Temporal Information Processing and Stability Analysis of the MHSN Neuron Model in DDF
DOI:
https://doi.org/10.9781/ijimai.2016.427Keywords:
Analysis, Neural Network, Dynamical System, Eigen ValueAbstract
Implementation of a neuron like information processing structure at hardware level is a burning research problem. In this article, we analyze the modified hybrid spiking neuron model (the MHSN model) in distributed delay framework (DDF) for hardware level implementation point of view. We investigate its temporal information processing capability in term of inter-spike-interval (ISI) distribution. We also perform the stability analysis of the MHSN model, in which, we compute nullclines, steady state solution, eigenvalues corresponding the MHSN model. During phase plane analysis, we notice that the MHSN model generates limit cycle oscillations which is an important phenomenon in many biological processes. Qualitative behavior of these limit cycle does not changes due to the variation in applied input stimulus, however, delay effect the spiking activity and duration of cycle get altered.Downloads
References
[1] A. Borst and F. E. Teunissen, “Information Theory and Neural Coding,” Nature Neuroscience, Vol. 2, No. 11, pp. 947-957, 1999.
[2] E. M. Izhikevich, “Neural Excitability, Spiking and Bursting,” International Journal of Bifurcation and Chaos, Vol. 10, No. 6, pp. 1171-1266, 2000.
[3] E. M. Izhikevich, “Hybrid Spiking Models,” Philosophical Transactions of The Royal Society A, Vol. 368, pp. 5061-5070, 2010.
[4] H. E. Plesser, “Aspects of Signal Processing in Noisy Neuron,” Dissertation submitted to Max-Planck-Institute, Gottigen, 1999.
[5] Joubert, Belhadj, O. Temam and R. Heliot, “Hardware Spiking Neurons Design: Analog or Digital?” IEEE World Congress on Computational Intelligence, 2012.
[6] D. J. Mar, C. C. Chow, W. Gerstner, R. W. Adams and J. J. Collins, “Noise Shaping in Populations of Coupled Model Neurons”, Proceedings of the National Academy of Sciences, USA, Vol. 96(18), pp. 10450-10455, 1999.
[7] E. M. Izhikevich, “Simple Model of Spiking Neurons,” IEEE Transactions on Neural Networks, Vol. 14, No. 6, pp. 1569-1572, 2003.
[8] E. M. Izhikevich, “Which Model to Use for Cortical Spiking Neurons?” IEEE Transactions on Neural Networks, Vol. 15, No. 5, pp. 1063-1070, 2004.
[9] H. Lim, V. Kornijuck et. al., “Reliability of Neuronal Information Conveyed by Unreliable Neuristor Based Leaky Integrate-and-Fire Neurons: A Model Study,” Nature: Scientific Reports, 5:09776 , DOI: 10.1038/srep09776, pp. 1-15, 2015.
[10] L. S. Liao and G. Chen, “Bifurcation Analysis on a Two Neuron System with Distributed Delay in the Frequency Domain”, Neural Network, Vol. 17, Issue 4, pp. 1654-1664, 2004.
[11] W. Gerstner and W. M. Kistler, “Spiking Neuron Models: Single Neurons, Populations, Plasticity,” Cambridge University Press, 2002.
[12] V. B. Semwal, M. Raj and G. C. Nandi, “Biometirc gait identification based on a multilayer perceptron”, Robotics and Autonomous Systems, Vol. 65, pp. 65-75, 2015.
[13] E. M. Izhikevich, “Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting,” The MIT Press, 2007.
[14] A. Fairhall, E. S. Brown and A. Barreiro, “Information Theoretic Approaches to Understanding Circuit Function,” Neurobiology, Vol. 22, pp. 653-659, 2012.
[15] E. M. Izhikevich and G. M. Edelman, “Large-Scale Model of Mammalian Thalamocortical Systems,” PNAS, Vol. 105, No. 9, pp. 3593-3598, 2008.
[16] M. I. Rabinovich, P. Varona, A. I. Selverston and H. D. I. Abarbanel, “Dynamical Principles in Neuroscience,” Reviews of Modern Physics, Vol. 78, No. 4, pp. 1213-1265, 2006.
[17] S. Millner, A. Grubl, K. Meier, J. Schemmel and M. Schwartz, “A VLSI Implementation of the Adaptive Exponential Integrate-and-Fire Neuron Model,” Advances in Neural Information Processing Systems, Vol. 23, pp. 1642-1650, 2010.
[18] A. V. Holden, “Models of the Stochastic Activity of Neurons”, Lecture Notes in Biomathematics, Springer, 1976.
[19] N. MacDonald, “Time Lags in Biological Models”, Lecture Notes in Biomathematics, Springer, 1978.
[20] Karmeshu, V. Gupta and K. V. Kadambari, “Neuronal model with distributed delay: analysis and simulation study for gamma distribution memory kernel,” Biological Cybernatics, Vol. 104, pp. 369-383, 2011.
[21] S. K. Sharma and Karmeshu, “Neuronal Model With Distributed Delay: Emergence of Unimodal and Bimodal ISI Distributions”, IEEE Transactions on Nanobioscience, Vol. 12, No. 1 pp. 1-12, 2013.
[22] S. K. Bharti, S. K. Choudhary and J. Singh, “Analytical Solution for Izhikevich Hybrid Spiking Neuron Model with Distributed Delay,” Utthan: The Journal of Applied Sciences & Humanities, Vol. 1, No. 2, pp. 19-24, 2014.
[23] S. K. Choudhary, K. Singh and H.O.S. Sinha, “Spiking Activity of Hybrid Spiking Neuron Model in DDF”, in International Conference on Research in Intelligent Computing in Engineering (RICE 2016), 08-09 April 2016, Nagpur, India , pp. 261-264.
[24] H. Smith, “An Introduction to Delay Differential Equations With Applications to the Life Sciences,” Texts in Applied Mathematics, Vol 57, Springer, Berlin, 2011.
[25] H. R. Wilson, “Spikes, Decision and Actions,” Oxford University Press, 2005.
[26] L. F. Abbott and P. Dayan, “Theoretical Neuroscience: Computational and mathematical modeling of neural systems”, The MIT press, 2001.
[27] P. E. Kloeden and E.Platen, “Numerical Solution of Stochastic Differential Equations,” Springer, Berlin, 1992.
[28] P. Glasserman, “Monte Carlo Methods in Financial Engineering”, Springer, 2004.
[29] R. J. Lal, “Algebra,” Volume II, Shail Publication, Allahabad, 2002.
[30] S. K. Choudhary, K. Singh and V. K. Solanki, “Spiking Activity of a LIF Neuron in Distributed Delay Framework”, in International Journal of Artificial Intelligence and Interactive Multimedia (In Press).
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