Abbott LF, Dayan P. (2001). Theoretical Neuroscience. Computational and Mathematical Modeling of Neural Systems.
Austin TD. (2008). The emergence of the deterministic Hodgkin–Huxley equations as a limit from the underlying stochastic ion-channel mechanism Ann Appl Probab. 18
Bruce IC. (2007). Implementation issues in approximate methods for stochastic Hodgkin-Huxley models. Annals of biomedical engineering. 35 [PubMed]
Bruce IC. (2009). Evaluation of stochastic differential equation approximation of ion channel gating models. Annals of biomedical engineering. 37 [PubMed]
Brunel N, Chance FS, Fourcaud N, Abbott LF. (2001). Effects of synaptic noise and filtering on the frequency response of spiking neurons. Physical review letters. 86 [PubMed]
Cannon RC, O'Donnell C, Nolan MF. (2010). Stochastic ion channel gating in dendritic neurons: morphology dependence and probabilistic synaptic activation of dendritic spikes. PLoS computational biology. 6 [PubMed]
Chow CC, White JA. (1996). Spontaneous action potentials due to channel fluctuations. Biophysical journal. 71 [PubMed]
Clay JR. (1998). Excitability of the squid giant axon revisited. Journal of neurophysiology. 80 [PubMed]
Clay JR. (2005). Axonal excitability revisited. Progress in biophysics and molecular biology. 88 [PubMed]
Cudmore RH, Fronzaroli-Molinieres L, Giraud P, Debanne D. (2010). Spike-time precision and network synchrony are controlled by the homeostatic regulation of the D-type potassium current. The Journal of neuroscience : the official journal of the Society for Neuroscience. 30 [PubMed]
De Vries G, Sherman A. (2000). Channel sharing in pancreatic beta -cells revisited: enhancement of emergent bursting by noise. Journal of theoretical biology. 207 [PubMed]
Faisal AA, Laughlin SB. (2007). Stochastic simulations on the reliability of action potential propagation in thin axons. PLoS computational biology. 3 [PubMed]
Faisal AA, Selen LP, Wolpert DM. (2008). Noise in the nervous system. Nature reviews. Neuroscience. 9 [PubMed]
Finke C, Vollmer J, Postnova S, Braun HA. (2008). Propagation effects of current and conductance noise in a model neuron with subthreshold oscillations. Mathematical biosciences. 214 [PubMed]
Fox RF. (1997). Stochastic versions of the Hodgkin-Huxley equations. Biophysical journal. 72 [PubMed]
Fox RF, Lu Yn. (1994). Emergent collective behavior in large numbers of globally coupled independently stochastic ion channels. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics. 49 [PubMed]
Freidlin M, Wentzell A. (1998). Random Perturbations of Dynamical Systems.
GERSTEIN GL, MANDELBROT B. (1964). RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. Biophysical journal. 4 [PubMed]
Gardiner CW. (2004). Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences Springer Series in Synergetics, 3rd ed.. 13
Gillespie DT. (1977). Exact stochastic simulation of coupled chemical reactions. Journal Of Physical Chemistry. 81
Goldwyn JH, Imennov NS, Famulare M, Shea-Brown E. (2011). Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons. Physical review. E, Statistical, nonlinear, and soft matter physics. 83 [PubMed]
HODGKIN AL, HUXLEY AF. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology. 117 [PubMed]
Higham DJ. (2001). An algorithmic introduction to numerical simulation of stochastic differential equation Siam Review. 43
Hille B. (2001). Ionic Channels of Excitable Membranes.
Hines ML, Morse T, Migliore M, Carnevale NT, Shepherd GM. (2004). ModelDB: A Database to Support Computational Neuroscience. Journal of computational neuroscience. 17 [PubMed]
Imennov NS, Rubinstein JT. (2009). Stochastic population model for electrical stimulation of the auditory nerve. IEEE transactions on bio-medical engineering. 56 [PubMed]
Izhikevich EM. (2007). Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting.
Jo J, Kang H, Choi MY, Koh DS. (2005). How noise and coupling induce bursting action potentials in pancreatic {beta}-cells. Biophysical journal. 89 [PubMed]
Johnston D, Wu SMS. (1995). Foundations of Cellular Neurophysiology with simulations and illustrations by Richard Gray Foundations of Cellular Neurophysiology.
Jones SW. (2006). Are rate constants constant? The Journal of physiology. 571 [PubMed]
Keener JP. (2009). Invariant manifold reductions for Markovian ion channel dynamics. Journal of mathematical biology. 58 [PubMed]
Keleshian AM, Edeson RO, Liu GJ, Madsen BW. (2000). Evidence for cooperativity between nicotinic acetylcholine receptors in patch clamp records. Biophysical journal. 78 [PubMed]
Laing C, Lord G. (2009). Stochastic Methods in Neuroscience.
Li YX, Rinzel J. (1994). Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. Journal of theoretical biology. 166 [PubMed]
Liebovitch LS, Scheurle D, Rusek M, Zochowski M. (2001). Fractal methods to analyze ion channel kinetics. Methods (San Diego, Calif.). 24 [PubMed]
Linaro D, Storace M, Giugliano M. (2011). Accurate and fast simulation of channel noise in conductance-based model neurons by diffusion approximation. PLoS computational biology. 7 [PubMed]
Mino H, Rubinstein JT, White JA. (2002). Comparison of algorithms for the simulation of action potentials with stochastic sodium channels. Annals of biomedical engineering. 30 [PubMed]
Pakdaman K, Thieullen M, Wainrib G. (2010). Fluid limit theorems for stochastic hybrid systems with application to neuron models Adv Appl Probab. 42(3)
Press WH, Teukolsky SA, Vetterling WT, Flannery BP. (1988). Numerical recipes in C: the art of scientific computing.
Rinzel J, Ermentrout B. (1998). Analysis of neural excitability and oscillations. Methods In Neuronal Modeling 2nd Edition.
Rolls ET, Deco G. (2010). The Noisy Brain: Stochastic Dynamics as a Principle of Brain Function.
Rowat P. (2007). Interspike interval statistics in the stochastic Hodgkin-Huxley model: coexistence of gamma frequency bursts and highly irregular firing. Neural computation. 19 [PubMed]
Rowat PF, Elson RC. (2004). State-dependent effects of Na channel noise on neuronal burst generation. Journal of computational neuroscience. 16 [PubMed]
Saarinen A, Linne ML, Yli-Harja O. (2008). Stochastic differential equation model for cerebellar granule cell excitability. PLoS computational biology. 4 [PubMed]
Sato D, Xie LH, Nguyen TP, Weiss JN, Qu Z. (2010). Irregularly appearing early afterdepolarizations in cardiac myocytes: random fluctuations or dynamical chaos? Biophysical journal. 99 [PubMed]
Schneidman E, Freedman B, Segev I. (1998). Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural computation. 10 [PubMed]
Sengupta B, Laughlin SB, Niven JE. (2010). Comparison of Langevin and Markov channel noise models for neuronal signal generation. Physical review. E, Statistical, nonlinear, and soft matter physics. 81 [PubMed]
Shardlow T, Alzubaidi H, Gilsing H. (2010). Stochastic Methods in Neuroscience.
Shuai JW, Jung P. (2002). Optimal intracellular calcium signaling. Physical review letters. 88 [PubMed]
Skaugen E, Walløe L. (1979). Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin-Huxley equations. Acta physiologica Scandinavica. 107 [PubMed]
Tuckwell HC. (1988). Introduction To Theoretical Neurobiology: Vol 1, Linear Cable Theory And Dendritic Structure. 1
Vandenberg CA, Bezanilla F. (1991). A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon. Biophysical journal. 60 [PubMed]
Wang M, Hou Z, Xin H. (2004). Double-system-size resonance for spiking activity of coupled Hodgkin-Huxley neurons. Chemphyschem : a European journal of chemical physics and physical chemistry. 5 [PubMed]
White JA, Klink R, Alonso A, Kay AR. (1998). Noise from voltage-gated ion channels may influence neuronal dynamics in the entorhinal cortex. Journal of neurophysiology. 80 [PubMed]
White JA, Rubinstein JT, Kay AR. (2000). Channel noise in neurons. Trends in neurosciences. 23 [PubMed]
Woloshyn R. (1999). http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/VERSIONS/FORTRAN/mtfort90.f Mersenne twister implemented in FORTRAN.
Woo J, Miller CA, Abbas PJ. (2010). The dependence of auditory nerve rate adaptation on electric stimulus parameters, electrode position, and fiber diameter: a computer model study. Journal of the Association for Research in Otolaryngology : JARO. 11 [PubMed]
Zeng S, Jung P. (2004). Mechanism for neuronal spike generation by small and large ion channel clusters. Physical review. E, Statistical, nonlinear, and soft matter physics. 70 [PubMed]
Dangerfield CE, Kay D, Burrage K. (2012). Modeling ion channel dynamics through reflected stochastic differential equations Physical review. E, Statistical, nonlinear, and soft matter physics. 85 [PubMed]
Kilinc D, Demir A. (2015). Simulation of noise in neurons and neuronal circuits Proceedings of the IEEE/ACM international conference on computer-aided design (ICCAD).
Kilinc D, Demir A. (2017). Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques. IEEE transactions on biomedical circuits and systems. 11 [PubMed]
Orio P, Soudry D. (2012). Simple, fast and accurate implementation of the diffusion approximation algorithm for stochastic ion channels with multiple states. PloS one. 7 [PubMed]
Pezo D, Soudry D, Orio P. (2014). Diffusion approximation-based simulation of stochastic ion channels: which method to use? Frontiers in computational neuroscience. 8 [PubMed]
Schmandt NT, Galán RF. (2012). Stochastic-shielding approximation of Markov chains and its application to efficiently simulate random ion-channel gating. Physical review letters. 109 [PubMed]
Schmerl BA, McDonnell MD. (2013). Channel noise induced stochastic facilitation in an auditory brainstem neuron model Physical review. E, Statistical, nonlinear, and soft matter physics. 88 [PubMed]