Dynamics of Biomimetic Electronic Artificial Neural Networks

We explore the key aspects of the dynamics of small networks of biomimetic artificial electronic neurons, including the role of local dynamics, network topology and noise. Models include Keener’s and Maeda and Makino’s “minimal” model circuits for FitzHugh-Nagumo neurons as well as the Belousov-Zhabotinsky chemical reaction, the prototype chemical oscillatory system. A wide variety of complex synchronization and emergent behavior is seen. There are potential applications to computer science, biology, and biomedicine.

[1]  I. Epstein,et al.  Pattern formation in a tunable medium: the Belousov-Zhabotinsky reaction in an aerosol OT microemulsion. , 2001, Physical review letters.

[2]  R. Williams,et al.  How We Found The Missing Memristor , 2008, IEEE Spectrum.

[3]  Harold M. Hastings,et al.  Microscopic fluctuations and pattern formation in a supercritical oscillatory chemical system , 2003 .

[4]  A. Winfree.  The geometry of biological time , 1991 .

[5]  Wiesenfeld,et al.  Theory of stochastic resonance. , 1989, Physical review. A, General physics.

[6]  Eugene M. Izhikevich,et al.  FitzHugh-Nagumo model , 2006, Scholarpedia.

[7]  A. Bulsara,et al.  Stochastic resonance in a single neuron model: theory and analog simulation. , 1991, Journal of theoretical biology.

[8]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[9]  S. Fraden,et al.  Creation and perturbation of planar networks of chemical oscillators. , 2015, Chaos.

[10]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[11]  Wulfram Gerstner,et al.  Neuronal Dynamics: From Single Neurons To Networks And Models Of Cognition , 2014 .

[12]  R. M. Noyes,et al.  Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system , 1972 .

[13]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[14]  Kurt Wiesenfeld,et al.  Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs , 1995, Nature.

[15]  Susan B. Johnson,et al.  Mechanism of Lethal Proarrhythmia Observed in the Cardiac Arrhythmia Suppression Trial: Role of Adrenergic Modulation of Drug Binding , 1997, Pacing and clinical electrophysiology : PACE.

[16]  Ditto,et al.  Stochastic Resonance in a Neuronal Network from Mammalian Brain. , 1996, Physical review letters.

[17]  David Terman,et al.  Mathematical foundations of neuroscience , 2010 .

[18]  A Garfinkel,et al.  Quasiperiodicity and chaos in cardiac fibrillation. , 1997, The Journal of clinical investigation.

[19]  Misha Mahowald,et al.  A silicon model of early visual processing , 1993, Neural Networks.

[20]  Irving R Epstein,et al.  Diffusively coupled chemical oscillators in a microfluidic assembly. , 2008, Angewandte Chemie.

[21]  C. Mead,et al.  Neuromorphic analogue VLSI. , 1995, Annual review of neuroscience.

[22]  L A Moyé,et al.  The cardiac arrhythmia suppression trial. Casting suppression in a different light. , 1995, Circulation.

[23]  Vladimir K. Vanag,et al.  Pattern Formation in a Tunable Medium , 2001 .

[24]  Leon O. Chua.  Resistance switching memories are memristors , 2011 .

[25]  Carver A. Mead,et al.  Neuromorphic electronic systems , 1990, Proc. IEEE.

[26]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[27]  Harold M Hastings,et al.  Bromide control, bifurcation and activation in the Belousov-Zhabotinsky reaction. , 2008, The journal of physical chemistry. A.

[28]  H L Greene,et al.  Mortality and morbidity in patients receiving encainide, flecainide, or placebo. The Cardiac Arrhythmia Suppression Trial. , 1991, The New England journal of medicine.

[29]  R. J. Field.  Chaos in the Belousov–Zhabotinsky reaction , 2015 .

[30]  S. Bressler,et al.  Large-scale brain networks in cognition: emerging methods and principles , 2010, Trends in Cognitive Sciences.

[31]  B Hess,et al.  Critical size and curvature of wave formation in an excitable chemical medium. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[32]  Wolfgang Klimesch,et al.  An algorithm for the EEG frequency architecture of consciousness and brain body coupling , 2013, Front. Hum. Neurosci..

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

[34]  A Beuter,et al.  Feedback and delays in neurological diseases: a modeling study using dynamical systems. , 1993, Bulletin of mathematical biology.

[35]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[36]  Leon Glass,et al.  Dynamical disease: Identification, temporal aspects and treatment strategies of human illness. , 1995, Chaos.

[37]  L. Chua.  Memristor-The missing circuit element , 1971 .

[38]  I. Epstein,et al.  Combined excitatory and inhibitory coupling in a 1-D array of Belousov-Zhabotinsky droplets. , 2014, Physical chemistry chemical physics : PCCP.

[39]  James P. Keener,et al.  Analog circuitry for the van der Pol and FitzHugh-Nagumo equations , 1983, IEEE Transactions on Systems, Man, and Cybernetics.

[40]  A. Kawczynski,et al.  Master equation simulations of a model of a thermochemical system. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Easwara Moorthy Essaki Arumugam,et al.  A chimeric path to neuronal synchronization. , 2015, Chaos.

[42]  D M Roden,et al.  Ionic mechanisms for prolongation of refractoriness and their proarrhythmic and antiarrhythmic correlates. , 1996, The American journal of cardiology.

[43]  Y. Maeda,et al.  A pulse-type hardware neuron model with beating, bursting excitation and plateau potential. , 2000, Bio Systems.

[44]  A. M. Zhabotinskii.  [PERIODIC COURSE OF THE OXIDATION OF MALONIC ACID IN A SOLUTION (STUDIES ON THE KINETICS OF BEOLUSOV'S REACTION)]. , 1964, Biofizika.

[45]  Michael Conrad,et al.  Scale change and the emergence of information processing primitives , 1985 .

[46]  Manuel Le Gallo,et al.  Stochastic phase-change neurons. , 2016, Nature nanotechnology.

[47]  John J. Tyson,et al.  Scaling and reducing the Field-Koros-Noyes mechanism of the Belousov-Zhabotinskii reaction , 1982 .