title: Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons.
abstract: We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the [Formula: see text]-[Formula: see text] plane ([Formula: see text]: synaptic inhibition strength and [Formula: see text]: noise intensity). As the rewiring probability [Formula: see text] is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the [Formula: see text]-[Formula: see text] plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.
authors.affiliation: Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea.
authors.forename: Sang-Yoon
authors.initials: SY
authors.lastname: Kim
authors.affiliation: Computational Neuroscience Lab., Department of Science Education, Daegu National University of Education, Daegu, 705-115 Korea.
authors.forename: Woochang
authors.initials: W
authors.lastname: Lim
keywords: Noise-induced burst and spike synchronizations; Small-world networks; Subthreshold bursting neurons
references.citation: J Neurosci. 1996 Oct 15;16(20):6402-13
references.pmid: 8815919
references.citation: Cogn Neurodyn. 2014 Jun;8(3):217-26
references.pmid: 24808930
references.citation: Nature. 1994 Jan 20;367(6460):270-3
references.pmid: 11407413
references.citation: Neural Comput. 1995 Mar;7(2):307-37
references.pmid: 8974733
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):740-6
references.pmid: 11046318
references.citation: Proc Natl Acad Sci U S A. 2006 Dec 19;103(51):19219-20
references.pmid: 17159140
references.citation: J Neurophysiol. 2013 Mar;109(5):1457-72
references.pmid: 23221419
references.citation: Artif Life. 2011 Fall;17(4):293-314
references.pmid: 21762020
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061905
references.pmid: 23005125
references.citation: Chaos. 2011 Mar;21(1):016110
references.pmid: 21456852
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Apr;73(4 Pt 1):041929
references.pmid: 16711858
references.citation: Phys Rev Lett. 2004 Jan 16;92(2):028101
references.pmid: 14753970
references.citation: Proc R Soc Lond B Biol Sci. 1984 Mar 22;221(1222):87-102
references.pmid: 6144106
references.citation: Phys Rev Lett. 2001 Aug 27;87(9):098101
references.pmid: 11531600
references.citation: J Comput Neurosci. 1998 Mar;5(1):5-16
references.pmid: 9580271
references.citation: Cogn Neurodyn. 2013 Aug;7(4):341-9
references.pmid: 24427210
references.citation: Annu Rev Neurosci. 2012;35:203-25
references.pmid: 22443509
references.citation: Cogn Neurodyn. 2013 Jun;7(3):197-212
references.pmid: 24427201
references.citation: Phys Rev Lett. 2000 Mar 20;84(12):2758-61
references.pmid: 11017318
references.citation: Chaos. 2008 Mar;18(1):015113
references.pmid: 18377094
references.citation: J Neurophysiol. 1996 Aug;76(2):1310-26
references.pmid: 8871238
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 2):016211
references.pmid: 23005511
references.citation: J Neurosci Methods. 2014 Apr 15;226:161-70
references.pmid: 24487016
references.citation: Neural Comput. 2001 Apr;13(4):751-63
references.pmid: 11255567
references.citation: PLoS Biol. 2005 Mar;3(3):e68
references.pmid: 15737062
references.citation: Cogn Neurodyn. 2013 Dec;7(6):495-503
references.pmid: 24427222
references.citation: Chaos. 2012 Dec;22(4):043149
references.pmid: 23278084
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Dec;76(6 Pt 2):066203
references.pmid: 18233900
references.citation: Proc Natl Acad Sci U S A. 2008 Mar 4;105(9):3593-8
references.pmid: 18292226
references.citation: Nat Rev Neurosci. 2009 Mar;10(3):186-98
references.pmid: 19190637
references.citation: Neuroscientist. 2006 Dec;12(6):512-23
references.pmid: 17079517
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Oct;78(4 Pt 1):041924
references.pmid: 18999472
references.citation: Phys Rev Lett. 2004 May 14;92(19):198101
references.pmid: 15169447
references.citation: Hippocampus. 2001;11(3):251-74
references.pmid: 11769308
references.citation: PLoS Comput Biol. 2006 Jul 21;2(7):e95
references.pmid: 16848638
references.citation: J Neurosci Methods. 2011 Jan 30;195(1):92-106
references.pmid: 21129402
references.citation: J Neurosci. 2008 Nov 19;28(47):12212-23
references.pmid: 19020015
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 2):016218
references.pmid: 17677554
references.citation: J Comput Neurosci. 2010 Aug;29(1-2):171-82
references.pmid: 19655238
references.citation: Nature. 1982 Mar 11;296(5853):162-4
references.pmid: 7063018
references.citation: Cogn Neurodyn. 2014 Apr;8(2):143-9
references.pmid: 24624233
references.citation: Proc R Soc Lond B Biol Sci. 1985 Aug 22;225(1239):161-93
references.pmid: 2864694
references.citation: Cogn Neurodyn. 2014 Apr;8(2):157-66
references.pmid: 24624235
references.citation: PLoS One. 2011 Jan 06;6(1):e15851
references.pmid: 21253015
references.citation: Physiol Rev. 2010 Jul;90(3):1195-268
references.pmid: 20664082
references.citation: Phys Rev Lett. 2004 Sep 24;93(13):134101
references.pmid: 15524723
references.citation: Nature. 2001 Mar 8;410(6825):268-76
references.pmid: 11258382
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 1):051906
references.pmid: 12059592
references.citation: Neural Comput. 2003 Mar;15(3):509-38
references.pmid: 12620157
references.citation: Neural Comput. 2005 Mar;17(3):557-608
references.pmid: 15802007
references.citation: Neural Comput. 2001 May;13(5):959-92
references.pmid: 11359640
references.citation: Chaos. 2007 Jun;17(2):026110
references.pmid: 17614697
references.citation: Chaos. 2011 Mar;21(1):013127
references.pmid: 21456841
references.citation: J Neurosci Methods. 2007 Sep 15;165(1):151-61
references.pmid: 17628690
references.citation: Phys Rev Lett. 2001 Nov 5;87(19):198701
references.pmid: 11690461
references.citation: Cogn Neurodyn. 2013 Apr;7(2):121-31
references.pmid: 24427196
references.citation: J Comput Neurosci. 2011 Nov;31(3):667-77
references.pmid: 21538140
references.citation: J Comput Neurosci. 1994 Dec;1(4):313-21
references.pmid: 8792237
references.citation: Cereb Cortex. 2000 Feb;10(2):127-41
references.pmid: 10667981
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):R1001-4
references.pmid: 11046523
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Dec;80(6 Pt 2):066202
references.pmid: 20365249
references.citation: PLoS Comput Biol. 2007 Feb 2;3(2):e17
references.pmid: 17274684
references.citation: Nature. 1998 Jun 4;393(6684):440-2
references.pmid: 9623998
references.citation: Trends Neurosci. 2004 Apr;27(4):186-93
references.pmid: 15046877
references.citation: Neural Comput. 1996 Feb 15;8(2):215-55
references.pmid: 8581883
references.citation: Cereb Cortex. 2008 Dec;18(12):2891-901
references.pmid: 18400792
references.citation: Nature. 2004 Oct 14;431(7010):782-8
references.pmid: 15483599
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Apr;65(4 Pt 1):040101
references.pmid: 12005793
references.citation: Int J Psychophysiol. 2000 Dec 1;38(3):315-36
references.pmid: 11102670
references.citation: Chaos. 2006 Mar;16(1):013113
references.pmid: 16599744