Wave propagation and synchronization induced by chemical autapse in chain Hindmarsh-Rose neural network

Abstract In this paper, based on a chain Hindmarsh–Rose (HR) neural network under the action of electromagnetic field, the effects of connection strength between adjacent neurons on the wave propagation are investigated by utilizing numerical simulations. When the connection strength is increased via the decreasing of distance from central neuron, it is found that the firing rates of neurons in chain HR neural network are increased, and the velocity of wave propagation also becomes fast with the increasing of connection strength maximum. The chemical autapse imposed on the central neuron has a great influence on the firing rates of neurons and the wave propagation with different autaptic intensities. The firing rates of neurons are high, and many neurons can stand the excited state by increasing the field coupling strength. However, when the connection strength is decreased via the decreasing of distance from central neuron, the influences of connection strength maximum on the wave propagation are very small. The synchronization factor of the chain HR neural network is investigated by changing the maximum of connection strength, the autaptic intensity, and the field coupling intensity, respectively. It is found that the larger the field coupling strength is, the better the synchronization of neurons in the chain neural network will be, and the firing rates of neurons are high.

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

[2]  Anqi Ling,et al.  Channel based generating function approach to the stochastic Hodgkin-Huxley neuronal system , 2016, Scientific Reports.

[3]  Qiming Pei,et al.  Effects of noise and synaptic weight on propagation of subthreshold excitatory postsynaptic current signal in a feed-forward neural network , 2018, Nonlinear Dynamics.

[4]  M S Baptista,et al.  Combined effect of chemical and electrical synapses in Hindmarsh-Rose neural networks on synchronization and the rate of information. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Yuangen Yao,et al.  Subthreshold Periodic Signal Detection by Bounded Noise-Induced Resonance in the FitzHugh-Nagumo Neuron , 2018, Complex..

[6]  Xu Xu,et al.  Dynamical model and control of a small-world network with memory , 2013 .

[7]  J. Casado,et al.  Noise-induced resonances in the Hindmarsh-Rose neuronal model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[9]  Z. Duan,et al.  Synchronization transitions on scale-free neuronal networks due to finite information transmission delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Min Jiang,et al.  Propagation of Spiking and Burst-Spiking Synchronous States in a Feed-Forward Neuronal Network , 2012 .

[11]  Dibakar Ghosh,et al.  Basin stability for chimera states , 2017, Scientific Reports.

[12]  Jun Tang,et al.  Wave emitting and propagation induced by autapse in a forward feedback neuronal network , 2015, Neurocomputing.

[13]  J M Bekkers,et al.  Neurophysiology: Are autapses prodigal synapses? , 1998, Current Biology.

[14]  Dong Jun,et al.  Dynamic behavior analysis of fractional-order Hindmarsh–Rose neuronal model , 2013, Cognitive Neurodynamics.

[15]  Soumen Majhi,et al.  Chimera states in uncoupled neurons induced by a multilayer structure , 2016, Scientific Reports.

[16]  Matjaz Perc,et al.  Multiple firing coherence resonances in excitatory and inhibitory coupled neurons , 2012, 1202.3539.

[17]  Idan Segev,et al.  On the Transmission of Rate Code in Long Feedforward Networks with Excitatory–Inhibitory Balance , 2003, The Journal of Neuroscience.

[18]  A. Karabelas,et al.  Evidence for autapses in the substantia nigra , 1980, Brain Research.

[19]  Ya Jia,et al.  Effect of external periodic signals and electromagnetic radiation on autaptic regulation of neuronal firing. , 2018, IET systems biology.

[20]  Tasawar Hayat,et al.  Phase synchronization between two neurons induced by coupling of electromagnetic field , 2017, Appl. Math. Comput..

[21]  Ming Yi,et al.  Breakup of Spiral Wave and Order-Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross-Correlated Sine-Wiener Noises in a Regular Network of Hodgkin-Huxley Neurons , 2018, Complex..

[22]  Matjaz Perc,et al.  Minimal model for spatial coherence resonance. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Yanjun Zeng,et al.  Control of bursting behavior in neurons by autaptic modulation , 2013, Neurological Sciences.

[24]  Mahmut Ozer,et al.  Autapse-induced multiple coherence resonance in single neurons and neuronal networks , 2016, Scientific Reports.

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

[26]  Alessandro E. P. Villa,et al.  Integration and transmission of distributed deterministic neural activity in feed-forward networks , 2012, Brain Research.

[27]  Soumen Majhi,et al.  Chimera states in a multilayer network of coupled and uncoupled neurons. , 2017, Chaos.

[28]  Feng Liu,et al.  Propagation of firing rate in a feed-forward neuronal network. , 2006, Physical review letters.

[29]  Markus Diesmann,et al.  The mechanism of synchronization in feed-forward neuronal networks , 2008 .

[30]  Keming Tang,et al.  Pinning synchronization of unilateral coupling neuron network with stochastic noise , 2014, Appl. Math. Comput..

[31]  Z. Duan,et al.  Delay-enhanced coherence of spiral waves in noisy Hodgkin–Huxley neuronal networks , 2008 .

[32]  Ya Jia,et al.  Energy dependence on modes of electric activities of neuron driven by different external mixed signals under electromagnetic induction , 2018, Science China Technological Sciences.

[33]  J. Lichtman,et al.  Synapse Elimination and Indelible Memory , 2000, Neuron.

[34]  Ahmed Alsaedi,et al.  Collective responses in electrical activities of neurons under field coupling , 2018, Scientific Reports.

[35]  Lianchun Yu,et al.  Response of Morris-Lecar neurons to various stimuli. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Ya Jia,et al.  Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation , 2017, Nonlinear Dynamics.

[37]  Z. Wang,et al.  Effects of small world connection on the dynamics of a delayed ring network , 2009 .

[38]  Jinzhi Lei,et al.  Burst synchronization transitions in a neuronal network of subnetworks. , 2011, Chaos.

[39]  Umeshkanta Singh Thounaojam,et al.  Phase switching in Hindmarsh-Rose relay neurons , 2016 .

[40]  Ya Jia,et al.  Mixed Stimulus-Induced Mode Selection in Neural Activity Driven by High and Low Frequency Current under Electromagnetic Radiation , 2017, Complex..

[41]  Matjaž Perc,et al.  Spatial coherence resonance in neuronal media with discrete local dynamics , 2007 .

[42]  Chengren Li,et al.  Projective synchronization of the small-world delayed network with uncertainty , 2014 .

[43]  Xiao-Shu Luo,et al.  Firing activity of complex space-clamped FitzHugh-Nagumo neural networks , 2008 .

[44]  Jun Ma,et al.  Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems , 2010, Appl. Math. Comput..

[45]  Tomoki Fukai,et al.  Complex evolution of spike patterns during burst propagation through feed-forward networks , 2008, Biological Cybernetics.

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

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

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

[49]  F. Pfrieger,et al.  Roles of glial cells in synapse development , 2009, Cellular and Molecular Life Sciences.

[50]  G. Bi,et al.  Synaptic Modifications in Cultured Hippocampal Neurons: Dependence on Spike Timing, Synaptic Strength, and Postsynaptic Cell Type , 1998, The Journal of Neuroscience.

[51]  Baocheng Li,et al.  Finite-time synchronization for complex dynamical networks with hybrid coupling and time-varying delay , 2014 .

[52]  Ya Jia,et al.  Autaptic modulation-induced neuronal electrical activities and wave propagation on network under electromagnetic induction , 2018, The European Physical Journal Special Topics.

[53]  Matjaz Perc,et al.  Chimera states: Effects of different coupling topologies , 2017, 1705.06786.

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

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

[56]  Sajad Jafari,et al.  Elimination of spiral waves in excitable media by magnetic induction , 2018, Nonlinear Dynamics.

[57]  Ergin Yılmaz,et al.  Stochastic resonance in hybrid scale-free neuronal networks , 2013 .

[58]  Ying Liu,et al.  Spiking activities in chain neural network driven by channel noise with field coupling , 2019, Nonlinear Dynamics.

[59]  Ying Xu,et al.  Effects of ion channel blocks on electrical activity of stochastic Hodgkin-Huxley neural network under electromagnetic induction , 2017, Neurocomputing.

[60]  Guanrong Chen,et al.  Synchronous Bursts on Scale-Free Neuronal Networks with Attractive and Repulsive Coupling , 2010, PloS one.

[61]  Lijian Yang,et al.  Propagation of firing rate by synchronization and coherence of firing pattern in a feed-forward multilayer neural network. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[62]  Daqing Guo,et al.  Stochastic and coherence resonance in feed-forward-loop neuronal network motifs. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[63]  Jian Shen,et al.  Propagation of firing rate by synchronization in a feed-forward multilayer Hindmarsh-Rose neural network , 2018, Neurocomputing.