{"title":"Neuron Dynamics of Single-Compartment Traub Model for Hardware Implementations","authors":"J. C. Moctezuma, V. Bre\u00f1a-Medina, Jose Luis Nunez-Yanez and Joseph P. McGeehan","volume":91,"journal":"International Journal of Computer and Information Engineering","pagesStart":1281,"pagesEnd":1285,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10003625","abstract":"In this work we make a bifurcation analysis for a
\r\nsingle compartment representation of Traub model, one of the most
\r\nimportant conductance-based models. The analysis focus in two
\r\nprincipal parameters: current and leakage conductance. Study of
\r\nstable and unstable solutions are explored; also Hop-bifurcation and
\r\nfrequency interpretation when current varies is examined. This study
\r\nallows having control of neuron dynamics and neuron response when
\r\nthese parameters change. Analysis like this is particularly important
\r\nfor several applications such as: tuning parameters in learning
\r\nprocess, neuron excitability tests, measure bursting properties of the
\r\nneuron, etc. Finally, a hardware implementation results were
\r\ndeveloped to corroborate these results.","references":"[1] Traub, R.D., et al., \"A model of a CA3 hippocampal pyramidal neuron\r\nincorporating voltage-clamp data on intrinsic conductances\". J\r\nNeurophysiol, 1991. 66(2): p. 635-50.\r\n[2] Zhang, Y., J. Nunez, and J. McGeehan, \"Biophysically Accurate\r\nFloating Point Neuroprocessor\"s. University of Bristol, 2010.\r\n[3] Pinsky, P.F. and J. Rinzel, \"Intrinsic and network rhythmogenesis in a\r\nreduced Traub model for Ca3 neuron\"s. Journal of Computational\r\nNeuroscience, 1995. 2(3): p. 275-275.\r\n[4] Guckenheimer, J. and I.S. Labouriau, \"Bifurcation of the Hodgkin and\r\nHuxley Equations - a New Twist\". Bulletin of Mathematical Biology,\r\n1993. 55(5): p. 937-952.\r\n[5] Jiang, W., G. Jianming, and F. Xiangyang, \"Two-parameter Hopf\r\nbifurcation in the Hodgkin-Huxley model\". Chaos, Solitons & Fractals,\r\n2005. 23: p. 973-980.\r\n[6] Beuter, A., et al., \"Nonlinear dynamics in Physiology and Medicine\".\r\n2003: Springer.\r\n[7] Izhikevich, E.M., \"Neural Excitability, Spiking and Bursting\".\r\nInternational Journal of Bifurcation and Chaos, 2000. 10(6): p. 1171-\r\n1266.\r\n[8] Guevara, M., \"Bifurcations Involving Fixed Points and Limit Cycles in\r\nBiological Systems, in Nonlinear Dynamics in Physiology and\r\nMedicine\", A. Beuter, et al., Editors. 2003, Springer New York. p. 41-\r\n85.\r\n[9] Fei, X.Y., Jiangwang, and L.Q. Chen, \"Bifurcation control of Hodgkin-\r\nHuxley model of nerve system\". WCICA 2006: Sixth World Congress on\r\nIntelligent Control and Automation, Vols 1-12, Conference Proceedings,\r\n2006: p. 9406-9410.\r\n[10] Moctezuma, J.C., J.P. McGeehan, and J.L. Nunez-Yanez. \"Numerically\r\nefficient and biophysically accurate neuroprocessing platform\".\r\nInternational Conference in Reconfigurable Computing and FPGAs\r\n(ReConFig). 2013.\r\n[11] Hirsch, M.W., S. Smale, and R.L. Devaney, \"Differential equations,\r\ndynamical systems, and an introduction to chaos\". 2004: ElSevier.\r\n[12] Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and\r\nChaos. 2000: Springer.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 91, 2014"}