Abstract
We are concerned about burst synchronization (BS), related to neural information processes in health and disease, in the Barabási–Albert scale-free network (SFN) composed of inhibitory bursting Hindmarsh–Rose neurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without considering iSTDP, BS was found to appear in a range of noise intensities for fixed synaptic inhibition strengths. In contrast, in our present work, we take into consideration iSTDP and investigate its effect on BS by varying the noise intensity. Our new main result is to find occurrence of a Matthew effect in inhibitory synaptic plasticity: good BS gets better via LTD, while bad BS get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). We note that, due to inhibition, the roles of LTD and LTP in inhibitory synaptic plasticity are reversed in comparison with those in excitatory synaptic plasticity. Moreover, emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre- and the post-synaptic burst onset times. Finally, in the presence of iSTDP we investigate the effects of network architecture on BS by varying the symmetric attachment degree \(l^*\) and the asymmetry parameter \(\varDelta l\) in the SFN.
Similar content being viewed by others
References
Abbott LF, Blum KI (1996) Functional significance of long-term potentiation for sequence learning and prediction. Cereb Cortex 6:406–416
Abbott LF, Nelson SB (2000) Synaptic plasticity: taming the beast. Nat Neurosci 3:1178–1183
Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97
Barabási AL, Albert R (1999) Emergence of scaling in random networks. Science 286:509–512
Bassett DS, Bullmore E (2006) Small-world brain networks. Neuroscientist 12:512–523
Batista CAS, Batista AM, de Pontes JAC, Viana RL, Lopes SR (2007) Chaotic phase synchronization in scale-free networks of bursting neuron. Phys Rev E 76:016218
Batista CAS, Batista AM, de Pontes JAC, Lopes SR, Viana RL (2009) Bursting synchronization in scale-free networks. Chaos Soliton Fract 41:2220–2225
Batista CAS, Lopes SR, Viana RL, Batista AM (2010) Delayed feedback control of bursting synchronization in a scale-free neuronal network. Neural Netw 23:114–124
Batista CA, Lameu EL, Batista AM, Lopes SR, Pereira T, Zamora-Lopez G, Kurths J, Viana RL (2012) Phase synchronization of bursting neurons in clustered small-world networks. Phys Rev E 86:016211
Bazhenov M, Timofeev I (2006) Thalamocortical oscillations. Scholarpedia 1(6):1319
Bevan M, Magill P, Terman D, Bolam J, Wilson C (2002) Move to the rhythm: oscillations in the subthalamic nucleus-external globus pallidus network. Trends Neurosci 25:525–531
Bi GQ, Poo MM (1998) Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J Neurosci 18:10464–10472
Bi GQ, Poo MM (2001) Synaptic modification by correlated activity: Hebb’s postulate revisited. Annu Rev Neurosci 24:139–166
Bienenstock EL, Cooper LN, Munro PW (1982) Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J Neurosci 2:32–48
Blum KI, Abbott LF (1996) A model of spatial map formation in the hippocampus of the rat. Neural Comput 8:85–93
Bonifazi P, Goldin M, Picardo MA, Jorquera I, Cattani A, Bianconi G, Represa A, Ben-Ari Y, Cossart R (2009) GABAergic hub neurons orchestrate synchrony in developing hippocampal networks. Science 326:1419–1424
Borges RR, Borges FS, Batista AM, Lameu EL, Viana RL, Iarosz KC, Caldas IL, Viana RL, Sanjuán MAF (2016) Effects of spike timing-dependent plasticity on the synchronization in a random Hodgkin–Huxley neuronal network. Commun Nonlinear Sci Numer Simul 34:12–22
Borges RR, Borges FS, Lameu EL, Batista AM, Iarosz KC, Caldas IL, Antonopoulos CG, Baptista MS (2017a) Spike timing-dependent plasticity induces non-trivial topology in the brain. Neural Netw 88:58–64
Borges RR, Borges FS, Lameu EE, Protachevicz PR, Iarosz KC, Caldas IL, Viana RL, Cacau EEN, Baptista MS, Grebogi C, Batista AM (2017b) Synaptic plasticity and spike synchronisation in neuronal networks. Braz J Phys 47:678–688
Brown P (2007) Abnormal oscillatory synchronisation in the motor system leads to impaired movement. Cur Opin Neurobiol 17:656–664
Brunel N, Wang XJ (2003) What determines the frequency of fast network oscillations with irregular neural discharges? I. Synaptic dynamics and excitation-inhibition balance. J Neurophysiol 90:415–430
Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10:186–198
Butera RJ, Rinzel J, Smith JC (1999) Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons. J Neurophysiol 82:382–397
Butz M, Wörgötter F, van Ooyen A (2007) Modelling structural plasticity. BMC Neurosci 2007(8):P194
Butz M, Wörgötter F, van Ooyen A (2008) Activity-dependent structural plasticity. Brain Res Rev 60:287–305
Butz M, Sttenbuck ID, van Ooyen A (2014) Homeostatic structural plasticity increases the efficiency of small-world networks. Front Synaptic Neurosci 6:7
Buzsáki G, Geisler C, Henze DA, Wang XJ (2004) Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci 27:186–193
Caporale N, Dan Y (2008) Spike timing-dependent plasticity: a Hebbian learning rule. Annu Rev Neurosci 31:25–46
Cardin JA (2012) Dissecting local circuits in vivo: integrated optogenetic and electrophysiology approaches for exploring inhibitory regulation of cortical activity. J Physiol (Paris) 106:104–111
Caroni P, Donato F, Muller D (2012) Structural plasticity upon learning: regulation and functions. Nat Rev Neurosci 13:478–490
Castilo PE, Chiu CQ, Carroll RC (2011) Long-term synaptic plasticity at inhibitory synapses. Curr Opin Neurobiol 21:328–338
Chay TR, Keizer J (1983) Minimal model for membrane oscillations in the pancreatic $\beta $-cell. Biophys J 42:181–190
Chklovskii DB, Mel BW, Svoboda K (2004) Cortical rewiring and information storage. Nature 431:782–788
Connors BW, Gutnick MJ (1990) Intrinsic firing patterns of diverse neocortical neurons. Trends Neurosci 13:99–104
Coombes S, Bressloff PC (eds) (2005) Bursting: the genesis of rhythm in the nervous system. World Scientific, Singapore
Dan Y, Poo MM (2004) Spike timing-dependent plasticity of neural circuits. Neuron 44:23–30
Dan Y, Poo MM (2006) Spike timing-dependent plasticity: from synapse to perception. Physiol Rev 86:1033–1048
Debanne D, Gähwiler BH, Thompson SM (1998) Long-term synaptic plasticity between pairs of individual CA3 pyramidal cells in rat hippocampal slice cultures. J Physiol 507(1):237–247
Deisseroth K, Feng G, Majewska AK, Miesenbóck G, Ting A, Schnitzer MJ (2006) Next-generation optical technologies for illuminating genetically targeted brain circuits. J Neurosci 26:10380–10386
Del Negro CA, Hsiao CF, Chandler SH, Garfinkel A (1998) Evidence for a novel bursting mechanism in rodent trigeminal neurons. Biophys J 75:174–182
Dhamala M, Jirsa V, Ding M (2004) Transitions to synchrony in coupled bursting neurons. Phys Rev Lett 92:028101
Duan L, Fan D, Lu Q (2013) Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling. Cogn Neurodyn 7:341–349
Egger V, Feldmeyer D, Sakmann B (1999) Coincidence detection and changes of synaptic efficacy in spiny stellate neurons in rat barrel cortex. Nat Neurosci 2:1098–1105
Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV (2005) Scale-free brain functional networks. Phys Rev Lett 94:018102
Elson RC, Selverston AI, Huerta R, Rulkov NF, Rabinovich MI, Abarbanel HDI (1998) Synchronous behavior of two coupled biological neurons. Phys Rev Lett 81:5691–5695
Engert F, Bonhoeffer T (1999) Dendritic spine changes associated with hippocampal long-term synaptic plasticity. Nature 399:66–70
Feldman DE (2000) Timing-based LTP and LTD at vertical inputs to layer II/III pyramidal cells in rat barrel cortex. Neuron 27:45–56
Feldman DE (2012) The spike-timing dependence of plasticity. Neuron 75:556–571
Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1:1–47
Ferrari FAS, Viana RL, Lopes SR, Stoop R (2015) Phase synchronization of coupled bursting neurons and the generalized Kuramoto model. Neural Netw 66:107–118
Fisher R, van Emde Boas W, Blume W, Elger C, Genton P, Lee P, Engel J (2005) Epileptic seizures and epilepsy: definitions proposed by the International League Against Epilepsy (ILAE) and the International Bureau for Epilepsy (IBE). Epilepsia 46:470–472
Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40:35–41
Freeman LC (1978) Centrality in social networks conceptual clarification. Soc Netw 1:215–239
Froemke RC (2015) Plasticity of cortical excitatory-inhibitory balance. Annu Rev Neurosci 38:195–219
Gafarov FM (2016) Emergence of the small-world architecture in neural networks by activity dependent growth. Physica A 461:409–418
Gafarov FM (2018) Neural electrical activity and neural network growth. Neural Netw 101:15–24
Gaiarsa JL, Caillard O, Ben-Ari Y (2002) Long-term plasticity at GABAergic and glycinergic synapses: mechanisms and functional significance. Trends Neurosci 25:564–570
Gais S, Plihal W, Wagner U, Born J (2000) Early sleep triggers memory for early visual discrimination skills. Nat Neurosci 3:1335–1339
Ganguly K, Poo M-M (2013) Activity-dependent neural plasticity from bench to bedside. Neuron 80:729–741
Gerstner W, Kempter R, van Hemmen JL, Wagner H (1996) A neuronal learning rule for sub-millisecond temporal coding. Nature 383:76–81
Grado L, Johnson M, Netoff T (2015) Optimization of deep brain stimulation parameters using computational models of the basal ganglia with spike-time dependent plasticity. Neuroscience 2015(212):05
Gray CM, McCormick DA (1996) Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274:109–113
Haas J, Nowotny T, Abarbanel H, Zavala B, Landisman C (2006) Spike-timing-dependent plasticity of inhibitory synapses in the entorhinal cortex. J Neurophysiol 96:3305–3313
Hammond C, Bergman H, Brown P (2007) Pathological synchronization in Parkinson’s disease: networks, models and treatments. Trends Neurosci 30:357–364
Hebb DO (1949) The organization of behavior; a neuropsychological theory. Wiley, New York
Hindmarsh JL, Rose RM (1982) A model of the nerve impulse using two first-order differential equations. Nature 296:162–164
Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond Ser B 221:87–102
Hrg D (2013) Synchronization of two Hindmarsh–Rose neurons with unidirectional coupling. Neural Netw 40:73–79
Ivanchenko MV, Osipov GV, Shalfeev VD, Kurths J (2004) Phase synchronization in ensembles of bursting oscillators. Phys Rev Lett 93:134101
Izhikevich EM (2000) Neural excitability, spiking and bursting. Int J Bifurc Chaos 10:1171–1266
Izhikevich EM (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 15:1063–1070
Izhikevich EM (2006) Bursting. Scholarpedia 1(3):1300
Izhikevich EM (2007) Dynamical systems in neuroscience. MIT Press, Cambridge
Izhikevich EM, Desai NS, Walcott EC, Hoppensteadt FC (2003) Bursts as a unit of neural information: selective communication via resonance. Trends Neurosci 26:161–167
Ji D, Wilson M (2007) Coordinated memory replay in the visual cortex and hippocampus during sleep. Nat Neurosci 10:100–107
Jun D, Gaung-jun Z, Yong X, Hong Y, Jeu W (2014) Dynamic behavior analysis of rational-order Hindmarsh–Rose neuronal model. Cogn Neurodyn 8:167–175
Kaiser M, Martin R, Andras P, Young MP (2007) Simulation of robustness against lesions of cortical networks. Eur J Neurosci 25:3185–3192
Kepecs A, van Rossum MCW, Song S, Tegner J (2002) Spike-timing-dependent plasticity: common themes and divergent vistas. Biol Cybern 87:446–458
Kim SY, Lim W (2015a) Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons. Cogn Neurodyn 9:179–200
Kim SY, Lim W (2015b) Thermodynamic order parameters and statistical–mechanical measures for characterization of the burst and spike synchronizations of bursting neurons. Physica A 438:544–559
Kim SY, Lim W (2016) Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons. Neural Netw 79:53–77
Kim SY, Lim W (2018a) Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity. Neural Netw 97:92–106
Kim SY, Lim W (2018b) Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network. Cogn Neurodyn 12:315–342
Kim SY, Lim W (2018c) Effect of spike-timing-dependent plasticity on stochastic spike synchronization in an excitatory neuronal population. In: Delgado-Garcia J, Pan X, Sanchez-Campusano R, Wang R (eds) Advances in Cognitive Neurodynamics (VI). Springer, Singapore, pp 335–341
Kim SY, Lim W (2018d) Effect of inhibitory spike-timing-dependent plasticity on fast sparsely synchronized rhythms in a small-world neuronal network. Neural Netw 106:50–66
Kinard TA, de Vries G, Sherman A, Satin LS (1999) Modulation of the bursting properties of single mouse pancreatic $\beta $-cells by artificial conductances. Biophys J 76:1423–1435
Kornoski J (1948) Conditional reflexes and neuron organization. Cambridge University Press, Cambridge
Krahe R, Gabbian F (2004) Burst firing in sensory system. Nat Rev Neurosci 5:13–23
Kullmann DM, Moreau AW, Bakiri Y, Nicholson E (2012) Plasticity of Inhibition. Neuron 75:951–962
Lameu EL, Batista CAS, Batista AM, Larosz K, Viana RL, Lopes SR, Kurths J (2012) Suppression of bursting synchronization in clustered scale-free (rich-club) neuronal networks. Chaos 22:043149
Lamsa KP, Kullmann DM, Woodin MA (2010) Spike-timing dependent plasticity in inhibitory circuits. Front Synaptic Neurosci 2:8
Larimer P, Strowbridge BW (2008) Nonrandom local circuits in the dentate gyrus. J Neurosci 28:12212–12223
Lee SH, Govindaiah G, Cox CL (2007) Heterogeneity of firing properties among rat thalamic reticular nucleus neurons. J Physiol 582:195–208
Li X, Ouyang G, Usami A, Ikegaya Y, Sik A (2010) Scale-free topology of the CA3 hippocampal network: a novel method to analyze functional neuronal assemblies. Biophys J 98:1733–1741
Lisman J (1997) Bursts as a unit of neural information: making unreliable synapse reliable. Trends Neurosci 20:38–43
Llinás RL, Jahnsen H (1982) Electrophysiology of mammalian thalamic neurons in vitro. Nature 297:406–408
Longtin A (1997) Autonomous stochastic resonance in bursting neurons. Phys Rev E 55:868–876
Lourens MAJ, Schwab BC, Nirody JA, Meijer HGE, van Gils SA (2015) Exploiting pallidal plasticity for stimulation in Parkinson’s disease. J Neural Eng 12:026005
Markram H, Lübke J, Frotscher M, Sakmann B (1997) Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275:213–215
Markram H, Gerstner W, Sjöström PJ (2012) Spike-timing-dependent plasticity: a comprehensive overview. Front Synaptic Neurosci 4:2
McCormick DA, Huguenard JR (1992) A Model of the electrophysiological properties of thalamocortical relay neurons. J Neurophysiol 8:1384–1400
Mehta MR, Wilson M (2000) From hippocampus to V1: effect of LTP on spatiotemporal dynamics of receptive fields. Neurocomputing 32:905–911
Meng P, Wang Q, Lu Q (2013) Bursting synchronization dynamics of pancreatic $\beta $-cells with electrical and chemical coupling. Cogn Neurodyn 7:197–212
Merton RK (1968) The Matthew effect in science. Science 159:56–63
Morgan RJ, Soltesz I (2008) Nonrandom connectivity of the epileptic dentate gyrus predicts a major role for neuronal hubs in seizures. Proc Natl Acad Sci U S A 105:6179–6184
Morrison A, Aertsen A, Diesmann M (2007) Spike-timing-dependent plasticity in balanced random networks. Neural Comput 19:1437–1467
Ngouonkadi EBM, Fostin HB, Nono MK, Fotso PHL (2016) Noise effects on robust synchronization of a small pacemaker neuronal ensemble via nonlinear controller: electronic circuit design. Cogn Neurodyn 10:385–404
Nishikawa T, Motter AE, Lai YC, Hoppensteadt FC (2003) Heterogeneity in oscillator networks: are smaller worlds easier to synchronize? Phys Rev Lett 91:014101
Park C, Worth RM, Rubchinsky LL (2010) Fine temporal structure of beta oscillations synchronization in subthalamic nucleus in Parkinson’s disease. J Neurophysiol 103:2707–2716
Pereira T, Baptista M, Kurths J (2007) Multi-time-scale synchronization and information processing in bursting neuron networks. Eur Phys J Spec Top 146:155–168
Pernarowski M, Miura RM, Kevorkian J (1992) Perturbation techniques for models of bursting electrical activity in pancreatic $\beta $-cells. SIAM J Appl Math 52:1627–1650
Popovych OV, Tass PA (2012) Desynchronizing electrical and sensory coordinated reset neuromodulation. Front Hum Neurosci 6:58
Popovych OV, Yanchuk S, Tass PA (2013) Self-organized noise resistance of oscillatory neural networks with spike-timing-dependent plasticity. Sci Rep 3:2926
Prado TdeL, Lopes SR, Batista CAS, Kurths J, Viana RL (2014) Synchronization of bursting Hodgkin–Huxley-type neurons in clustered networks. Phys Rev E 90:032818
Rinzel J (1985) Bursting oscillations in an excitable membrane model. In: Sleeman BD, Jarvis RJ (eds) Lecture notes in mathematics, ordinary and partial differential equations, vol 1151. Springer, Berlin, pp 304–316
Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: Teramoto E, Yamaguti M (eds) Lecture notes in biomathematics, mathematical topics in population biology, morphogenesis, and neurosciences, vol 71. Springer, Berlin, pp 267–281
Rose RM, Hindmarsh JL (1985) A model of a thalamic neuron. Proc R Soc Lond Ser B 225:161–193
Rostami Z, Jafari S (2018) Defects formation and spiral waves in a network of neurons in presence of electromagnetic induction. Cogn Neurodyn 12:235–254
Rubin J, Lee DD, Sompolinsky H (2001) Equilibrium properties of temporally asymmetric Hebbian plasticity. Phys Rev Lett 86:364–367
San Miguel M, Toral R (2000) Stochastic effects in physical systems. In: Martinez J, Tiemann R, Tirapegui E (eds) Instabilities and nonequilibrium structures VI. Kluwer Academic Publisher, Dordrecht, pp 35–130
Scannell JW, Blakemore C, Young MP (1995) Analysis of connectivity in the cat cerebral cortex. J Neurosci 15:1463–1483
Scannell JW, Burns GAPC, Hilgetag CC, O’Neil MA, Young MP (1999) The connectional organization of the cortico-thalamic system of the cat. Cereb Cortex 9:277–299
Sejnowski TJ (1977) Storing covariance with nonlinearly interacting neurons. J Math Biol 4:303–321
Sejnowski TJ, Destexhe A (2000) Why do we sleep? Brain Res 886:208–223
Shatz CJ (1992) The developing brain. Sci Am 267:60–67
Shi X, Lu Q (2005) Firing patterns and complete synchronization of coupled Hindmarsh–Rose neurons. Chin Phys 14:77–85
Shi X, Lu Q (2009) Burst synchronization of electrically and chemically coupled map-based neurons. Physica A 388:2410–2419
Shilnikov A, Cymbalyuk G (2005) Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Phys Rev Lett 94:048101
Shimazaki H, Shinomoto S (2010) Kernel bandwidth optimization in spike rate estimation. J Comput Neurosci 29:171–182
Song S, Abbott LF (2001) Cortical development and remapping through spike timing-dependent plasticity. Neuron 32:339–350
Song S, Miller KD, Abbott LF (2000) Competitive Hebbian learning through spike-timing-dependent plasticity synaptic plasticity. Nat Neurosci 3:919–926
Song S, Sjöström PJ, Reigl M, Nelson S, Chklovskii DB (2005) Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol 3:e68
Soto-Trevino C, Thoroughman KA, Marder E, Abbott LF (2001) Activity-dependent modification of inhibitory synapses in models of rhythmic neural networks. Nat Neurosci 4:297–303
Sporns O (2011) Networks of the brain. MIT Press, Cambridge
Sporns O, Honey CJ (2006) Small worlds inside big brains. Proc Natl Acad Sci U S A 103:19219–19220
Sporns O, Tononi G, Edelman GM (2000) Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex 10:127–141
Sporns O, Chialvo DR, Kaiser M, Hilgetag CC (2004) Organization, development and function of complex brain networks. Trends Cogn Sci 8:418–425
Stent GS (1973) A physiological mechanism for Hebb’s postulate of learning. Proc Natl Acad Sci U S A 70:997–1001
Steriade M, McCormick DA, Sejnowski TJ (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262:679–685
Stern EA, Jaeger D, Wilson CJ (1998) Membrane potential synchrony of simultaneously recorded striatal spiny neurons in vivo. Nature 394:475–478
Su H, Alroy G, Kirson ED, Yaari Y (2001) Extracellular calcium modulates persistent sodium current-dependent burst-firing in hippocampal pyramidal neurons. J Neurosci 21:4173–4182
Sun X, Lei J, Perc M, Kurths J, Chen G (2011) Burst synchronization transitions in a neuronal network of subnetworks. Chaos 21:016110
Talathi SS, Hwang DU, Ditto WL (2008) Spike timing dependent plasticity promotes synchrony of inhibitory networks in the presence of heterogeneity. J Comput Neurosci 25:262–281
Tanaka G, Ibarz B, Sanjuan MA, Aihara K (2006) Synchronization and propagation of bursts in networks of coupled map neurons. Chaos 16:013113
Tzounopoulos T, Kim Y, Oertel D, Trussell LO (2004) Cell-specific, spike timing-dependent plasticities in the dorsal cochlear nucleus. Nat Neurosci 7:719–725
Uhlhaas PJ, Singer W (2006) Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology. Neuron 52:155–168
van Vreeswijk C, Hansel D (2001) Patterns of synchrony in neural networks with spike adaptation. Neural Comput 13:959–992
Varona P, Torres JJ, Abarbanel HDI, Rabinovych MI, Elson RC (2001) Dynamics of two electrically coupled chaotic neurons: experimental observations and model analysis. Biol Cybern 84:91–101
Vogels TP, Sprekeler H, Zenke F, Clopath C, Gerstner W (2011) Inhibitory plasticity balances excitation and inhibition in sensory pathways and memory networks. Science 334:1569–1573
Vogels TP, Froemke RC, Doyon N, Gilson M, Haas JS, Liu R, Maffei A, Miller P, Wierenga CJ, Wooding MA, Zenke F, Sprekeler H (2013) Inhibitory synaptic plasticity: spike timing-dependence and putative network function. Front Neural Circuits 7:119
von der Malsburg C (1973) Self-organization of orientation sensitive cells in the striate cortex. Kybernetik 14:85–100
Wang Q, Perc M, Duan Z, Chen G (2009) Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. Phys Rev E 80:026206
Wang QY, Murks A, Perc M, Lu QS (2011a) Taming desynchronized bursting with delays in the Macaque cortical network. Chin Phys B 20:040504
Wang Q, Chen G, Perc M (2011b) Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling. PLoS One 6:e15851
Wang H, Wang Q, Lu Q, Zheng Y (2013) Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction. Cogn Neurodyn 7:121–131
Wiedemann C (2010) Neuronal networks: a hub of activity. Nat Rev Neurosci 11:74
Wittenberg GM, Wang SS (2006) Malleability of spike-timing-dependent plasticity at the CA3–CA1 synapse. J Neurosci 26:6610–6617
Womack MD, Khodakhah K (2002) Active contribution of dendrites to the tonic and trimodal patterns of activity in cerebellar Purkinje neurons. J Neurosci 22:10603–10612
Woodin MA, Ganguly K, Poo MM (2003) Coincident pre- and postsynaptic activity modifies GABAergic synapses by postsynaptic changes in Cl-transporter activity. Neuron 39:807–820
Young MP (1993) The organization of neural systems in the primate cerebral cortex. Philos Trans R Soc 252:13–18
Young MP, Scannell JW, Burns GA, Blakemore C (1994) Analysis of connectivity: neural systems in the cerebral cortex. Rev Neurosci 5:227–250
Yu H, Wang J, Deng B, Wei X, Wong YK, Chan WL, Tsang KM, Yu Z (2011) Chaotic phase synchronization in small-world networks of bursting neurons. Chaos 21:013127
Zhang LI, Tao HW, Holt CE, Harris WA, Poo M (1998) A critical window for cooperation and competition among developing retinorectal synapses. Nature 395:37–44
Zhu J, Liu X (2018) Measuring spike timing distance in the Hindmarsh–Rose neurons. Cogn Neurodyn 12:225–234
Acknowledgements
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 20162007688).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kim, SY., Lim, W. Burst synchronization in a scale-free neuronal network with inhibitory spike-timing-dependent plasticity. Cogn Neurodyn 13, 53–73 (2019). https://doi.org/10.1007/s11571-018-9505-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11571-018-9505-1