Digital Multiplierless Realization of Coupled Wilson Neuron Model

The human brain is composed of 1011 neurons with a switching speed of about 1 ms. Studying spiking neural networks, including the modeling, simulation, and implementation of the biological neuron models, helps us to learn about the brain and the related diseases, or to design more efficient bio-mimic processors and smarter robots. Such applications have made this part of neuromorphic research works very popular. In this paper, the Wilson neuron model has been implemented as an approximation of the Hodgkin–Huxley biological model that is adjusted for the efficient digital realization on the platforms. Results show that the proposed model can adequately reproduce neuron dynamical behaviors. The hardware implementation on the field-programmable gate array (FPGA) shows that our modifications on the Wilson original model imitate the biological behavior of neurons, besides using feasibility, targeting a low cost and high efficiency. The modifications raised a 15% speed-up compared with the original model. The mean normalized root-mean-square error, root-mean-square error, and the mean absolute error parameters are 6.43, 0.44, and 0.31, respectively.

[1]  Sundarapandian Vaidyanathan,et al.  Anti-Synchronization of the FitzHugh-Nagumo Chaotic Neuron Models via Adaptive Control Method , 2015 .

[2]  G. Ermentrout,et al.  Gamma rhythms and beta rhythms have different synchronization properties. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[3]  Huiyan Li,et al.  Synchronization of coupled equations of Morris–Lecar model , 2008 .

[4]  Tetsuya Hishiki,et al.  A Novel Rotate-and-Fire Digital Spiking Neuron and its Neuron-Like Bifurcations and Responses , 2011, IEEE Transactions on Neural Networks.

[5]  Karim Faez,et al.  A novel digital implementation of neuron–astrocyte interactions , 2015 .

[6]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[7]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1990 .

[8]  Dmitry E. Postnov,et al.  Functional modeling of neural-glial interaction , 2007, Biosyst..

[9]  Andrew S. Cassidy,et al.  Design of silicon brains in the nano-CMOS era: Spiking neurons, learning synapses and neural architecture optimization , 2013, Neural Networks.

[10]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[11]  Dominique M. Durand,et al.  Phase synchronization in two coupled chaotic neurons , 1999 .

[12]  Sanja Jeremic,et al.  Mathematical modeling of the neuron morphology using two dimensional images. , 2016, Journal of theoretical biology.

[13]  Stephen P. DeWeerth,et al.  Adaptation in a VLSI model of a neuron , 1999 .

[14]  Wulfram Gerstner,et al.  SPIKING NEURON MODELS Single Neurons , Populations , Plasticity , 2002 .

[15]  J. Kelso,et al.  Bidirectional Coupling between Astrocytes and Neurons Mediates Learning and Dynamic Coordination in the Brain: A Multiple Modeling Approach , 2011, PloS one.

[16]  Derek Abbott,et al.  Digital Multiplierless Realization of Two Coupled Biological Morris-Lecar Neuron Model , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  Jonathan Touboul,et al.  Dynamics and bifurcations of the adaptive exponential integrate-and-fire model , 2008, Biological Cybernetics.

[18]  J. Nagumo,et al.  On a response characteristic of a mathematical neuron model , 1972, Kybernetik.

[19]  E. Oja.  Simplified neuron model as a principal component analyzer , 1982, Journal of mathematical biology.

[20]  H. Wilson.  Simplified dynamics of human and mammalian neocortical neurons. , 1999, Journal of theoretical biology.

[21]  Ben H. Jansen,et al.  A neurophysiologically-based mathematical model of flash visual evoked potentials , 2004, Biological Cybernetics.

[22]  Timoleon Crepin Kofane,et al.  Stability of the synchronized network of Hindmarsh-Rose neuronal models with nearest and global couplings , 2015, Commun. Nonlinear Sci. Numer. Simul..

[23]  A. Selverston,et al.  Synchronous Behavior of Two Coupled Biological Neurons , 1998, chao-dyn/9811010.

[24]  F. Gage,et al.  Neuronal medium that supports basic synaptic functions and activity of human neurons in vitro , 2015, Proceedings of the National Academy of Sciences.

[25]  Steve Furber,et al.  High-performance computing for systems of spiking neurons , 2006 .