Synchronous firing patterns and transitions in small-world neuronal network

Synchronous firing patterns and transitions of Hindmarsh–Rose small-world neuronal network are studied in this work. With the same external stimuli current, it is shown that the synchronous state of the Newman and Watts (NW) small-world neuronal network is completely determined by its external stimuli current, have nothing about the coupling strength $$C$$C as well as the connection probability $$p$$p; a qualitative explanation is proposed for the opposite changes of the minimum critical coupling strength $$C_{\mathrm{mcc}}$$Cmcc and the minimum connection probability $$p_{\mathrm{mcp}}$$pmcp. With two different amplitude stimuli current, only almost complete synchronization can be achieved, and the firing patterns of the synchronized NW small-world neuronal network only distributes the interval with two endpoints, which just correspond to the two modes in a single model neuron with these two kinds of amplitude stimuli current.

[1]  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.

[2]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .

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

[4]  You-Quan Li,et al.  Dynamical magnetoelectric effects in the distorted spiral multiferroic magnets , 2013 .

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

[6]  Qishao Lu,et al.  Bursting synchronization dynamics of pancreatic β-cells with electrical and chemical coupling , 2012, Cognitive Neurodynamics.

[7]  Guanrong Chen,et al.  Impact of delays and rewiring on the dynamics of small-world neuronal networks with two types of coupling , 2010 .

[8]  Guanrong Chen,et al.  Synchronization transitions on small-world neuronal networks: Effects of information transmission delay and rewiring probability , 2008 .

[9]  M. Newman,et al.  Renormalization Group Analysis of the Small-World Network Model , 1999, cond-mat/9903357.

[10]  Chibing Hu,et al.  The complete synchronization of Morris–Lecar neurons influenced by noise , 2013 .

[11]  Guanrong Chen,et al.  Stimulus-induced transition of clustering firings in neuronal networks with information transmission delay , 2013 .

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

[13]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[14]  K. Kyamakya,et al.  Analog circuit implementation and synchronization of a system consisting of a van der Pol oscillator linearly coupled to a Duffing oscillator , 2012 .

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

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

[17]  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.

[18]  Guanrong Chen,et al.  Synaptic plasticity induced transition of spike propagation in neuronal networks , 2013, Commun. Nonlinear Sci. Numer. Simul..

[19]  Aihua Zhang,et al.  EFFECTS OF TIME DELAY ON CHAOTIC NEURONAL DISCHARGES , 2010 .

[20]  Diyi Chen,et al.  Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization , 2013 .

[21]  Guanrong Chen,et al.  Synchronization stability and firing transitions in two types of class I neuronal networks with short-term plasticity , 2014, Neural Networks.

[22]  Mingzhou Ding,et al.  Enhancement of neural synchrony by time delay. , 2004, Physical review letters.

[23]  Matjaž Perc,et al.  Effects of small-world connectivity on noise-induced temporal and spatial order in neural media , 2007 .

[24]  Jun Ma,et al.  Cooperative dynamics in neuronal networks , 2013 .

[25]  H. Nijmeijer,et al.  Partial synchronization in diffusively time-delay coupled oscillator networks. , 2012, Chaos.

[26]  Bin Deng,et al.  Chaotic phase synchronization in a modular neuronal network of small-world subnetworks. , 2011, Chaos.