Abstract
We examine the effects of changing the coefficient of variation (CV) of the inter-stimulus interval on the CV of the output interspike interval (ISI), using constant magnitude, supra-threshold point-process stimuli of the membrane potential variable in the FitzHugh-Nagumo model. The coefficient of variation of the input is changed within the context of a displaced exponential distribution. We find that for some values of mean inter-stimulus interval, CV of ISI has an inverse relationship with input coefficient of variation, whereas for other mean stimulation rates, CV of ISI increases with input coefficient of variation. Over a wide range of input regularity CV of ISI is approximately constant, and is less than 0.4.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
David Brown, Jonathan P.A. Foweraker, and Robert W. Marrs. Dynamic equilibria and oscillations of a periodicially stimulated excitable system. Chaos, Solitons and Fractals, 5(3/4):359–369, 1995.
David Brown, Allan E. Herbison, Jane E. Robinson, Robert W. Marrs, and Gareth Leng. Modelling the luteinizing hormone-releasing hormone pulse generator. Neuroscience, 63:869–869, 1994.
Neil P. Evans, Geoffrey E. Dahl, David T. Mauger, Vasantha Padmanabhan, and L.A. Thrun. Does estradiol induce the pre-ovulatory gonadotropin-releasing hormone surge in the ewe by inducing a progressive change in the model of operation of the GnRH neurosecretory system. Endocrinology, 136(12):5511–5519, 1995.
Robert FitzHugh. Impulses and physiological states in theoretical models of nerve membranes. Biophysical Journal, 1:445–466, 1961.
J.P.A. Foweraker and D. Brown. The effects of random variation in stimulation timing and magnitude on excitable and oscillatory forms of a luteinizing hormone pulse generator model. In Computation in Cellular and Molecular Biological Systems, pages 315–327. World Scientific, 1996.
J.P.A. Foweraker, D. Brown, and R.W. Marrs. Discrete-time simulation of the oscillatory and excitable forms of a FitzHugh-Nagumo model applied to the pulsatile release of luteinizing hormone releasing hormone. Chaos, 5(1):200–208, 1994.
L. Glass and M.C. Mackey. From Clocks to Chaos: The Rhythms of Life. Princeton University Press, 1988.
John D. Gordan, Barbara J. Attardi, and Donald W. Pfaff. Mathematical exploration of pulsality in cultured gonadotropin-releasing hormone neurons. Neuroendocrinology, 67:2–17, 1998.
Gareth Leng, editor. Pulsatility in neuroendocrine systems. CRC Press, Inc., Boca Raton, Florida, first edition, 1988.
Gareth Leng, and David Brown. The origins and significance of pulsatility in hormone secretion from the pituitary. Journal of Neuroendocrinology, 9:493–513, 1997.
André Longtin. Stocastic resonance in neuron models. Journal of Statistical Physics, 70(1–2):309–327, 1993.
J. Nagumo, S. Arimoto, and S. Yoshizawa. An active pulse transmission line simulating nerve axon. Proceedings of the Institute of Radio Engineers, 50:2061–2071, 1962.
Shunsuke Sato and Shinji Doi. Response characteristics of the BVP neuron model to periodic pulse inputs. Mathematical Biosciences, 112:243–259, 1992.
T. Tanaka, Y. Mori, and K. Hosino. Hypothalamic GnRH pulse-generator activity during the estradiol-induced LH surge in ovariectomized goats. Neuroendocrinology, 56(5):641–645, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Feerick, S., Feng, J., Brown, D. (1999). Paradoxical relationship between output and input regularity for the FitzHugh-Nagumo model. In: Mira, J., Sánchez-Andrés, J.V. (eds) Foundations and Tools for Neural Modeling. IWANN 1999. Lecture Notes in Computer Science, vol 1606. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098177
Download citation
DOI: https://doi.org/10.1007/BFb0098177
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66069-9
Online ISBN: 978-3-540-48771-5
eBook Packages: Springer Book Archive