Abstract
We study spike–burst neural activity and investigate its transitions to synchronized states under electrical coupling. Our reported results include the following: (1) Synchronization of spike–burst activity is a multi-time scale phenomenon and burst synchrony is easier to achieve than spike synchrony. (2) Synchrony of networks with time-delayed connections can be achieved at lower coupling strengths than within the same network with instantaneous couplings. (3) The introduction of parameter dispersion into the network destroys the existence of synchrony in the strict sense, but the network dynamics in major regimes of the parameter space can still be effectively captured by a mean field approach if the couplings are excitatory. Our results on synchronization of spiking networks are general of nature and will aid in the development of minimal models of neuronal populations. The latter are the building blocks of large scale brain networks relevant for cognitive processing.
Similar content being viewed by others
References
Abeles M (1991) Corticonics. Cambridge University Press, New York
Abeles M, Bergman H, Margalit E, Vaadia E (1993) Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. J Neurophysiol 70:1629–1638
Amzica F, Steriade M (1998) Electrophysiological correlates of sleep delta waves. Electroencephalogr Clin Neurophysiol 107(2):69–83
Aradi I, Soltesz I (2002) Modulation of network behaviour by changes in variance in interneuronal properties. J Physiol 538(Pt 1):227–251
Assisi CG, Jirsa VK, Kelso JAS (2005) Synchrony and clustering in heterogeneous networks with global coupling and parameter dispersion. Phys Rev Lett 94(1):018106
Avoli M, Gloor P, Kostopoulos G, Naquet R (1990) Generalized epilepsy. Neurobiological approaches. Birkhauser, Boston
Breakspear M, Jirsa V (2007) Handbook of Brain Connectivity, chapter Neuronal Dynamics and Brain Connectivity. Springer, New York
Bressler S (1990) The gamma wave: a cortical information carrier?. Trends Neurosci 13(5):161–162
Bressler S, Kelso JAS (2001) Cortical coordination dynamics. Trends Cogn Sci 5:26–36
Bressler SL, Tognoli E (2006) Operational principles of neurocognitive networks. Int J Psychophysiol 60(2):139–148
Buhmann J (1989) Oscillations and low firing rates in associative memory neural networks. Phys Rev A 40(7):4145–4148
Bullmore E, Rabe-Hesketh S, Morris RG, Williams SC, Gregory L, Gray JA, Brammer MJ (1996) Functional magnetic resonance image analysis of a large-scale neurocognitive network. Neuroimage 4:16–33
Crick F, Koch C (1990) Towards a neurobiological theory of consciousness. Semin Neurosci 2:263–275
Desmedt JE, Tomberg C (1994) Transient phase-locking of 40 hz electrical oscillations in prefrontal and parietal human cortex reflects the process of conscious somatic perception. Neurosci Lett 168(1–2):126–129
Dhamala M, Jirsa VK, Ding M (2004a) Enhancement of neural synchrony by time delay. Phys Rev Lett 92(7):074104
Dhamala M, Jirsa VK, Ding M (2004b). Transitions to synchrony in coupled bursting neurons. Phys Rev Lett 92(2):028101
Freeman AS, Meltzer LT, Bunney BS (1985) Firing properties of substantia nigra dopaminergic neurons in freely moving rats. Life Sci 36(20):1983–1994
Grace AA, Bunney BS (1984) The control of firing pattern in nigral dopamine neurons: burst firing. J Neurosci 4(11):2877–2890
Hindmarsh JL, Rose RM (1982) A model of the nerve impulse using two first-order differential equations. Nature 296(5853):162–164
Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B Biol Sci 221(1222):87–102
Hosford DA, Clark S, Cao Z, Wilson WA, Lin FH, Morrisett RA, Huin A (1992) The role of GABAB receptor activation in absence seizures of lethargic (lh/lh) mice. Science 257(5068):398–401
Izhikevich EM (2000) Neural excitability, spiking and bursting. Int J Bifurcation Chaos 10(6):1171–1266 doi:10.1142/S0218127400000840
Jirsa VK (2004) Connectivity and dynamics of neural information processing. Neuroinformatics 2(2):183–204
Jirsa VK, McIntosh AR (2007) Handbook of brain connectivity. Springer, Berlin Heidelberg New York
Koch C (1999) Biophysics of computation. Information processing in single neurons, Oxford University Press
Koob GF, Vaccarino FJ, Amalric M, Bloom FE (1987) Brain reward systems and abuse. Raven Press, New York, pp 35
Ljungberg T, Apicella P, Schultz W (1992) Responses of monkey dopamine neurons during learning of behavioral reactions. J Neurophysiol 67(1):145–163
MacDonald N (1989) Biological delay systems: linear stability theory. Cambridge University Press ISBN: 0521340845
Matthews PC, Strogatz SH (1990) Phase diagram for the collective behavior of limit-cycle oscillators. Phys Rev Lett 65(14):1701–1704
McCormick DA, Feeser HR (1990) Functional implications of burst firing and single spike activity in lateral geniculate relay neurons. Neuroscience 39(1):103–113
McIntosh AR (2000) Towards a network theory of cognition. Neural Netw 13:861–876
Mesulam MM (1998) From sensation to cognition. Ann Neurol 28:597–613
Miltner WH, Braun C, Arnold M, Witte H, Taub E (1999) Coherence of gamma-band EEG activity as a basis for associative learning. Nature 397(6718):434–6
Milton J, Chkhenkeli S, Towle V (2007) Handbook of Brain Connectivity, chapter Brain Connectivity and the Spread of Epileptic Seizures. Springer, Berlin Heidelberg New York
Monte SD, d’Ovidio F, Mosekilde E (2003) Coherent regimes of globally coupled dynamical systems. Phys Rev Lett 90(5):054102
Mountcastle VB (1998) Perceptual Neuroscience: the cerebral cortex. Harvard University Press, Cambridge
Pecora LM, Carroll TL (1990). Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824
Pecora LM, Carroll TL (1998) Master stability functions for synchronized coupled systems. Phys Rev Lett 80(10):2109–2112
Rinzel J, Lee YS (1987) Dissection of a model for neuronal parabolic bursting. J Math Biol 25(6):653–675
Roelfsema PR, Engel AK, Knig P, Singer W (1997) Visuomotor integration is associated with zero time-lag synchronization among cortical areas. Nature 385(6612):157–161
Rosenblum MG, Pikovsky AS, Kurths J (1996) Phase synchronization of chaotic oscillators. Physical Review Letters 76(11):1804–1807
Rubin J, Terman D (2000) Analysis of clustered firing patterns in synaptically coupled networks of oscillators. J Math Biol 41(6):513–545
Schultz W (1998) Predictive reward signal of dopamine neurons. J Neurophysiol 80(1):1–27
Sherman SM, Kock C (1986) The control of retinogeniculate transmission in the mammalian lateral geniculate nucleus. Exp Brain Res 63:120
Singer W, Gary CM (1995) Visual feature integration and the temporal correlation hypothesis. Annu Rev Neurosci 18:555–586
Snead OC (1995) Basic mechanisms of generalized absence seizures. Ann Neurol 37(2):146–157
Sporns O, Gally JA, Reeke GN, Edelman GM (1989) Reentrant signaling among simulated neuronal groups leads to coherency in their oscillatory activity. Proc Natl Acad Sci USA, 86(18):7265–7269
Steriade M, Llinas RR (1988) The functional states of the thalamus and the associated neuronal interplay. Physiol Rev 68(3):649–742
Steriade M, McCormick DA, Sejnowski TJ (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262(5134):679–685
Strogatz SH, Mirollo RE (1993). Splay states in globally coupled Josephson arrays: analytical prediction of Floquet multipliers. Physical Review E 47(1):220–227
Tallon-Baudry C, Bertrand O, Fischer C (2001) Oscillatory synchrony between human extrastriate areas during visual short-term memory maintenance. J Neurosci 21(RC177):1–5
Treisman A (1996) The binding problem. Curr Opin Neurobiol 6:171–178
Von Stein A, Rappelsberger P, Sarnthein J, Petsche H (1999) Synchronization between temporal and parietal cortex during multimodal object processing in man. Cereb Cortex 9:137–150
Weinberger DR (1987) Implications of normal brain development for the pathogenesis of schizophrenia. Arch Gen Psychiatry 44(7):660–669
Acknowledgments
I wish to thank Mukesh Dhamala and Collins Assisi for many discussions, as well as assistance with some of the numerical simulations. This research was previously presented at the ENOC 2005 and funded by the grants Brain NRG JSM22002082, ATIP (CNRS), and ONR grant N000140510104.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jirsa, V.K. Dispersion and time delay effects in synchronized spike–burst networks. Cogn Neurodyn 2, 29–38 (2008). https://doi.org/10.1007/s11571-007-9030-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11571-007-9030-0