Nicola W, Campbell SA. (2013). Bifurcations of large networks of two-dimensional integrate and fire neurons. Journal of computational neuroscience. 35 [PubMed]

See more from authors: Nicola W · Campbell SA

References and models cited by this paper

Abbott LF, van Vreeswijk C. (1993). Asynchronous states in networks of pulse-coupled oscillators. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics. 48 [PubMed]

Apfaltrer F, Ly C, Tranchina D. (2006). Population density methods for stochastic neurons with realistic synaptic kinetics: firing rate dynamics and fast computational methods. Network (Bristol, England). 17 [PubMed]

Brette R, Gerstner W. (2005). Adaptive exponential integrate-and-fire model as an effective description of neuronal activity. Journal of neurophysiology. 94 [PubMed]

Casti AR et al. (2002). A population study of integrate-and-fire-or-burst neurons. Neural computation. 14 [PubMed]

Champneys A et al. (2008). Bifurcations in non-smooth dynamical systems Siam Review. 50

Dur-e-Ahmad M, Nicola W, Campbell SA, Skinner FK. (2012). Network bursting using experimentally constrained single compartment CA3 hippocampal neuron models with adaptation. Journal of computational neuroscience. 33 [PubMed]

Ermentrout GB, Terman DH. (2010). Mathematical Foundations of Neuroscience Interdisciplinary Applied Mathematics. 35

Fitzhugh R. (1952). Impulses and phsyiological states in theoretical models of nerve membrane Biophysical Journal. 1(6)

Hemond P et al. (2008). Distinct classes of pyramidal cells exhibit mutually exclusive firing patterns in hippocampal area CA3b. Hippocampus. 18 [PubMed]

Hines ML, Morse T, Migliore M, Carnevale NT, Shepherd GM. (2004). ModelDB: A Database to Support Computational Neuroscience. Journal of computational neuroscience. 17 [PubMed]

Ho EC, Zhang L, Skinner FK. (2009). Inhibition dominates in shaping spontaneous CA3 hippocampal network activities in vitro. Hippocampus. 19 [PubMed]

Izhikevich EM. (2003). Simple model of spiking neurons. IEEE transactions on neural networks. 14 [PubMed]

Kistler WM, Gerstner W. (2002). Spiking neuron models.

Knight BW. (2000). Dynamics of encoding in neuron populations: some general mathematical features. Neural computation. 12 [PubMed]

Knight BW, Omurtag A, Sirovich L. (2000). Dynamics of neuronal populations: The equilibrium solution. Siam J Applied Math. 60

Kuznetsov YA, Dhooge A, Govaerts W. (2003). MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs Acm Trans Math Softw. 29

La Camera G, Giugliano M, Senn W, Fusi S. (2008). The response of cortical neurons to in vivo-like input current: theory and experiment : I. Noisy inputs with stationary statistics. Biological cybernetics. 99 [PubMed]

La Camera G, Rauch A, Lüscher HR, Senn W, Fusi S. (2004). Minimal models of adapted neuronal response to in vivo-like input currents. Neural computation. 16 [PubMed]

Ly C, Tranchina D. (2007). Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling. Neural computation. 19 [PubMed]

Markram H et al. (2004). Interneurons of the neocortical inhibitory system. Nature reviews. Neuroscience. 5 [PubMed]

MathWorks Inc (2012). (2012). MATLAB Version 7.10.0 (R2012a).

Naud R, Marcille N, Clopath C, Gerstner W. (2008). Firing patterns in the adaptive exponential integrate-and-fire model. Biological cybernetics. 99 [PubMed]

Nesse WH, Borisyuk A, Bressloff PC. (2008). Fluctuation-driven rhythmogenesis in an excitatory neuronal network with slow adaptation. Journal of computational neuroscience. 25 [PubMed]

Nykamp DQ, Tranchina D. (2000). A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning. Journal of computational neuroscience. 8 [PubMed]

Omurtag A, Knight BW, Sirovich L. (2000). On the simulation of large populations of neurons. Journal of computational neuroscience. 8 [PubMed]

Sejnowski TJ, Destexhe A, Mainen ZF. (1998). Kinetic models of synaptic transmission Methods In Neuronal Modeling.

Sirovich L, Omurtag A, Lubliner K. (2006). Dynamics of neural populations: stability and synchrony. Network (Bristol, England). 17 [PubMed]

Strogatz SH, Mirollo RE. (1991). Stability of incoherence in a population of coupled oscillators J Stat Phys. 63

Tikhonov A. (1952). Systems of differential equations containing small parameters in the derivatives (in Russian) Matematicheskii Sbornik (NS). 31(73)

Touboul J. (2008). Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons. Siam Appl Math. 68

Treves A. (1993). Mean field analysis of neuronal spike dynamics. Network. 4

Van Vreeswijk C, Abbott LF, Ermentrout GB. (1994). When inhibition not excitation synchronizes neural firing. Journal of computational neuroscience. 1 [PubMed]

Vladimirski BB, Tabak J, O'Donovan MJ, Rinzel J. (2008). Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field. Journal of computational neuroscience. 25 [PubMed]

Vreeswijk Cv. (1996). Partial synchronization in populations of pulse-coupled oscillators. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics. 54 [PubMed]

Wu Y, Lu W, Lin W, Leng G, Feng J. (2012). Bifurcations of emergent bursting in a neuronal network. PloS one. 7 [PubMed]

van Vreeswijk C, Hansel D. (2001). Patterns of synchrony in neural networks with spike adaptation. Neural computation. 13 [PubMed]

References and models that cite this paper

Ferguson KA, Huh CY, Amilhon B, Williams S, Skinner FK. (2014). Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context. F1000Research. 3 [PubMed]

Ferguson KA, Njap F, Nicola W, Skinner FK, Campbell SA. (2015). Examining the limits of cellular adaptation bursting mechanisms in biologically-based excitatory networks of the hippocampus. Journal of computational neuroscience. 39 [PubMed]

Truccolo W, Ho EC. (2016). Interaction between Synaptic Inhibition and Glial-Potassium Dynamics leads to Diverse Seizure Transition Modes in Biophysical Models of Human Focal Seizures J Comput Neurosci.

Visser S, van Gils SA. (2014). Lumping Izhikevich neurons EPJ Nonlinear Biomedical Physics. 25(12)

This website requires cookies and limited processing of your personal data in order to function. By continuing to browse or otherwise use this site, you are agreeing to this use. See our Privacy policy and how to cite and terms of use.