Multiple resonances with time delays and enhancement by non-Gaussian noise in Newman-Watts networks of Hodgkin-Huxley neurons

In this paper, we study the effect of time delay on the spiking activity in Newman-Watts small-world networks of Hodgkin-Huxley neurons with non-Gaussian noise, and investigate how the non-Gaussian noise affects the delay-induced behaviors. It was found that, as the delay increases, the neuron spiking intermittently performs the most ordered and synchronized behavior when the delay lengths are integer multiples of the spiking periods, which shows multiple temporal resonances and spatial synchronizations, and reveals that the locking between the delay lengths and the spiking periods might be the mechanism behind the behaviors. It was also found that the delay-optimized spiking behaviors could be enhanced when non-Gaussian noise's deviation from the Gaussian noise is appropriate. These results show that time delay and non-Gaussian noise would cooperate to play more constructive and efficient roles in the information processing of neural networks.

[1]  Raúl Toral,et al.  Effective Markovian approximation for non-Gaussian noises: a path integral approach , 2002 .

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

[3]  Z. D. Wang,et al.  Stochastic resonance in a Hodgkin-Huxley neuron in the absence of external noise. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  S. Schultz.  Principles of Neural Science, 4th ed. , 2001 .

[5]  Matjaz Perc,et al.  Establishing the stochastic nature of intracellular calcium oscillations from experimental data. , 2008, Biophysical chemistry.

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

[7]  Alexander B. Neiman,et al.  Coherence resonance in a Hodgkin-Huxley neuron , 1998 .

[8]  J. Kurths,et al.  Array-Enhanced Coherence Resonance , 2001 .

[9]  Yubing Gong,et al.  Coherence resonance induced by non-Gaussian noise in a deterministic Hodgkin–Huxley neuron , 2009 .

[10]  I. Goychuk,et al.  Stochastic resonance as a collective property of ion channel assemblies , 2001, physics/0106036.

[11]  A. Longtin.  AUTONOMOUS STOCHASTIC RESONANCE IN BURSTING NEURONS , 1997 .

[12]  Hang-Hyun Jo,et al.  Effect of spatially correlated noise on coherence resonance in a network of excitable cells. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Peter Hänggi,et al.  Stochastic resonance in biology. How noise can enhance detection of weak signals and help improve biological information processing. , 2002, Chemphyschem : a European journal of chemical physics and physical chemistry.

[14]  Raúl Toral,et al.  Enhancement of stochastic resonance: the role of non Gaussian noises , 2001 .

[15]  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.

[16]  Matjaz Perc,et al.  Flights towards defection in economic transactions , 2007 .

[17]  Hsing-Yin Chen,et al.  Theoretical evidence of barrier-free proton transfer in 7-azaindole-water cluster anions. , 2009, The Journal of chemical physics.

[18]  Yubing Gong,et al.  Coherence resonance induced by the deviation of non-Gaussian noise in coupled Hodgkin-Huxley neurons. , 2009, The Journal of chemical physics.

[19]  O. Kwon,et al.  Coherence resonance in small-world networks of excitable cells , 2002 .

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

[21]  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.

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

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

[24]  Current and efficiency enhancement in Brownian motors driven by non Gaussian noises , 2004, cond-mat/0403504.

[25]  Wei Wang,et al.  40-Hz coherent oscillations in neuronal systems , 1997 .

[26]  Olaf Sporns,et al.  The small world of the cerebral cortex , 2007, Neuroinformatics.

[27]  S. Solla,et al.  Self-sustained activity in a small-world network of excitable neurons. , 2003, Physical review letters.

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

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

[30]  Yubing Gong,et al.  Optimal spike coherence and synchronization on complex Hodgkin-Huxley neuron networks. , 2005, Chemphyschem : a European journal of chemical physics and physical chemistry.

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

[32]  Wiesenfeld,et al.  Stochastic resonance on a circle. , 1994, Physical review letters.

[33]  Gang Hu,et al.  Stochastic resonance of small-world networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[36]  J. M. Sancho,et al.  Spatial coherence resonance near pattern-forming instabilities , 2004 .

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

[38]  J. M. Sancho,et al.  Spatiotemporal order out of noise , 2007 .

[39]  H S Wio,et al.  Experimental evidence of stochastic resonance without tuning due to non-Gaussian noises. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  J. Kurths,et al.  Frequency and phase locking of noise-sustained oscillations in coupled excitable systems: array-enhanced resonances. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[42]  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.

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

[44]  J. Kurths,et al.  Array-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise. , 2001, Physical review letters.

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

[46]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[47]  Peter Grigg,et al.  Effects of Colored Noise on Stochastic Resonance in Sensory Neurons , 1999 .

[48]  Guanrong Chen,et al.  Spatio-temporal patterns in a square-lattice Hodgkin-Huxley neural network , 2006 .

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

[50]  Zhonghuai Hou,et al.  Optimal network size for Hodgkin–Huxley neurons , 2005 .

[51]  Lisa Borland,et al.  Ito-Langevin equations within generalized thermostatistics , 1998 .

[52]  Wulfram Gerstner,et al.  Spiking Neuron Models , 2002 .

[53]  H. Wio,et al.  A random walker on a ratchet potential: effect of a non Gaussian noise , 2007, 0707.3206.

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

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

[56]  Raul Toral,et al.  Effect of non-Gaussian noise sources in a noise-induced transition , 2004 .

[57]  S. -. Lee,et al.  Parameter dependence of stochastic resonance in the stochastic Hodgkin-Huxley neuron. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[59]  M. Nicolelis,et al.  Sensorimotor encoding by synchronous neural ensemble activity at multiple levels of the somatosensory system. , 1995, Science.

[60]  C. Tsallis,et al.  Generalized statistical mechanics : connection with thermodynamics , 1991 .

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

[62]  D. McCormick,et al.  On the cellular and network bases of epileptic seizures. , 2001, Annual review of physiology.

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

[64]  M. Perc.  Transition from Gaussian to Levy distributions of stochastic payoff variations in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[65]  M. Steriade,et al.  Dynamic properties of corticothalamic neurons and local cortical interneurons generating fast rhythmic (30-40 Hz) spike bursts. , 1998, Journal of neurophysiology.

[66]  Lisa Borland,et al.  Microscopic dynamics of the nonlinear Fokker-Planck equation: A phenomenological model , 1998 .

[67]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .