Multi-channels coupling-induced pattern transition in a tri-layer neuronal network

Abstract Neurons in nerve system show complex electrical behaviors due to complex connection types and diversity in excitability. A tri-layer network is constructed to investigate the signal propagation and pattern formation by selecting different coupling channels between layers. Each layer is set as different states, and the local kinetics is described by Hindmarsh–Rose neuron model. By changing the number of coupling channels between layers and the state of the first layer, the collective behaviors of each layer and synchronization pattern of network are investigated. A statistical factor of synchronization on each layer is calculated. It is found that quiescent state in the second layer can be excited and disordered state in the third layer is suppressed when the first layer is controlled by a pacemaker, and the developed state is dependent on the number of coupling channels. Furthermore, the collapse in the first layer can cause breakdown of other layers in the network, and the mechanism is that disordered state in the third layer is enhanced when sampled signals from the collapsed layer can impose continuous disturbance on the next layer.

[1]  M. Perc,et al.  Gap Junctions and Epileptic Seizures – Two Sides of the Same Coin? , 2011, PloS one.

[2]  Matjaž Perc,et al.  Pacemaker-guided noise-induced spatial periodicity in excitable media , 2009 .

[3]  Ergin Yılmaz,et al.  Enhancement of pacemaker induced stochastic resonance by an autapse in a scale-free neuronal network , 2016, Science China Technological Sciences.

[4]  Xiaofang Zhang,et al.  Dynamical analysis of periodic bursting in piece-wise linear planar neuron model , 2015, Cognitive Neurodynamics.

[5]  Mahmut Ozer,et al.  Effect of channel noise on the time-course of recovery from inactivation of sodium channels , 2005 .

[6]  Matjaz Perc,et al.  Weak signal propagation through noisy feedforward neuronal networks , 2010, Neuroreport.

[7]  Jian Xu,et al.  An introduction and guidance for neurodynamics , 2015 .

[8]  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.

[9]  Guanrong Chen,et al.  Biological experimental demonstration of bifurcations from bursting to spiking predicted by theoretical models , 2014 .

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

[11]  M. Perc.  Stochastic resonance on excitable small-world networks via a pacemaker. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Henk Nijmeijer,et al.  State and Parameter Estimation for Canonic Models of Neural oscillators , 2010, Int. J. Neural Syst..

[13]  Mahmut Ozer,et al.  Effect of the sub-threshold periodic current forcing on the regularity and the synchronization of neuronal spiking activity , 2006 .

[14]  Ying Wu,et al.  Emitting waves from defects in network with autapses , 2015, Commun. Nonlinear Sci. Numer. Simul..

[15]  Wuyin Jin,et al.  Dislocation Coupling-Induced Transition of Synchronization in Two-Layer Neuronal Networks , 2014 .

[16]  S. Cullheim,et al.  The microglial networks of the brain and their role in neuronal network plasticity after lesion , 2007, Brain Research Reviews.

[17]  M. Sanjuán,et al.  Map-based models in neuronal dynamics , 2011 .

[18]  Jun Tang,et al.  A review for dynamics in neuron and neuronal network , 2017, Nonlinear Dynamics.

[19]  Terrence J. Sejnowski,et al.  Computational models of neuron-astrocyte interaction in epilepsy , 2012, Front. Comput. Neurosci..

[20]  Yong Chen,et al.  Effect of an autapse on the firing pattern transition in a bursting neuron , 2014, Commun. Nonlinear Sci. Numer. Simul..

[21]  Jiang Wang,et al.  Synchronization of neuron population subject to steady DC electric field induced by magnetic stimulation , 2012, Cognitive Neurodynamics.

[22]  M. Hashemi,et al.  Effect of duration of synaptic activity on spike rate of a Hodgkin-Huxley neuron with delayed feedback. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Mahmut Ozer,et al.  Collective temporal coherence for subthreshold signal encoding on a stochastic small-world Hodgkin-Huxley neuronal network , 2008 .

[24]  Jun Tang,et al.  Astrocyte calcium wave induces seizure-like behavior in neuron network , 2017 .

[25]  Guodong Ren,et al.  Collapse of ordered spatial pattern in neuronal network , 2016 .

[26]  Ma Jun,et al.  Transition of electric activity of neurons induced by chemical and electric autapses , 2015 .

[27]  Eugene M. Izhikevich,et al.  Which model to use for cortical spiking neurons? , 2004, IEEE Transactions on Neural Networks.

[28]  M. Perc,et al.  Complex synchronous behavior in interneuronal networks with delayed inhibitory and fast electrical synapses. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Shenquan Liu,et al.  Bifurcation analysis of a Morris–Lecar neuron model , 2013, Biological Cybernetics.

[30]  Jun Ma,et al.  Autapse-induced target wave, spiral wave in regular network of neurons , 2014 .

[31]  Romain Brette,et al.  The Cauchy problem for one-dimensional spiking neuron models , 2008, Cognitive Neurodynamics.

[32]  M. Perc,et al.  Regulation of Irregular Neuronal Firing by Autaptic Transmission , 2016, Scientific Reports.

[33]  Qishao Lu,et al.  Equilibrium analysis and phase synchronization of two coupled HR neurons with gap junction , 2012, Cognitive Neurodynamics.

[34]  Long Huang,et al.  Parameters estimation, mixed synchronization, and antisynchronization in chaotic systems , 2014, Complex..

[35]  Woochang Lim,et al.  Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons , 2014, Cognitive Neurodynamics.

[36]  Mahmut Ozer,et al.  Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks , 2016 .

[37]  Jun Ma,et al.  Model of electrical activity in a neuron under magnetic flow effect , 2016 .

[38]  Jun Ma,et al.  Pattern selection in neuronal network driven by electric autapses with diversity in time delays , 2015 .

[39]  Matjaz Perc,et al.  Firing regulation of fast-spiking interneurons by autaptic inhibition , 2016, 1606.01358.

[40]  Jun Ma,et al.  Autapse-induced synchronization in a coupled neuronal network , 2015 .

[41]  Tim Gollisch,et al.  Modeling Single-Neuron Dynamics and Computations: A Balance of Detail and Abstraction , 2006, Science.

[42]  Christoph S. Herrmann,et al.  Autapse Turns Neuron into oscillator , 2004, Int. J. Bifurc. Chaos.

[43]  Wuyin Jin,et al.  Pattern selection and self-organization induced by random boundary initial values in a neuronal network , 2016 .

[44]  Ma Jun,et al.  A review for dynamics of collective behaviors of network of neurons , 2015 .

[45]  Jun Tang,et al.  Formation of Autapse Connected to Neuron and Its Biological Function , 2017, Complex..

[46]  Jun Tang,et al.  Autaptic Modulation of Electrical Activity in a Network of Neuron-Coupled Astrocyte , 2017, Complex..

[47]  Lubica Benuskova,et al.  Modeling brain dynamics using computational neurogenetic approach , 2008, Cognitive Neurodynamics.

[48]  F. L. D. Silva,et al.  Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network , 2004, Neuroscience.

[49]  Matjaž Perc,et al.  Thoughts out of noise , 2006 .

[50]  M. Ozer,et al.  Stochastic resonance on Newman–Watts networks of Hodgkin–Huxley neurons with local periodic driving , 2009 .

[51]  Chunni Wang,et al.  Dynamics of electric activities in neuron and neurons of network induced by autapses , 2014 .

[52]  J. Hindmarsh,et al.  A model of the nerve impulse using two first-order differential equations , 1982, Nature.

[53]  Alexandre Wagemakers,et al.  Vibrational resonance in a heterogeneous scale free network of neurons , 2015, Commun. Nonlinear Sci. Numer. Simul..

[54]  Huaguang Gu,et al.  A four-dimensional neuronal model to describe the complex nonlinear dynamics observed in the firing patterns of a sciatic nerve chronic constriction injury model , 2015 .

[55]  Jun Ma,et al.  Prediction for breakup of spiral wave in a regular neuronal network , 2016 .

[56]  Jun Ma,et al.  Multiple modes of electrical activities in a new neuron model under electromagnetic radiation , 2016, Neurocomputing.

[57]  J. Bekkers.  Synaptic Transmission: Functional Autapses in the Cortex , 2003, Current Biology.