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Guckenheimer J, Holmes P (1983) Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 2nd edition.

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]
Akman OE, Broomhead DS, Clement RA, Abadi RV (2006) Nonlinear time series analysis of jerk congenital nystagmus. J Comput Neurosci 21:153-70 [Journal] [PubMed]
Atencia M, Joya G, Sandoval F (2005) Dynamical analysis of continuous higher-order hopfield networks for combinatorial optimization. Neural Comput 17:1802-19 [Journal] [PubMed]
Barreto E, Cressman JR (2011) Ion concentration dynamics as a mechanism for neuronal bursting. J Biol Phys 37:361-73 [Journal] [PubMed]
   Ion concentration dynamics as a mechanism for neuronal bursting (Barreto & Cressman 2011) [Model]
Behn CG, Brown EN, Scammell TE, Kopell NJ (2007) Mathematical model of network dynamics governing mouse sleep-wake behavior. J Neurophysiol 97:3828-40 [Journal] [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]
Brown E, Moehlis J, Holmes P, Clayton E, Rajkowski J, Aston-Jones G (2004) The influence of spike rate and stimulus duration on noradrenergic neurons. J Comput Neurosci 17:13-29 [Journal] [PubMed]
Clewley R, Rotstein HG, Kopell N (2005) A Computational Tool for the Reduction of Nonlinear ODE Systems Possessing Multiple Scales Multiscale modeling & simulation 4(3):732-759 [Journal]
   Reduction of nonlinear ODE systems possessing multiple scales (Clewley et al. 2005) [Model]
Destexhe A, Babloyantz A, Sejnowski TJ (1993) Ionic mechanisms for intrinsic slow oscillations in thalamic relay neurons. Biophys J 65:1538-52 [Journal] [PubMed]
   Thalamocortical Relay cell under current clamp in high-conductance state (Zeldenrust et al 2018) [Model]
Doi S, Kumagai S (2005) Generation of very slow neuronal rhythms and chaos near the Hopf bifurcation in single neuron models. J Comput Neurosci 19:325-56 [Journal] [PubMed]
Doiron B, Laing C, Longtin A, Maler L (2002) Ghostbursting: a novel neuronal burst mechanism. J Comput Neurosci 12:5-25 [PubMed]
Gao J, Holmes P (2007) On the dynamics of electrically-coupled neurons with inhibitory synapses. J Comput Neurosci 22:39-61 [Journal] [PubMed]
Gottschalk A, Haney P (2003) Computational aspects of anesthetic action in simple neural models. Anesthesiology 98:548-64 [PubMed]
Govaerts W, Sautois B (2006) Computation of the phase response curve: a direct numerical approach. Neural Comput 18:817-47 [Journal] [PubMed]
Kanamaru T, Sekine M (2005) Synchronized firings in the networks of class 1 excitable neurons with excitatory and inhibitory connections and their dependences on the forms of interactions. Neural Comput 17:1315-38 [Journal] [PubMed]
Kim HC, Lee J (2007) Clustering based on gaussian processes. Neural Comput 19:3088-107 [Journal] [PubMed]
Mandelblat Y, Etzion Y, Grossman Y, Golomb D (2001) Period doubling of calcium spike firing in a model of a Purkinje cell dendrite. J Comput Neurosci 11:43-62 [PubMed]
Shpiro A, Curtu R, Rinzel J, Rubin N (2007) Dynamical characteristics common to neuronal competition models. J Neurophysiol 97:462-73 [Journal] [PubMed]
Stollenwerk L, Bode M (2003) Lateral neural model of binocular rivalry. Neural Comput 15:2863-82 [Journal] [PubMed]
Várkonyi PL, Kiemel T, Hoffman K, Cohen AH, Holmes P (2008) On the derivation and tuning of phase oscillator models for lamprey central pattern generators. J Comput Neurosci 25:245-61 [Journal] [PubMed]
   Phase oscillator models for lamprey central pattern generators (Varkonyi et al. 2008) [Model]
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