`a`
Mathematical Biosciences and Engineering (MBE)
 

On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model
Pages: 285 - 302, Issue 2, April 2014

doi:10.3934/mbe.2014.11.285      Abstract        References        Full text (429.4K)                  Related Articles

Virginia Giorno - Dipartimento di Studi e Ricerche Aziendali (Management &Information Technology), Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy (email)
Serena Spina - Dipartimento di Matematica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy (email)

1 A. Buonocore, A. G. Nobile and L. M. Ricciardi, A new integral equation for the evaluation of first-passage-time probability densities, Adv. Appl. Prob., 19 (1987), 784-800.       
2 A. Buonocore, L. Caputo and E. Pirozzi, On the evaluation of firing densities for periodically driven neuron models, Math. Biosci., 214 (2008), 122-133.       
3 R. M. Capocelli and L. M. Ricciardi, Diffusion approximation and first passage time problem for a model neuron, Kybernetik (Berlin), 8 (1971), 214-223.       
4 S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model, Phys. Rev. E (3), 71 (2005), 011907, 9 pp.       
5 S. Ditlevsen and P. Lansky, Comparison of statistical methods for estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model from first-passage times data, in Collective Dynamics: Topics on Competition and Cooperation in the Biosciences (eds. L. M. Ricciardi, A. Buonocore and E. Pirozzi), AIP Conf. Proc., 1028, Amer. Inst. Phys., Melville, NY, 2008, 171-185.       
6 G, Esposito, V. Giorno, A. G. Nobile, L. M. Ricciardi and C. Valerio, Neuronal modeling in the presence of random refractoriness, Sci. Math. Jpn., 64 (2006), 1-36.       
7 G. L. Gerstein and B. Mandelbrot, Random walk models for the spike activity of a single neuron, Biophys. J., 4 (1964), 41-68.
8 V. Giorno, A. G. Nobile and L. M. Ricciardi, On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries, Adv. in Appl. Probab., 22 (1990), 883-914.       
9 M. T. Giraudo and L. Sacerdote, Jump-diffusion processes as models for neuronal activity, BioSystems, 40 (1997), 75-82.
10 P. Lansky and L. Sacerdote, The Ornstein-Uhlenbeck neuronal model with signal-dependent noise, Physics Letters A, 285 (2001), 132-140.       
11 P. Lansky, P. Sanda and J. He, The parameters of the stochastic leaky integrate-and-fire neuronal model, J. Comput. Neurosci., 21 (2006), 211-223.       
12 L. M. Ricciardi and F. Esposito, On some distribution functions for non-linear switching elements with finite dead time, Kybernetik, 3 (1966), 148-152.
13 L. M. Ricciardi, A. Di Crescenzo, V. Giorno and A. G. Nobile, An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling, Math. Japon., 50 (1999), 247-322.       
14 L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biol. Cyb., 35 (1979), 1-9.
15 M. C. Teich, L. Matin and B. I. Cantor, Refractoriness in the maintained discharge of the cat's retinal ganglion cell, J. Opt. Soc. Am., 68 (1978), 386-402.

Go to top