Citation Relationships



Oh M, Matveev V (2009) Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons. J Comput Neurosci 26:303-20 [PubMed]

   Loss of phase-locking in non-weakly coupled inhib. networks of type-I neurons (Oh and Matveev 2009)

References and models cited by this paper

References and models that cite this paper

Acker CD, Kopell N, White JA (2003) Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics. J Comput Neurosci 15:71-90 [PubMed]

Bose A, Kopell N, Terman D (2000) Almost-synchronous solutions for mutually coupled excitatory neurons. Physica D 140:69-94

Bressloff PC, Coombes S (1998) Desynchronization, mode locking, and bursting in strongly coupled integrate-and-fire oscillators Phys Rev Lett 81:2168-2171

Bressloff PC, Coombes S (2000) Dynamics of strongly-coupled spiking neurons. Neural Comput 12:91-129 [PubMed]

Brown E, Moehlis J, Holmes P (2004) On the phase reduction and response dynamics of neural oscillator populations. Neural Comput 16:673-715 [Journal] [PubMed]

Canavier CC, Baxter DA, Clark JW, Byrne JH (1999) Control of multistability in ring circuits of oscillators. Biol Cybern 80:87-102 [Journal] [PubMed]

Ermentrout B (1996) Type I membranes, phase resetting curves, and synchrony. Neural Comput 8:979-1001 [PubMed]

Ermentrout B, Kopell N (1984) Frequency plateaus in a chain of weakly coupled oscillators. Siam J Math Anal 15:215-237

Ermentrout GB, Kopell N (1990) Oscillator death in systems of coupled neural oscillators SIAM J App Math 51:125-146

Ermentrout GB, Kopell N (1991) Multiple pulse interactions and averaging in systems of coupled neural oscillators. J Math Biol 29:195-217

Glass L, Guevara MR, Belair J, Shrier A (1984) Global bifurcations of a periodically forced biological oscillator Physical Review A 29:1348-1357

Goel P, Ermentrout B (2002) Synchrony, stability, and firing patterns in pulse coupled oscillators Physica D 163:191-216

Golubitsky M, Josic K, Shea-brown E (2006) Winding numbers and average frequencies in phase oscillator networks Journal Of Nonlinear Science 16:201-231

Golubitsky M, Stewart I, Buono PL, Collins JJ (1999) Symmetry in locomotor central pattern generators and animal gaits. Nature 401:693-5 [Journal] [PubMed]

Hansel D, Mato G, Meunier C (1995) Synchrony in excitatory neural networks. Neural Comput 7:307-37 [PubMed]

Hoppensteadt FC, Izhikevich EM (1997) Weakly Connected Neural Networks :90

Izhikevich EM (2000) Phase equations for relaxation oscillations Siam J Appl Mat 60:1789-1804

Izhikevich EM (2007) Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting [Journal]

   Artificial neuron model (Izhikevich 2003, 2004, 2007) [Model]

Izhikevich EM, Kuramoto Y (2006) Weakly coupled oscillators. ncyclopedia of Mathematical Physics 5:448

Jones SR, Pinto DJ, Kaper TJ, Kopell N (2000) Alpha-frequency rhythms desynchronize over long cortical distances: a modeling study. J Comput Neurosci 9:271-91 [PubMed]

Kopell N (1988) Toward a theory of modelling central pattern generators Neural Control Of Rhythmic Movements In Vertebrates, Cohen AH:Rossignol S:Grillner S, ed. pp.369

Kopell N, Ermentrout GB (2002) Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators Handbook of dynamical systems, Fiedler B, ed, ed. pp.5

Kopell N, Ermentrout GB, Whittington MA, Traub RD (2000) Gamma rhythms and beta rhythms have different synchronization properties. Proc Natl Acad Sci U S A 97:1867-72 [PubMed]

Kuramoto Y (1984) Chemical oscillations, waves, and turbulence

Maran SK, Canavier CC (2008) Using phase resetting to predict 1:1 and 2:2 locking in two neuron networks in which firing order is not always preserved. J Comput Neurosci 24:37-55 [Journal] [PubMed]

Mirollo RE, Strogatz SH (1990) Synchronization of pulse-coupled biological oscillators. Siam J Appl Math 6:1645-1657

Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35:193-213 [Journal] [PubMed]

   Morris-Lecar model of the barnacle giant muscle fiber (Morris, Lecar 1981) [Model]

Netoff TI, Banks MI, Dorval AD, Acker CD, Haas JS, Kopell N, White JA (2005) Synchronization in hybrid neuronal networks of the hippocampal formation. J Neurophysiol 93:1197-208 [Journal] [PubMed]

Oprisan SA, Canavier CC (2001) Stability analysis of rings of pulse-coupled oscillators: The effect of phase-resetting in the second cycle after the pulse is important at synchrony and for long pulses Differential Equations And Dynamical Systems 9:243-258

Oprisan SA, Canavier CC (2002) The influence of limit cycle topology on the phase resetting curve. Neural Comput 14:1027-57 [Journal] [PubMed]

Oprisan SA, Prinz AA, Canavier CC (2004) Phase resetting and phase locking in hybrid circuits of one model and one biological neuron. Biophys J 87:2283-98 [Journal] [PubMed]

Peskin CS (1975) Mathematical Aspects of Heart Physiology Courant Institute of Mathematical Sciences

Rinzel J, Ermentrout B (1998) Analysis of neural excitability and oscillations. Methods In Neuronal Modeling 2nd Edition, Segev I, Koch C, ed. pp.251

Rubin J, Terman D (2000) Geometric analysis of population rhythms in synaptically coupled neuronal networks. Neural Comput 12:597-645 [PubMed]

Sato YD, Shiino M (2007) Generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena. Phys Rev E Stat Nonlin Soft Matter Phys 75:011909 [Journal] [PubMed]

Somers D, Kopell N (1993) Rapid synchronization through fast threshold modulation. Biol Cybern 68:393-407 [PubMed]

Van Vreeswijk C, Abbott LF, Ermentrout GB (1994) When inhibition not excitation synchronizes neural firing. J Comput Neurosci 1:313-21 [PubMed]

Wang XJ, Buzsáki G (1996) Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. J Neurosci 16:6402-13 [Journal] [PubMed]

   Gamma oscillations in hippocampal interneuron networks (Wang, Buzsaki 1996) [Model]

White JA, Chow CC, Ritt J, Soto-Treviño C, Kopell N (1998) Synchronization and oscillatory dynamics in heterogeneous, mutually inhibited neurons. J Comput Neurosci 5:5-16 [PubMed]

Winfree A (2001) The Geometry of Biological Time (2nd ed)

Chandrasekaran L, Matveev V, Bose A (2009) Multistability of clustered states in a globally inhibitory network Physica D: Nonlinear Phenomena 238(3):253-263 [Journal]

   Multistability of clustered states in a globally inhibitory network (Chandrasekaran et al. 2009) [Model]

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