Simulating electric activities of neurons by using PSPICE

Electric activities in the Morris–Lecar neuron and Josephson junction coupled resonator are investigated in a numerical way, and electric circuits are also designed by using the Personal Simulation Program with Integrated Circuit Emphasis (PSPICE). Within the improved Morris–Lecar circuit, a new integrator for the ion channel of potassium is designed, and the transition of electric activities, quiescent state to spiking to bursting to quiescent state could be observed. In the circuit of the Josephson-junction coupled resonator, an equivalent circuit is designed to reproduce several types of electric activity. The detailed parameter regions are detected to generate spiking and bursting states in the electric circuits for neurons, and these results are consistent with the numerical results. Bifurcation diagrams for interspike interval (ISI) vs. the forcing current are calculated to detect the excitability of the neuron model.

[1]  L. Chua,et al.  On the dynamics of Josephson-junction circuits , 1979 .

[2]  Thomas Nowotny,et al.  Dynamical origin of independent spiking and bursting activity in neural microcircuits. , 2007, Physical review letters.

[3]  Hiroyuki Kitajima,et al.  Bifurcations in Morris-Lecar neuron model , 2006, Neurocomputing.

[4]  L. F Abbott,et al.  Lapicque’s introduction of the integrate-and-fire model neuron (1907) , 1999, Brain Research Bulletin.

[5]  C. Koch,et al.  Methods in Neuronal Modeling: From Ions to Networks , 1998 .

[6]  Jacobo D Sitt,et al.  Versatile biologically inspired electronic neuron. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[8]  Andrey Shilnikov,et al.  Complete dynamical analysis of a neuron model , 2012 .

[9]  Kazuyuki Aihara,et al.  Building Electronic Bursters with the Morris-lecar Neuron Model , 2006, Int. J. Bifurc. Chaos.

[10]  Sheng-Chieh Huang,et al.  Generating tri-chaos attractors with three positive Lyapunov exponents in new four order system via linear coupling , 2012, Nonlinear Dynamics.

[11]  S. K. Dana,et al.  Spiking and Bursting in Josephson Junction , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[12]  Yongjian Liu,et al.  Circuit implementation and finite-time synchronization of the 4D Rabinovich hyperchaotic system , 2011, Nonlinear Dynamics.

[13]  G. Mykolaitis,et al.  Chaotic Colpitts Oscillator for the Ultrahigh Frequency Range , 2006 .

[14]  Jing Xia Li,et al.  Experimental demonstration of 1.5 GHz chaos generation using an improved Colpitts oscillator , 2013 .

[15]  Sungwon Park,et al.  Effects of periodic stimulation on an overly activated neuronal circuit. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[17]  Heinz Georg Schuster,et al.  Role of inhibitory feedback for information processing in thalamocortical circuits. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Y Wang,et al.  Information coding via spontaneous oscillations in neural ensembles. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[19]  Syamal K. Dana,et al.  Chaotic dynamics in Josephson junction , 2001 .

[20]  Whan Cb,et al.  Complex dynamical behavior in RCL-shunted Josephson tunnel junctions. , 1996 .

[21]  J. Hindmarsh,et al.  A model of neuronal bursting using three coupled first order differential equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

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

[23]  Ronilson Rocha,et al.  Experimental characterization of nonlinear systems: a real-time evaluation of the analogous Chua’s circuit behavior , 2010 .

[24]  Cheng-Fang Huang,et al.  Robust synchronization of chaotic behavior in unidirectional coupled RCLSJ models subject to uncertainties , 2009 .

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

[26]  Patrick Crotty,et al.  Josephson junction simulation of neurons. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Nicolas Brunel,et al.  How Connectivity, Background Activity, and Synaptic Properties Shape the Cross-Correlation between Spike Trains , 2009, The Journal of Neuroscience.

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

[29]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[30]  Ma Jun,et al.  Simulated test of electric activity of neurons by using Josephson junction based on synchronization scheme , 2012 .

[31]  Y. Lai,et al.  Coherence resonance in coupled chaotic oscillators. , 2001, Physical review letters.

[32]  M. Perc Spatial coherence resonance in excitable media. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  B. Josephson Possible new effects in superconductive tunnelling , 1962 .

[34]  Yi Xiao,et al.  Current–voltage characteristic of the Josephson chaos , 2000 .

[35]  J. Danckaert,et al.  Solitary and coupled semiconductor ring lasers as optical spiking neurons. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  R. Keynes,et al.  Calcium and potassium systems of a giant barnacle muscle fibre under membrane potential control , 1973, The Journal of physiology.

[37]  Alexander Kozlov,et al.  Computer simulations of stimulus dependent state switching in basic circuits of bursting neurons , 1998 .

[38]  Paul Woafo,et al.  Dynamics of a cantilever arm actuated by a nonlinear electrical circuit , 2011 .

[39]  Jun Tang,et al.  Simulating the electric activity of FitzHugh–Nagumo neuron by using Josephson junction model , 2012 .

[40]  Victor B. Kazantsev,et al.  Synaptic Coupling Between Two Electronic Neurons , 2006 .

[41]  J. Kurths,et al.  Coherence Resonance in a Noise-Driven Excitable System , 1997 .

[42]  Wei Wang,et al.  INTERNAL-NOISE-ENHANCED SIGNAL TRANSDUCTION IN NEURONAL SYSTEMS , 1997 .

[43]  Huaguang Gu,et al.  White noise-induced spiral waves and multiple spatial coherence resonances in a neuronal network with type I excitability ☆ , 2013 .

[44]  Henry D I Abarbanel,et al.  Neural circuitry for recognizing interspike interval sequences. , 2006, Physical review letters.