Chaotic States Induced By Resetting Process In Izhikevich Neuron Model

[1] M.I. Rabinovich, P. Varona, A.I. Selverston, H.D.I. Abarbanel, ”Dynamical principles in neuroscience”, Reviews of Modern Physics, vol.78, no.4, pp.1213–1265, Nov. 2006.Search in Google Scholar

[2] J. Wojcik, A. Shilnikov, ”Voltage interval mappings for activity transitions in neuron models for elliptic bursters”, Physica D: Nonlinear Phenomena, vol.240, no.14, pp.1164-1180, Apr. 2011.Search in Google Scholar

[3] H.A. Braun, J. Schwabedal, M. Dewald, C. Finke, S. Postnova, M.T. Huber, B. Wollweber, H. Schneider, M.C. Hirsch, K. Voigt, U. Feudel, F. Moss, ”Noise-induced precursors of tonic-to-bursting transitions in hypothalamic neurons and in a conductance-based model”, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.21, no.4, 047509, Dec. 2011.10.1063/1.367132622225383Search in Google Scholar

[4] A.L. Hodgkin, A.F. Huxley, ”A quantitative description of membrane current and application to conduction and excitation in nerve”, Journal of Physiology vol.117, no.4, pp.500–544, Aug. 1952.10.1113/jphysiol.1952.sp004764139241312991237Search in Google Scholar

[5] E.M. Izhikevich, ”Simple Model of Spiking Neurons”, IEEE Transactions on Neural Networks, vol.14, no.6, pp. 1569–1572, Nov. 2003.Search in Google Scholar

[6] E.M. Izhikevich, ”Which Model to Use for Cortical Spiking Neurons?”, IEEE Transactions on Neural Networks, vol.15, no.5, pp.1063–1070, Sep. 2004.Search in Google Scholar

[7] K. Aihara, H. Suzuki, ”Theory of hybrid dynamical systems and its applications to biological and medical systems”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences vol.368, no.1930, pp.4893–4914, May 2010.Search in Google Scholar

[8] S. Coombes, R. Thul, K.C.A. Wedgwood, ”Nonsmooth dynamics in spiking neuron models”, Physica D: Nonlinear Phenomena, vol.241, no.22, pp.2042–2057, Nov. 2012.Search in Google Scholar

[9] W.J. Freeman, ”Tutorial on neurobiology: from single neurons to brain chaos”, International journal of bifurcation and chaos, vol.2, no.3, pp.451–482, Sept. 1992.10.1142/S0218127492000653Search in Google Scholar

[10] N. Schweighofer, K. Doya, H. Fukai, J.V. Chiron, T. Furukawa, M. Kawato, ”Chaos may enhance information transmission in the inferior olive”, Proceedings of the National Academy of Sciences, vol.101, no.13, pp.4655–4660, Sept. 2004.Search in Google Scholar

[11] S. Nobukawa, H. Nishimura, ”Characteristic of Signal Response in Coupled Inferior Olive Neurons with Velarde-Llinás Model”, In SICE Annual Conference, pp.1367–1374, Sept. 2013.Search in Google Scholar

[12] I. T. Tokuda, H. Hoang, N. Schweighofer, M. Kawato, ”Adaptive coupling of inferior olive neurons in cerebellar learning” Neural Networks, vol.47, pp.42–50, Dec. 2013.10.1016/j.neunet.2012.12.00623337637Search in Google Scholar

[13] A. Tamura, T. Ueta, S. Tsuji, ”Bifurcation analysis of Izhikevich neuron model”, Dynamics of continuous, discrete and impulsive systems, Series A: mathematical analysis vol.16, no.6, pp.849–862, 2009.Search in Google Scholar

[14] D. Itou, T. Ueta, K. Aihara, ”Bifurcation Analysis with Threshold Values for Interrupt Autonomous Systems”, IEICE Trans. Fundamentals, vol.94-A, no.8, pp.596–603, Aug. 2011.Search in Google Scholar

[15] S. Nobukawa, H. Nishimura, T. Yamanishi, J.-Q. Liu, ”Chaotic Dynamical States in Izhikevich Neuron Model”, Emerging Trends in Computational Biology, Bioinformatics, and Systems Biology - Algorithms and Software Tools, Elsevier/MK (to be published).Search in Google Scholar

[16] N. Sugiura, K. Fujiwara, R. Hosakawa, K. Jin’no, T. Ikeguchi, ”Estimation of Lyapunov exponents of chaotic response in the Izhikevich neuron model”, IEICE Technical report NLP2013-113, pp.1–6, Dec. 2013Search in Google Scholar

[17] F. Bizzarri, A. Brambilla, G.S. Gajani, ”Lyapunov exponents computation for hybrid neurons”, J. Comput. Neurosci. vol.35, no.2, pp.201–212, Feb. 2013.10.1007/s10827-013-0448-623463130Search in Google Scholar

[18] S. Nobukawa, H. Nishimura, T. Yamanishi, J.-Q. Liu, ”Analysis of Routes to Chaos in Izhikevich Neuron Model with Resetting Process”, Proc. The 7th International Conference on Soft Computing and Intelligent Systems, The 15th International Symposium on Advanced Intelligent Systems (SCIS-ISIS2014), pp.813–818, Dec. 2014.10.1109/SCIS-ISIS.2014.7044746Search in Google Scholar

[19] A.C. Hindmarsh, P.N. Brown, K.E. Grant, S.L. Lee, R. Serban, D.E. Shumaker, C.S. Woodward, ”SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers”, ACM Transactions on Mathematical Software, vol.31, no.3, pp.363–396, Sep. 2005.10.1145/1089014.1089020Search in Google Scholar

[20] M.D. Bernardo (Ed.), Piecewise-smooth dynamical systems: theory and applications, Springer, 2008.Search in Google Scholar

[21] T.S. Parker, L.O. Chua, Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag New York Inc, 1989.10.1007/978-1-4612-3486-9Search in Google Scholar

[22] S. Zambrano, I.P. Mario, J.M. Seoane, M.A. Sanjun, S. Euzzor, A. Geltrude, R. Meucci, F.T. Arecchi, ”Synchronization of uncoupled excitable systems induced by white and coloured noise”, New Journal of Physics, vol.12, no.5, 053040, May 2010.10.1088/1367-2630/12/5/053040Search in Google Scholar

[23] H. Nagashima, Y. Baba, Introduction to chaos: physics and mathematics of chaotic phenomena, CRC Press, 1998.Search in Google Scholar

[24] P. Berge, Y. Pomeau, C. Vidal, Order in chaos, The Deterministic Approach to Turbulence, 1984.Search in Google Scholar