Skip to main content
Top
Published in: Cognitive Neurodynamics 1/2020

10-07-2019 | Research Article

Cluster burst synchronization in a scale-free network of inhibitory bursting neurons

Authors: Sang-Yoon Kim, Woochang Lim

Published in: Cognitive Neurodynamics | Issue 1/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We consider a scale-free network of inhibitory Hindmarsh–Rose (HR) bursting neurons, and make a computational study on coupling-induced cluster burst synchronization by varying the average coupling strength \(J_0\). For sufficiently small \(J_0\), non-cluster desynchronized states exist. However, when passing a critical point \(J^*_c~(\simeq 0.16)\), the whole population is segregated into 3 clusters via a constructive role of synaptic inhibition to stimulate dynamical clustering between individual burstings, and thus 3-cluster desynchronized states appear. As \(J_0\) is further increased and passes a lower threshold \(J^*_l~(\simeq 0.78)\), a transition to 3-cluster burst synchronization occurs due to another constructive role of synaptic inhibition to favor population synchronization. In this case, HR neurons in each cluster make burstings every 3rd cycle of the instantaneous burst rate \(R_w(t)\) of the whole population, and exhibit burst synchronization. However, as \(J_0\) passes an intermediate threshold \(J^*_m~(\simeq 5.2)\), HR neurons fire burstings intermittently at a 4th cycle of \(R_w(t)\) via burst skipping rather than at its 3rd cycle, and hence they begin to make intermittent hoppings between the 3 clusters. Due to such intermittent intercluster hoppings via burst skippings, the 3 clusters become broken up (i.e., the 3 clusters are integrated into a single one). However, in spite of such break-up (i.e., disappearance) of the 3-cluster states, (non-cluster) burst synchronization persists in the whole population, which is well visualized in the raster plot of burst onset times where bursting stripes (composed of burst onset times and indicating burst synchronization) appear successively. With further increase in \(J_0\), intercluster hoppings are intensified, and bursting stripes also become dispersed more and more due to a destructive role of synaptic inhibition to spoil the burst synchronization. Eventually, when passing a higher threshold \(J^*_h~(\simeq 17.8)\) a transition to desynchronization occurs via complete overlap between the bursting stripes. Finally, we also investigate the effects of stochastic noise on both 3-cluster burst synchronization and intercluster hoppings.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
go back to reference Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97CrossRef Albert R, Barabási AL (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97CrossRef
go back to reference Aronson DG, Golubitsky M, Krupa M (1991) Coupled arrays of Josephson junctions and bifurcation of maps with \(S_N\) symmetry. Nonlinearity 4:861–902CrossRef Aronson DG, Golubitsky M, Krupa M (1991) Coupled arrays of Josephson junctions and bifurcation of maps with \(S_N\) symmetry. Nonlinearity 4:861–902CrossRef
go back to reference 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 76:016218CrossRef 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 76:016218CrossRef
go back to reference Batista CAS, Batista AM, de Pontes JAC, Lopes SR, Viana RL (2009) Bursting synchronization in scale-free networks. Chaos Soliton Fract 41:2220–2225CrossRef Batista CAS, Batista AM, de Pontes JAC, Lopes SR, Viana RL (2009) Bursting synchronization in scale-free networks. Chaos Soliton Fract 41:2220–2225CrossRef
go back to reference Batista CAS, Lopes SR, Viana RL, Batista AM (2010) Delayed feedback control of bursting synchronization in a scale-free neuronal network. Neural Netw 23:114–124PubMedCrossRef Batista CAS, Lopes SR, Viana RL, Batista AM (2010) Delayed feedback control of bursting synchronization in a scale-free neuronal network. Neural Netw 23:114–124PubMedCrossRef
go back to reference 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 86:016211CrossRef 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 86:016211CrossRef
go back to reference Bazhenov M, Timofeev I (2006) Thalamocortical oscillations. Scholarpedia 1(6):1319CrossRef Bazhenov M, Timofeev I (2006) Thalamocortical oscillations. Scholarpedia 1(6):1319CrossRef
go back to reference Belykh I, Hasler M (2011) Mesoscale and clusters of synchrony in networks of bursting neurons. Chaos 21:016106PubMedCrossRef Belykh I, Hasler M (2011) Mesoscale and clusters of synchrony in networks of bursting neurons. Chaos 21:016106PubMedCrossRef
go back to reference Belykh VN, Osipov GV, Petrov VS, Suykens JAK, Vandewalle J (2008) Cluster synchronization in oscillatory networks. Chaos 18:037106PubMedCrossRef Belykh VN, Osipov GV, Petrov VS, Suykens JAK, Vandewalle J (2008) Cluster synchronization in oscillatory networks. Chaos 18:037106PubMedCrossRef
go back to reference 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 25:525–531PubMedCrossRef 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 25:525–531PubMedCrossRef
go back to reference 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 326:1419–1424PubMedCrossRef 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 326:1419–1424PubMedCrossRef
go back to reference Brown P (2007) Abnormal oscillatory synchronisation in the motor system leads to impaired movement. Cur Opin Neurobiol 17:656–664CrossRef Brown P (2007) Abnormal oscillatory synchronisation in the motor system leads to impaired movement. Cur Opin Neurobiol 17:656–664CrossRef
go back to reference 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 90:415–430PubMedCrossRef 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 90:415–430PubMedCrossRef
go back to reference Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10:186–198PubMedCrossRef Bullmore E, Sporns O (2009) Complex brain networks: graph theoretical analysis of structural and functional systems. Nat Rev Neurosci 10:186–198PubMedCrossRef
go back to reference Butera RJ, Rinzel J, Smith JC (1999) Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons. J Neurophysiol 82:382–397PubMedCrossRef Butera RJ, Rinzel J, Smith JC (1999) Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons. J Neurophysiol 82:382–397PubMedCrossRef
go back to reference Buzsáki G, Geisler C, Henze DA, Wang XJ (2004) Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci 27:186–193PubMedCrossRef Buzsáki G, Geisler C, Henze DA, Wang XJ (2004) Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci 27:186–193PubMedCrossRef
go back to reference Chik DTW, Coombes S, Wang ZD (2004) Clustering through postinhibitory rebound in synaptically coupled neurons. Phys Rev E 70:011908CrossRef Chik DTW, Coombes S, Wang ZD (2004) Clustering through postinhibitory rebound in synaptically coupled neurons. Phys Rev E 70:011908CrossRef
go back to reference Chklovskii DB, Mel BW, Svoboda K (2004) Cortical rewiring and information storage. Nature 431:782–788PubMedCrossRef Chklovskii DB, Mel BW, Svoboda K (2004) Cortical rewiring and information storage. Nature 431:782–788PubMedCrossRef
go back to reference Connors BW, Gutnick MJ (1990) Intrinsic firing patterns of diverse neocortical neurons. Trends Neurosci 13:99–104PubMedCrossRef Connors BW, Gutnick MJ (1990) Intrinsic firing patterns of diverse neocortical neurons. Trends Neurosci 13:99–104PubMedCrossRef
go back to reference Coombes S, Bressloff PC (eds) (2005) Bursting: the genesis of rhythm in the nervous system. World Scientific, Singapore Coombes S, Bressloff PC (eds) (2005) Bursting: the genesis of rhythm in the nervous system. World Scientific, Singapore
go back to reference Dhamala M, Jirsa V, Ding M (2004) Transitions to synchrony in coupled bursting neurons. Phys Rev Lett 92:028101PubMedCrossRef Dhamala M, Jirsa V, Ding M (2004) Transitions to synchrony in coupled bursting neurons. Phys Rev Lett 92:028101PubMedCrossRef
go back to reference Duan L, Fan D, Lu Q (2013) Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling. Cogn Neurodyn 7:341–349PubMedPubMedCentralCrossRef Duan L, Fan D, Lu Q (2013) Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling. Cogn Neurodyn 7:341–349PubMedPubMedCentralCrossRef
go back to reference Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV (2005) Scale-free brain functional networks. Phys Rev Lett 94:018102PubMedCrossRef Eguíluz VM, Chialvo DR, Cecchi GA, Baliki M, Apkarian AV (2005) Scale-free brain functional networks. Phys Rev Lett 94:018102PubMedCrossRef
go back to reference Elson RC, Selverston AI, Huerta R, Rulkov NF, Rabinovich MI, Abarbanel HDI (1998) Synchronous behavior of two coupled biological neurons. Phys Rev Lett 81:5691–5695CrossRef Elson RC, Selverston AI, Huerta R, Rulkov NF, Rabinovich MI, Abarbanel HDI (1998) Synchronous behavior of two coupled biological neurons. Phys Rev Lett 81:5691–5695CrossRef
go back to reference Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1:1–47PubMedCrossRef Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in the primate cerebral cortex. Cereb Cortex 1:1–47PubMedCrossRef
go back to reference Ferrari FAS, Viana RL, Lopes SR, Stoop R (2015) Phase synchronization of coupled bursting neurons and the generalized Kuramoto model. Neural Netw 66:107–118PubMedCrossRef Ferrari FAS, Viana RL, Lopes SR, Stoop R (2015) Phase synchronization of coupled bursting neurons and the generalized Kuramoto model. Neural Netw 66:107–118PubMedCrossRef
go back to reference Fisher R, van Emde BW, 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 46:470–472PubMedCrossRef Fisher R, van Emde BW, 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 46:470–472PubMedCrossRef
go back to reference Gais S, Plihal W, Wagner U, Born J (2000) Early sleep triggers memory for early visual discrimination skills. Nat Neurosci 3:1335–1339PubMedCrossRef Gais S, Plihal W, Wagner U, Born J (2000) Early sleep triggers memory for early visual discrimination skills. Nat Neurosci 3:1335–1339PubMedCrossRef
go back to reference Golomb D, Rinzel J (1994) Clustering in globally coupled inhibitory neurons. Phys D 72:259–282CrossRef Golomb D, Rinzel J (1994) Clustering in globally coupled inhibitory neurons. Phys D 72:259–282CrossRef
go back to reference Gray CM, McCormick DA (1996) Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274:109–113PubMedCrossRef Gray CM, McCormick DA (1996) Chattering cells: superficial pyramidal neurons contributing to the generation of synchronous oscillations in the visual cortex. Science 274:109–113PubMedCrossRef
go back to reference Hammond C, Bergman H, Brown P (2007) Pathological synchronization in Parkinson’s disease: networks, models and treatments. Trends Neurosci 30:357–364PubMedCrossRef Hammond C, Bergman H, Brown P (2007) Pathological synchronization in Parkinson’s disease: networks, models and treatments. Trends Neurosci 30:357–364PubMedCrossRef
go back to reference Hindmarsh JL, Rose RM (1982) A model of the nerve impulse using two first-order differential equations. Nature 296:162–164PubMedCrossRef Hindmarsh JL, Rose RM (1982) A model of the nerve impulse using two first-order differential equations. Nature 296:162–164PubMedCrossRef
go back to reference Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond Ser B 221:87–102CrossRef Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond Ser B 221:87–102CrossRef
go back to reference Ivanchenko MV, Osipov GV, Shalfeev VD, Kurths J (2004) Phase synchronization in ensembles of bursting oscillators. Phys Rev Lett 93:134101PubMedCrossRef Ivanchenko MV, Osipov GV, Shalfeev VD, Kurths J (2004) Phase synchronization in ensembles of bursting oscillators. Phys Rev Lett 93:134101PubMedCrossRef
go back to reference Izhikevich EM (2000) Neural excitability, spiking and bursting. Int J Bifurcat Chaos 10:1171–1266CrossRef Izhikevich EM (2000) Neural excitability, spiking and bursting. Int J Bifurcat Chaos 10:1171–1266CrossRef
go back to reference Izhikevich EM (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 15:1063–1070PubMedCrossRef Izhikevich EM (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 15:1063–1070PubMedCrossRef
go back to reference Izhikevich EM (2007) Dynamical systems in neuroscience. MIT Press, Cambridge Izhikevich EM (2007) Dynamical systems in neuroscience. MIT Press, Cambridge
go back to reference Izhikevich EM, Desai NS, Walcott EC, Hoppensteadt FC (2003) Bursts as a unit of neural information: selective communication via resonance. Trends Neurosci 26:161–167PubMedCrossRef Izhikevich EM, Desai NS, Walcott EC, Hoppensteadt FC (2003) Bursts as a unit of neural information: selective communication via resonance. Trends Neurosci 26:161–167PubMedCrossRef
go back to reference Kaiser M, Martin R, Andras P, Young MP (2007) Simulation of robustness against lesions of cortical networks. Eur J Neurosci 25:3185–3192PubMedCrossRef Kaiser M, Martin R, Andras P, Young MP (2007) Simulation of robustness against lesions of cortical networks. Eur J Neurosci 25:3185–3192PubMedCrossRef
go back to reference Kim SY, Lim W (2015a) Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons. Cogn Neurodyn 9:179–200PubMedCrossRef Kim SY, Lim W (2015a) Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons. Cogn Neurodyn 9:179–200PubMedCrossRef
go back to reference Kim SY, Lim W (2015b) Thermodynamic order parameters and statistical-mechanical measures for characterization of the burst and spike synchronizations of bursting neurons. Phys A 438:544–559CrossRef Kim SY, Lim W (2015b) Thermodynamic order parameters and statistical-mechanical measures for characterization of the burst and spike synchronizations of bursting neurons. Phys A 438:544–559CrossRef
go back to reference Kim SY, Lim W (2016) Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons. Neural Netw 79:53–77PubMedCrossRef Kim SY, Lim W (2016) Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons. Neural Netw 79:53–77PubMedCrossRef
go back to reference Kim SY, Lim W (2018) Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network. Cogn Neurodyn 12:315–342PubMedPubMedCentralCrossRef Kim SY, Lim W (2018) Effect of spike-timing-dependent plasticity on stochastic burst synchronization in a scale-free neuronal network. Cogn Neurodyn 12:315–342PubMedPubMedCentralCrossRef
go back to reference 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 76:1423–1435PubMedPubMedCentralCrossRef 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 76:1423–1435PubMedPubMedCentralCrossRef
go back to reference Kiss IZ, Zhai Y, Hudson H (2005) Predicting mutual entrainment of oscillators with experiment-based phase models. Phys Rev Lett 94:248301PubMedCrossRef Kiss IZ, Zhai Y, Hudson H (2005) Predicting mutual entrainment of oscillators with experiment-based phase models. Phys Rev Lett 94:248301PubMedCrossRef
go back to reference 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 22:043149PubMedCrossRef 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 22:043149PubMedCrossRef
go back to reference Langdon AJ, Breakspear M, Coombes S (2012) Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations. Phys Rev E 86:061903CrossRef Langdon AJ, Breakspear M, Coombes S (2012) Phase-locked cluster oscillations in periodically forced integrate-and-fire-or-burst neuronal populations. Phys Rev E 86:061903CrossRef
go back to reference 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 98:1733–1741PubMedPubMedCentralCrossRef 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 98:1733–1741PubMedPubMedCentralCrossRef
go back to reference Lisman J (1997) Bursts as a unit of neural information: making unreliable synapse reliable. Trends Neurosci 20:38–43PubMedCrossRef Lisman J (1997) Bursts as a unit of neural information: making unreliable synapse reliable. Trends Neurosci 20:38–43PubMedCrossRef
go back to reference Llinás RL, Jahnsen H (1982) Electrophysiology of mammalian thalamic neurons in vitro. Nature 297:406–408PubMedCrossRef Llinás RL, Jahnsen H (1982) Electrophysiology of mammalian thalamic neurons in vitro. Nature 297:406–408PubMedCrossRef
go back to reference Longtin A (1997) Autonomous stochastic resonance in bursting neurons. Phys Rev E 55:868–876CrossRef Longtin A (1997) Autonomous stochastic resonance in bursting neurons. Phys Rev E 55:868–876CrossRef
go back to reference McCormick DA, Huguenard JR (1992) A Model of the electrophysiological properties of thalamocortical relay neurons. J Neurophysiol 8:1384–1400CrossRef McCormick DA, Huguenard JR (1992) A Model of the electrophysiological properties of thalamocortical relay neurons. J Neurophysiol 8:1384–1400CrossRef
go back to reference Meng P, Wang Q, Lu Q (2013) Bursting synchronization dynamics of pancreatic \(\beta \)-cells with electrical and chemical coupling. Cogn Neurodyn 7:197–212PubMedCrossRef Meng P, Wang Q, Lu Q (2013) Bursting synchronization dynamics of pancreatic \(\beta \)-cells with electrical and chemical coupling. Cogn Neurodyn 7:197–212PubMedCrossRef
go back to reference Miyakawa K, Okano T, Yamazaki S (2013) Cluster synchronization in a chemical oscillator network with adaptive coupling. J Phy Soc Jpn 82:034005CrossRef Miyakawa K, Okano T, Yamazaki S (2013) Cluster synchronization in a chemical oscillator network with adaptive coupling. J Phy Soc Jpn 82:034005CrossRef
go back to reference Moon SJ, Cook KA, Rajendran K, Kevrekidis KG, Cisternas J, Liang CR (2015) Coarse-grained clustering dynamics of heterogeneously coupled neurons. J Math Neurosci 5:2PubMedPubMedCentralCrossRef Moon SJ, Cook KA, Rajendran K, Kevrekidis KG, Cisternas J, Liang CR (2015) Coarse-grained clustering dynamics of heterogeneously coupled neurons. J Math Neurosci 5:2PubMedPubMedCentralCrossRef
go back to reference 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 USA 105:6179–6184PubMedCrossRefPubMedCentral 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 USA 105:6179–6184PubMedCrossRefPubMedCentral
go back to reference Park C, Worth RM, Rubchinsky LL (2010) Fine temporal structure of beta oscillations synchronization in subthalamic nucleus in Parkinson’s disease. J Neurophysiol 103:2707–2716PubMedPubMedCentralCrossRef Park C, Worth RM, Rubchinsky LL (2010) Fine temporal structure of beta oscillations synchronization in subthalamic nucleus in Parkinson’s disease. J Neurophysiol 103:2707–2716PubMedPubMedCentralCrossRef
go back to reference Pereira T, Baptista M, Kurths J (2007) Multi-time-scale synchronization and information processing in bursting neuron networks. Eur Phys J Spec Top 146:155–168CrossRef Pereira T, Baptista M, Kurths J (2007) Multi-time-scale synchronization and information processing in bursting neuron networks. Eur Phys J Spec Top 146:155–168CrossRef
go back to reference Pernarowski M, Miura RM, Kevorkian J (1992) Perturbation techniques for models of bursting electrical activity in pancreatic \(\beta \)-cells. SIAM J Appl Math 52:1627–1650cCrossRef Pernarowski M, Miura RM, Kevorkian J (1992) Perturbation techniques for models of bursting electrical activity in pancreatic \(\beta \)-cells. SIAM J Appl Math 52:1627–1650cCrossRef
go back to reference Plant RE (1981) Bifurcation and resonance in a model for bursting nerve cells. J Math Biol 11:15–32PubMedCrossRef Plant RE (1981) Bifurcation and resonance in a model for bursting nerve cells. J Math Biol 11:15–32PubMedCrossRef
go back to reference Prado TdeL, Lopes SR, Batista CAS, Kurths J, Viana RL (2014) Synchronization of bursting Hodgkin-Huxley-type neurons in clustered networks. Phys Rev E 90:032818CrossRef Prado TdeL, Lopes SR, Batista CAS, Kurths J, Viana RL (2014) Synchronization of bursting Hodgkin-Huxley-type neurons in clustered networks. Phys Rev E 90:032818CrossRef
go back to reference Rose RM, Hindmarsh JL (1985) A model of a thalamic neuron. Proc R Soc Lond Ser B 225:161–193CrossRef Rose RM, Hindmarsh JL (1985) A model of a thalamic neuron. Proc R Soc Lond Ser B 225:161–193CrossRef
go back to reference Rinzel J (1985) Bursting oscillations in an excitable membrane model. In: Sleeman BD, Jarvis RJ (eds) Lecture notes in mathematics, vol 1151. Ordinary and partial differential equations. Springer, Berlin, pp 304–316 Rinzel J (1985) Bursting oscillations in an excitable membrane model. In: Sleeman BD, Jarvis RJ (eds) Lecture notes in mathematics, vol 1151. Ordinary and partial differential equations. Springer, Berlin, pp 304–316
go back to reference Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: Teramoto E, Yamaguti M (eds) Lecture notes in biomathematics, vol 71. Mathematical topics in population biology, morphogenesis, and neurosciences. Springer, Berlin, pp 267–281 Rinzel J (1987) A formal classification of bursting mechanisms in excitable systems. In: Teramoto E, Yamaguti M (eds) Lecture notes in biomathematics, vol 71. Mathematical topics in population biology, morphogenesis, and neurosciences. Springer, Berlin, pp 267–281
go back to reference 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 35–130CrossRef 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 35–130CrossRef
go back to reference 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 9:277–299PubMedCrossRef 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 9:277–299PubMedCrossRef
go back to reference Shi X, Lu Q (2005) Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons. Chin Phys 14:77–85CrossRef Shi X, Lu Q (2005) Firing patterns and complete synchronization of coupled Hindmarsh-Rose neurons. Chin Phys 14:77–85CrossRef
go back to reference Shi X, Lu Q (2009) Burst synchronization of electrically and chemically coupled map-based neurons. Phys A 388:2410–2419CrossRef Shi X, Lu Q (2009) Burst synchronization of electrically and chemically coupled map-based neurons. Phys A 388:2410–2419CrossRef
go back to reference Shilnikov A, Cymbalyuk G (2005) Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Phys Rev Lett 94:048101PubMedCrossRef Shilnikov A, Cymbalyuk G (2005) Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Phys Rev Lett 94:048101PubMedCrossRef
go back to reference Shimazaki H, Shinomoto S (2010) Kernel bandwidth optimization in spike rate estimation. J Comput Neurosci 29:171–182PubMedCrossRef Shimazaki H, Shinomoto S (2010) Kernel bandwidth optimization in spike rate estimation. J Comput Neurosci 29:171–182PubMedCrossRef
go back to reference Song S, Sjöström PJ, Reigl M, Nelson S, Chklovskii DB (2005) Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol 3:e68PubMedPubMedCentralCrossRef Song S, Sjöström PJ, Reigl M, Nelson S, Chklovskii DB (2005) Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol 3:e68PubMedPubMedCentralCrossRef
go back to reference Sporns O (2011) Networks of the brain. MIT Press, Cambridge Sporns O (2011) Networks of the brain. MIT Press, Cambridge
go back to reference Sporns O, Tononi G, Edelman GM (2000) Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex 10:127–141PubMedCrossRef Sporns O, Tononi G, Edelman GM (2000) Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cereb Cortex 10:127–141PubMedCrossRef
go back to reference Sporns O, Chialvo DR, Kaiser M, Hilgetag CC (2004) Organization, development and function of complex brain networks. Trends Cogn Sci 8:418–425PubMedCrossRef Sporns O, Chialvo DR, Kaiser M, Hilgetag CC (2004) Organization, development and function of complex brain networks. Trends Cogn Sci 8:418–425PubMedCrossRef
go back to reference Steriade M, McCormick DA, Sejnowski TJ (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262:679–685PubMedCrossRef Steriade M, McCormick DA, Sejnowski TJ (1993) Thalamocortical oscillations in the sleeping and aroused brain. Science 262:679–685PubMedCrossRef
go back to reference Stern EA, Jaeger D, Wilson CJ (1998) Membrane potential synchrony of simultaneously recorded striatal spiny neurons in vivo. Nature 394:475–478PubMedCrossRef Stern EA, Jaeger D, Wilson CJ (1998) Membrane potential synchrony of simultaneously recorded striatal spiny neurons in vivo. Nature 394:475–478PubMedCrossRef
go back to reference Su H, Alroy G, Kirson ED, Yaari Y (2001) Extracellular calcium modulates persistent sodium current-dependent burst-firing in hippocampal pyramidal neurons. J Neurosci 21:4173–4182PubMedPubMedCentralCrossRef Su H, Alroy G, Kirson ED, Yaari Y (2001) Extracellular calcium modulates persistent sodium current-dependent burst-firing in hippocampal pyramidal neurons. J Neurosci 21:4173–4182PubMedPubMedCentralCrossRef
go back to reference Sun X, Lei J, Perc M, Kurths J, Chen G (2011) Burst synchronization transitions in a neuronal network of subnetworks. Chaos 21:016110PubMedCrossRef Sun X, Lei J, Perc M, Kurths J, Chen G (2011) Burst synchronization transitions in a neuronal network of subnetworks. Chaos 21:016110PubMedCrossRef
go back to reference Tanaka G, Ibarz B, Sanjuan MA, Aihara K (2006) Synchronization and propagation of bursts in networks of coupled map neurons. Chaos 16:013113PubMedCrossRef Tanaka G, Ibarz B, Sanjuan MA, Aihara K (2006) Synchronization and propagation of bursts in networks of coupled map neurons. Chaos 16:013113PubMedCrossRef
go back to reference Taylor AF, Kapetanopoulos P, Whitaker BJ, Toth R, Bull L, Tinsley MR (2008) Clusters and switchers in globally coupled photochemical oscillators. Phys Rev Lett 100:214101PubMedCrossRef Taylor AF, Kapetanopoulos P, Whitaker BJ, Toth R, Bull L, Tinsley MR (2008) Clusters and switchers in globally coupled photochemical oscillators. Phys Rev Lett 100:214101PubMedCrossRef
go back to reference Uhlhaas PJ, Singer W (2006) Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology. Neuron 52:155–168PubMedCrossRef Uhlhaas PJ, Singer W (2006) Neural synchrony in brain disorders: relevance for cognitive dysfunctions and pathophysiology. Neuron 52:155–168PubMedCrossRef
go back to reference 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 84:91–101PubMedCrossRef 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 84:91–101PubMedCrossRef
go back to reference van Vreeswijk C, Hansel D (2001) Patterns of synchrony in neural networks with spike adaptation. Neural Comput 13:959–992PubMedCrossRef van Vreeswijk C, Hansel D (2001) Patterns of synchrony in neural networks with spike adaptation. Neural Comput 13:959–992PubMedCrossRef
go back to reference 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 80:026206CrossRef 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 80:026206CrossRef
go back to reference Wang QY, Murks A, Perc M, Lu QS (2011a) Taming desynchronized bursting with delays in the Macaque cortical network. Chin Phys B 20:040504CrossRef Wang QY, Murks A, Perc M, Lu QS (2011a) Taming desynchronized bursting with delays in the Macaque cortical network. Chin Phys B 20:040504CrossRef
go back to reference Wang H, Wang Q, Lu Q, Zheng Y (2013) Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction. Cogn Neurodyn 7:121–131PubMedCrossRef Wang H, Wang Q, Lu Q, Zheng Y (2013) Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction. Cogn Neurodyn 7:121–131PubMedCrossRef
go back to reference Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442PubMedCrossRef Watts DJ, Strogatz SH (1998) Collective dynamics of ‘small-world’ networks. Nature 393:440–442PubMedCrossRef
go back to reference Wisenfeld K, Colet P, Wisenfeld S (1996) Synchronization transitions in a disordered Josephson series array. Phys Rev Lett 76:404–407CrossRef Wisenfeld K, Colet P, Wisenfeld S (1996) Synchronization transitions in a disordered Josephson series array. Phys Rev Lett 76:404–407CrossRef
go back to reference Womack MD, Khodakhah K (2002) Active contribution of dendrites to the tonic and trimodal patterns of activity in cerebellar Purkinje neurons. J Neurosci 22:10603–10612PubMedPubMedCentralCrossRef Womack MD, Khodakhah K (2002) Active contribution of dendrites to the tonic and trimodal patterns of activity in cerebellar Purkinje neurons. J Neurosci 22:10603–10612PubMedPubMedCentralCrossRef
go back to reference Young MP (1993) The organization of neural systems in the primate cerebral cortex. Philos Trans R Soc 252:13–18 Young MP (1993) The organization of neural systems in the primate cerebral cortex. Philos Trans R Soc 252:13–18
go back to reference Young MP, Scannell JW, Burns GA, Blakemore C (1994) Analysis of connectivity: neural systems in the cerebral cortex. Rev Neurosci 5:227–250PubMedCrossRef Young MP, Scannell JW, Burns GA, Blakemore C (1994) Analysis of connectivity: neural systems in the cerebral cortex. Rev Neurosci 5:227–250PubMedCrossRef
go back to reference 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 21:013127PubMedCrossRef 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 21:013127PubMedCrossRef
go back to reference Zhang J, Yuan Z, Zhou T (2009) Synchronization and clustering of synthetic genetic networks: a role for cis-regulatory modules. Phys Rev E 79:041903CrossRef Zhang J, Yuan Z, Zhou T (2009) Synchronization and clustering of synthetic genetic networks: a role for cis-regulatory modules. Phys Rev E 79:041903CrossRef
Metadata
Title
Cluster burst synchronization in a scale-free network of inhibitory bursting neurons
Authors
Sang-Yoon Kim
Woochang Lim
Publication date
10-07-2019
Publisher
Springer Netherlands
Published in
Cognitive Neurodynamics / Issue 1/2020
Print ISSN: 1871-4080
Electronic ISSN: 1871-4099
DOI
https://doi.org/10.1007/s11571-019-09546-9

Other articles of this Issue 1/2020

Cognitive Neurodynamics 1/2020 Go to the issue