical model for excitable and oscillatory neuron, Biol. Cybernet. 65 (1991) 487-500.
5. D.L. Benson and P.A. Cohen, Activity-independent segregation of excitatory and inhibitory synaptic terminals in cultured hippocampal neurons, J. Neurosci. 16 (1996) 6414-6432.
6. T.W. Blackstad and P.R. Flood, Ultrastructure of hippocampal axo-somatic synapses, Nature 198 (1963) 542-543.
7. V. Braitenberg and A. Schuz, Anatomy of the Cortex: Statistics and Geometry (Springer, Berlin, 1991).
8. G. Buzsáki and J.J. Chrobak, Temporal structure in spatially organized neuronal ensembles: a role for interneuronal networks, Current Biology 5 (1995) 504-510.
9. C.E. Carr and M. Konishi, Axonal delay line for time measurement in the owl's brainstem, Proc. Nat. Academy Sci. 85 (1988) 8311-8315.
10. A. Destexhe, Z. Mainen and T.J. Sejnowski, Synaptic currents, neuromodulation and kinetics models, in: The Handbook of Brain Theory and Neural Networks, ed. A. Arbib (MIT Press, Cambridge, MA, 1995) pp. 956-959.
11. U. Ernst, K. Pawelzik and T. Geisel, Synchronization induced by temporal delays in pulse-coupled oscillators, Phys. Rev. Lett. 74 (1995) 1570-1573.
12. W. Gerstner, R. Ritz and J. Leo van Hemmen, Why spikes? Hebbian learning and retrieval of time resolved excitation patterns, Biol. Cybernet. 69 (1993) 503-515.
13. J. Grasman, Asymptotic Methods for Relaxation Oscillations and Applications (Springer, Berlin, 1987).
14. E.G. Gray, Axo-somatic and axo-dendritic synapses of the cerebral cortex: An electron microscope study, J. Anat. 93 (1959) 420-433.
15. L.B. Haberly, Summed potentials evoked in opossum prepyriform cortex, J. Neurophysiology 36 (1973) 775-788.
16. C. Hammond and D. Trisch, Neurobiologie Cellulaire (Doin, Paris, 1990).
17. D. Hansel, G. Mato and C. Meunier, Phase dynamics for weakly coupled Hodgkin-Huxley neurons, Europhys. Lett. 23 (1993) 369-372.
18. D. Hansel, G. Mato and C. Meunier, Synchrony in excitatory neural networks, Neural Comput. 7 (1995) 307-337.
19. A.L. Hodgkin and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117 (1952) 500-544.
20. E.R. Kandel and J.H. Schwartz, Directly gated transmission at central synapses, in: Principles of Neural Science, eds. E.R. Kandel, J.H. Schwartz and T.M. Jessell, Ch. 11 (Prentice-Hall, London, 1991) pp. 153-172.
21. E.R. Kandel, J.H. Schwartz and T.M. Jessell, Principles of Neural Science, 3rd Ed. (Prentice-Hall, London, 1991).
22. T.B. Kepler, L.F. Abbott and E. Marder, Reduction of conductance based neuron models, Biol. Cybernet. 66 (1992) 381-387.
23. J. Koester, Passive membrane properties of the neuron, in: Principles of Neural Science, eds. E.R. Kandel, J.H. Schwartz and T.M. Jessell, Ch. 7 (Prentice-Hall, London, 1991) pp. 96-103.
24. V.I. Krinskii and Y.M. Kokoz, Analysis of the equations of excitable membranes: I. Reduction of the Hodgkin-Huxley equations to a second order system, Biofizika 18 (1973) 506-511.
25. R. Miles, R.D. Traub and R.K.S. Wong, Spread of synchronous firing in longitudinal slices from the CA3 region in the Hippocampus, J. Neurophysiology 60 (1988) 1471-1496.
26. C. Morris and H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophys. Journal 35 (1981) 193-213.
27. E. Niebur, H.G. Schuster and D.M. Kammen, Collective frequencies and metastability in networks of limit-cycle oscillators with time delays, Phys. Rev. Lett. 67 (1991) 2753-2756.
28. A. Nischwitz and H. Glünder, Local lateral inhibition: A key to spike synchronization?, Biol. Cybernet. 73 (1995) 389-400.
29. L.G. Nowak and J. Bullier, The timing of information transfer in the visual system, Cerebral Cortex 12 (1997) in press.
30. R.E. Plant, Simple analogs for nerve membrane equations, in: Nonlinear Systems and Applications, ed. V. Lakshmikantham (Academic Press, New York, 1997) pp. 647-654.
31. G. Renversez and O. Parodi, Synchronization in neural oscillators through local delayed inhibition, in: Spatiotemporal Models in Biological and Artificial Systems, eds. F.L. Silva, J.C. Principe and L.B. Almeida (IOS Press, Amsterdam, 1996) pp. 144-151.
32. J. Rinzel and G.B. Ermentrout, Analysis of neural excitability and oscillations, in: Methods in Neuronal Modeling: From synapses to Networks, eds. C. Koch and I. Segev (MIT Press, Cambridge, MA, 1989) pp. 135-169.
33. J. Rinzel and J.B. Keller, Traveling waves solutions of a nerve conduction equation, Biophys. J. 13 (1973) 1313-1337.
34. M. Robertson and K.G. Pearson, Neural circuits in the flight system of the locust, J. Neurophysiology 53 (1985) 110-128.
35. H.G. Schuster and P. Wagner, Mutual entrainment of two limit cycle oscillators with time delayed couplings, Prog. Theor. Phys. 81 (1989) 939-945.
36. D. Somers and N. Kopell, Rapid synchronization through fast threshold modulation, Biol. Cybernet. 68 (1993) 393-407.
37. D. Somers and N. Kopell, Waves and synchrony in networks of oscillators of relaxation and non-relaxation type, Physica D 89 (1995) 169-183.
38. D. Terman and D. Wang, Global competition and local cooperation in a network of neural oscillators, Physica D 81 (1995) 148-176.
39. S. Thorpe, Spike arrival times: A highly efficient coding scheme for neural networks, in: Parallel Processing in Neural Systems, eds. R. Eckmiller, G. Hartman and G. Hauske (Elsevier, Amsterdam, 1990) pp. 91-94.
40. C. van Vreeswijk, L.F. Abbott and G.B. Ermentrout, When inhibition not excitation synchronizes neural firing, J. Comput. Neurosci. 1 (1994) 313-321.
41. M.A. Whittington, R.D. Traub and J.G.R. Jefferys, Synchronized oscillations in interneuron networks driven by metabotropic glutamate receptor activation, Nature 373 (1995) 612-615.