Multiple synchronization transitions due to periodic coupling strength in delayed Newman–Watts networks of chaotic bursting neurons

In this paper, we numerically study the effect of time-periodic coupling strength on the synchronization of firing activity in delayed Newman–Watts networks of chaotic bursting neurons. We first examine how the firing synchronization transitions induced by time delay under fixed coupling strength changes in the presence of time-periodic coupling strength, and then focus on how time-periodic coupling strength induces synchronization transitions in the networks. It is found that time delay can induce more synchronization transitions in the presence of time-periodic coupling strength compared to fixed coupling strength. As the frequency of time-periodic coupling strength is varied, the firing exhibits multiple synchronization transitions between spiking antiphase synchronization and in-phase synchronization of various firing behaviors including bursting, spiking, and both bursting and spiking, depending on the values of time delay. These results show that time-periodic coupling strength can increase the synchronization transitions by time delay and can induce multiple synchronization transitions of various firing behaviors in the neuronal networks. This means that time-periodic coupling strength plays an important role in the information processing and transmission in neural systems.

[1]  Matjaz Perc,et al.  Delay-induced multiple stochastic resonances on scale-free neuronal networks. , 2009, Chaos.

[2]  Johan A K Suykens,et al.  Introduction to Focus Issue: synchronization in complex networks. , 2008, Chaos.

[3]  Awadhesh Prasad,et al.  Time-delay-induced phase-transition to synchrony in coupled bursting neurons. , 2011, Chaos.

[4]  C. Gray.  The Temporal Correlation Hypothesis of Visual Feature Integration Still Alive and Well , 1999, Neuron.

[5]  Martin Tobias Huber,et al.  Computer Simulations of Neuronal Signal Transduction: The Role of Nonlinear Dynamics and Noise , 1998 .

[6]  Frank Moss,et al.  Homoclinic bifurcation in a Hodgkin-Huxley model of thermally sensitive neurons. , 2000, Chaos.

[7]  Kristina Todorović,et al.  Synchronization of bursting neurons with delayed chemical synapses. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  M. Newman,et al.  Scaling and percolation in the small-world network model. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Guanrong Chen,et al.  Ordered bursting synchronization and complex wave propagation in a ring neuronal network , 2007 .

[10]  Frank Moss,et al.  Low-Dimensional Dynamics in Sensory Biology 2: Facial Cold Receptors of the Rat , 1999, Journal of Computational Neuroscience.

[11]  J. Dostrovsky,et al.  High-frequency Synchronization of Neuronal Activity in the Subthalamic Nucleus of Parkinsonian Patients with Limb Tremor , 2000, The Journal of Neuroscience.

[12]  Zhonghuai Hou,et al.  Transition to burst synchronization in coupled neuron networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Miguel A F Sanjuán,et al.  Bursting regimes in map-based neuron models coupled through fast threshold modulation. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[15]  Yanhong Zheng,et al.  Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network , 2008 .

[16]  G Bard Ermentrout,et al.  Effects of axonal time delay on synchronization and wave formation in sparsely coupled neuronal oscillators. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Frank Moss,et al.  Low-Dimensional Dynamics in Sensory Biology 1: Thermally Sensitive Electroreceptors of the Catfish , 1997, Journal of Computational Neuroscience.

[18]  Guanrong Chen,et al.  Subthreshold stimulus-aided temporal order and synchronization in a square lattice noisy neuronal network , 2007 .

[19]  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.

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

[21]  W. Singer,et al.  The gamma cycle , 2007, Trends in Neurosciences.

[22]  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.

[23]  K. Krischer,et al.  Resonance tongues in a system of globally coupled FitzHugh-Nagumo oscillators with time-periodic coupling strength. , 2010, Chaos.

[24]  K. Schäfer,et al.  Oscillation and noise determine signal transduction in shark multimodal sensory cells , 1994, Nature.

[25]  Mark Newman,et al.  Models of the Small World , 2000 .

[26]  Masahiko Yoshioka.  Chaos synchronization in gap-junction-coupled neurons. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Du Qu Wei,et al.  Ordering spatiotemporal chaos in discrete neural networks with small-world connections , 2007 .

[28]  Bo Xu,et al.  Multiple coherence resonances by time-periodic coupling strength in scale-free networks of bursting neurons , 2012 .

[29]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[30]  Guanrong Chen,et al.  Synchronization Transition Induced by Synaptic Delay in Coupled Fast-Spiking Neurons , 2008, Int. J. Bifurc. Chaos.

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

[32]  Hans A Braun,et al.  Neural Synchronization at Tonic-to-Bursting Transitions , 2007, Journal of biological physics.

[33]  M. Alexander,et al.  Principles of Neural Science , 1981 .

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

[35]  Matjaz Perc,et al.  Synchronization of Regular and Chaotic oscillations: the Role of Local Divergence and the Slow Passage Effect - a Case Study on calcium oscillations , 2004, Int. J. Bifurc. Chaos.

[36]  H. Hasegawa.  Synchronizations in small-world networks of spiking neurons: diffusive versus sigmoid couplings. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  F. Mormann,et al.  Epileptic seizures are preceded by a decrease in synchronization , 2003, Epilepsy Research.

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

[39]  Jürgen Kurths,et al.  Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons. , 2003, Chaos.

[40]  Sonya Bahar.  BURST-ENHANCED SYNCHRONIZATION IN AN ARRAY OF NOISY COUPLED NEURONS , 2004 .

[41]  M. Perc.  Optimal spatial synchronization on scale-free networks via noisy chemical synapses. , 2009, Biophysical chemistry.

[42]  Jianfeng Feng,et al.  Stability of synchronous oscillations in a system of Hodgkin-Huxley neurons with delayed diffusive and pulsed coupling. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[44]  Yubing Gong,et al.  Multiple coherence resonance induced by time-periodic coupling in stochastic Hodgkin-Huxley neuronal networks. , 2011, Chaos.

[45]  Qiang Xu,et al.  Ordering spatiotemporal chaos in complex thermosensitive neuron networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[46]  D. Hansel,et al.  Role of delays in shaping spatiotemporal dynamics of neuronal activity in large networks. , 2005, Physical review letters.

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

[48]  W. Singer.  Synchronization of cortical activity and its putative role in information processing and learning. , 1993, Annual review of physiology.