Bursting oscillations, bifurcation and synchronization in neuronal systems

[1]  Mingzhou Ding,et al.  Transitions to synchrony in coupled bursting neurons. , 2004, Physical review letters.

[2]  S. R. Lopes,et al.  Chaotic phase synchronization in scale-free networks of bursting neurons. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Frank C. Hoppensteadt,et al.  Bursts as a unit of neural information: selective communication via resonance , 2003, Trends in Neurosciences.

[4]  C. Rocsoreanu,et al.  Hopf bifurcation in a system of two coupled advertising oscillators , 2005 .

[5]  Guanrong Chen,et al.  Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability , 2008 .

[6]  R. Dzakpasu,et al.  Discriminating differing types of synchrony in neural systems , 2005 .

[7]  Qingyun Wang,et al.  Taming desynchronized bursting with delays in the Macaque cortical network , 2011 .

[8]  Eugene M. Izhikevich,et al.  Neural excitability, Spiking and bursting , 2000, Int. J. Bifurc. Chaos.

[9]  H. D. Landahl,et al.  Mathematical biophysics of cell respiration II , 1939 .

[10]  QiShao Lu,et al.  Different types of bursting in Chay neuronal model , 2008 .

[11]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[12]  P. Shorten,et al.  A Hodgkin-Huxley model exhibiting bursting oscillations , 2000, Bulletin of mathematical biology.

[13]  M. Pernarowski.  Fast subsystem bifurcations in strongly coupled heterogeneous collections of excitable cells , 2000, Bulletin of mathematical biology.

[14]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[15]  J. Henquin,et al.  Glucose Regulation of Insulin Secretion Independent of the Opening or Closure of Adenosine Triphosphate-Sensitive K+ Channels in β Cells. , 1999, Endocrinology.

[16]  Matjaz Perc,et al.  Synchronization of Regular and Chaotic oscillations: the Role of Local Divergence and the Slow Passage Effect - a Case Study on calcium oscillations , 2004, Int. J. Bifurc. Chaos.

[17]  Andrey Shilnikov,et al.  When weak inhibition synchronizes strongly desynchronizing networks of bursting neurons. , 2008, Physical review letters.

[18]  Matjaz Perc,et al.  Local dissipation and coupling properties of cellular oscillators: a case study on calcium oscillations. , 2004, Bioelectrochemistry.

[19]  Willy Govaerts,et al.  MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs , 2003, TOMS.

[20]  John Rinzel,et al.  Bursting oscillations in an excitable membrane model , 1985 .

[21]  Martin Hasler,et al.  Synchronization of bursting neurons: what matters in the network topology. , 2005, Physical review letters.

[22]  Qishao Lu,et al.  Bursting and synchronization transition in the coupled modified ML neurons , 2008 .

[23]  J. Lisman,et al.  Bidirectional synaptic plasticity induced by a single burst during cholinergic theta oscillation in CA1 in vitro , 1995, Neuron.

[24]  Andrey Shilnikov,et al.  Fast reciprocal inhibition can synchronize bursting neurons. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  R. Bertram,et al.  Topological and phenomenological classification of bursting oscillations. , 1995, Bulletin of mathematical biology.

[26]  Arthur Sherman,et al.  Full system bifurcation analysis of endocrine bursting models. , 2010, Journal of theoretical biology.

[27]  Daizhan Cheng,et al.  Bursting of Morris-Lecar neuronal model with current-feedback control , 2009 .

[28]  Arthur Sherman,et al.  From spikers to bursters via coupling: Help from heterogeneity , 2001, Bulletin of mathematical biology.

[29]  J. Milton,et al.  Epilepsy as a Dynamic Disease , 2003 .

[30]  C. Koch,et al.  Encoding of visual information by LGN bursts. , 1999, Journal of neurophysiology.

[31]  Andrey Shilnikov,et al.  Burst-duration mechanism of in-phase bursting in inhibitory networks , 2010 .

[32]  Y. Kuznetsov.  Elements of Applied Bifurcation Theory , 2023, Applied Mathematical Sciences.

[33]  Matjaž Perc,et al.  Different types of bursting calcium oscillations in non-excitable cells , 2003 .

[34]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[35]  Z. Duan,et al.  Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Jiang Wang,et al.  Asymptotic behavior of Morris–Lecar system , 2008 .

[37]  J. M. Gonzalez-Miranda,et al.  Block structured dynamics and neuronal coding. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Zhonghuai Hou,et al.  Transition to burst synchronization in coupled neuron networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  E. Izhikevich,et al.  Weakly connected neural networks , 1997 .

[40]  Guanrong Chen,et al.  Synchronous Bursts on Scale-Free Neuronal Networks with Attractive and Repulsive Coupling , 2010, PloS one.

[41]  Peter Ashwin,et al.  Within-Burst Synchrony Changes for Coupled Elliptic Bursters , 2009, SIAM J. Appl. Dyn. Syst..