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Hahn PJ, Durand DM (2003) Bistability dynamics in simulations of neural activity in high-extracellular-potassium conditions. J Comput Neurosci 11:5-18

References and models cited by this paper

References and models that cite this paper

Aihara K, Matsumoto G (1983) Two stable steady states in the Hodgkin-Huxley axons. Biophys J 41:87-9 [Journal] [PubMed]

Best EN (1979) Null space in the Hodgkin-Huxley Equations. A critical test. Biophys J 27:87-104 [Journal] [PubMed]

Bikson M, Ghai RS, Baraban SC, Durand DM (1999) Modulation of burst frequency, duration, and amplitude in the zero-Ca(2+) model of epileptiform activity. J Neurophysiol 82:2262-70 [Journal] [PubMed]

Booth V, Rinzel J (1995) A minimal, compartmental model for a dendritic origin of bistability of motoneuron firing patterns. J Comput Neurosci 2:299-312 [PubMed]

Chay TR, Lee YS (1984) Impulse responses of automaticity in the Purkinje fiber. Biophys J 45:841-9 [Journal] [PubMed]

Clay JR (1998) Excitability of the squid giant axon revisited. J Neurophysiol 80:903-13 [Journal] [PubMed]

Dietzel I, Heinemann U, Lux HD (1989) Relations between slow extracellular potential changes, glial potassium buffering, and electrolyte and cellular volume changes during neuronal hyperactivity in cat brain. Glia 2:25-44 [Journal] [PubMed]

Doedel EJ, Kernevez JP (1986) Software for Continuation Problems in Ordinary Differential Equations with Applications

Durand DM, Warman EN (1994) Desynchronization of epileptiform activity by extracellular current pulses in rat hippocampal slices. J Physiol 480 ( Pt 3):527-37

Ermentrout B (1997) http:--www.pitt.edu-‚uphase-

Glass L, Winfree AT (1984) Discontinuities in phase-resetting experiments. Am J Physiol 246:R251-8 [Journal] [PubMed]

Guckenheimer J, Labouriau IS (1993) Bifurcation of the Hodgkin and Huxley equations: a new twist Bull Math Biol 55:937-952

Guttman R, Lewis S, Rinzel J (1980) Control of repetitive firing in squid axon membrane as a model for a neuroneoscillator. J Physiol 305:377-95 [PubMed]

Heinemann U, Lux HD, Gutnick MJ (1977) Extracellular free calcium and potassium during paroxsmal activity in the cerebral cortex of the cat. Exp Brain Res 27:237-43 [PubMed]

Hille B (1992) Potassium channels and chloride channels Ionic Channels of Excitable Membrane, Hille B, ed. pp.115

HODGKIN AL, HUXLEY AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed]

   Squid axon (Hodgkin, Huxley 1952) (LabAXON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (NEURON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SNNAP) [Model]
   Squid axon (Hodgkin, Huxley 1952) used in (Chen et al 2010) (R language) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SBML, XPP, other) [Model]

Holden AV, Yoda M (1981) Ionic channel density of excitable membranes can act a bifurcation parameter. Biol Cybern 42:29-38 [PubMed]

Izhikevich EM (2000) Neural excitability, spiking and bursting Int J Bifurcat Chaos Appl Sci Eng 10:1171-1266

Jahangiri A (1998) Phase resetting of high potassium epileptiform activity in the Ca3 region of rat hippocampal slices Ph.D. thesis

Jahangiri A, Durand DM, Lin JC (1997) Singular stimulus parameters to annihilate spontaneous activity in the Hodgkin- Huxley model with elevated potassium IEEE-EMBS Proceedings

Jalife J, Antzelevitch C (1979) Phase resetting and annihilation of pacemaker activity in cardiac tissue. Science 206:695-7 [PubMed]

Jefferys JG (1995) Nonsynaptic modulation of neuronal activity in the brain: electric currents and extracellular ions. Physiol Rev 75:689-723 [Journal] [PubMed]

Jensen MS, Azouz R, Yaari Y (1994) Variant firing patterns in rat hippocampal pyramidal cells modulated by extracellular potassium. J Neurophysiol 71:831-9 [Journal] [PubMed]

Jensen MS, Yaari Y (1988) The relationship between interictal and ictal paroxysms in an in vitro model of focal hippocampal epilepsy. Ann Neurol 24:591-8 [Journal] [PubMed]

Jensen MS, Yaari Y (1997) Role of intrinsic burst firing, potassium accumulation, and electrical coupling in the elevated potassium model of hippocampal epilepsy. J Neurophysiol 77:1224-33 [Journal] [PubMed]

Korn SJ, Giacchino JL, Chamberlin NL, Dingledine R (1987) Epileptiform burst activity induced by potassium in the hippocampus and its regulation by GABA-mediated inhibition. J Neurophysiol 57:325-40 [Journal] [PubMed]

Mcbain CJ, Traynelis SF, Dingledine R (1993) High potassiuminduced synchronous bursts and electrographic seizures Epilepsy: Models, Mechanisms and Concepts, Schwartzkroin P, ed. pp.437

Mines GR (1914) On circulating excitation on heart muscles and their possible relation to tachycardia and fibrillation Trans R Soc Can 4:43-53

Pinsky P (1994) Mathematical models of hippocampal neurons and neural networks: Exploiting multiple time scales Ph.D. Thesis

Pinsky PF, Rinzel J (1994) Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons. J Comput Neurosci 1:39-60 [PubMed]

   CA3 pyramidal cell: rhythmogenesis in a reduced Traub model (Pinsky, Rinzel 1994) [Model]

Rinzel J (1985) Excitation dynamics: insights from simplified membrane models. Fed Proc 44:2944-6 [PubMed]

Rinzel J, Ermentrout GB (1989) Analysis of neuronal excitability and oscillations Methods In Neuronal Modeling: From Synapses To Networks, Koch C:Segev I, ed. pp.135

Rutecki PA, Lebeda FJ, Johnston D (1985) Epileptiform activity induced by changes in extracellular potassium in hippocampus. J Neurophysiol 54:1363-74 [Journal] [PubMed]

Traub RD, Dingledine R (1990) Model of synchronized epileptiform bursts induced by high potassium in CA3 region of rat hippocampal slice. Role of spontaneous EPSPs in initiation. J Neurophysiol 64:1009-18 [Journal] [PubMed]

Traub RD, Miles R (1991) Neuronal Networks Of The Hippocampus

Traub RD, Miles R (1991) Multiple modes of neuronal population activity emerge after modifying specific synapses in a model of the CA3 region of the hippocampus. Ann N Y Acad Sci 627:277-90 [PubMed]

Traub RD, Wong RK, Miles R, Michelson H (1991) A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J Neurophysiol 66:635-50 [Journal] [PubMed]

   CA3 hippocampal pyramidal neuron with voltage-clamp intrinsic conductance data (Traub et al 1991) [Model]

Traynelis SF, Dingledine R (1988) Potassium-induced spontaneous electrographic seizures in the rat hippocampal slice. J Neurophysiol 59:259-76 [Journal] [PubMed]

Williams SR, Tóth TI, Turner JP, Hughes SW, Crunelli V (1997) The 'window' component of the low threshold Ca2+ current produces input signal amplification and bistability in cat and rat thalamocortical neurones. J Physiol 505 ( Pt 3):689-705 [PubMed]

Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12:1-24 [Journal] [PubMed]

   Excitatory and inhibitory interactions in populations of model neurons (Wilson and Cowan 1972) [Model]

Winfree AT (1980) The geometry of biological time.

Winfree AT (1987) When Time Breaks Down

Wong RK, Traub RD, Miles R (1986) Cellular basis of neuronal synchrony in epilepsy. Adv Neurol 44:583-92 [PubMed]

Zipes DP (1975) Electrophysiological mechanisms involved in ventricular fibrillation. Circulation 52:III120-30 [PubMed]

Fröhlich F, Jezernik S (2004) Annihilation of single cell neural oscillations by feedforward and feedback control. J Comput Neurosci 17:165-78 [Journal] [PubMed]

Gruber AJ, Solla SA, Surmeier DJ, Houk JC (2003) Modulation of striatal single units by expected reward: a spiny neuron model displaying dopamine-induced bistability. J Neurophysiol 90:1095-114 [Journal] [PubMed]

   Spiny neuron model with dopamine-induced bistability (Gruber et al 2003) [Model]

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