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Stochastic resonance of localized activity driven by common noise

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Abstract

We study the influence of spatially correlated noise on the transient dynamics of a recurrent network with Mexican-Hat-type connectivity. We derive the closed form of the order parameter functional in the thermodynamical limit of neuron number N. Our analysis shows that network dynamics is qualitatively changed by the presence of common noise. Network dynamics driven by common noise obtains the global level of fluctuation, which is not observed in a network driven by independent noise only. We show that the optimal level of global fluctuation enhances the transition from non-localized firing states to spatially localized firing states, and also enhances the rotation speed of localized activity.

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References

  • LF Abbott P Dayan (1999) ArticleTitleThe effect of correlated variability on the accuracy of a population code Neural Comp 11 IssueID1 91–101 Occurrence Handle10.1162/089976699300016827 Occurrence Handle1:STN:280:DyaK1M7js1Smug%3D%3D

    Article  CAS  Google Scholar 

  • S Amari (1977) ArticleTitleDynamics of pattern formation in lateral-inhibition type neural fields Biol Cybern 27 77–87 Occurrence Handle10.1007/BF00337259 Occurrence Handle1:STN:280:CSeD387hs1U%3D Occurrence Handle911931

    Article  CAS  PubMed  Google Scholar 

  • S Amari H Nakahara S Wu Y Sakai (2003) ArticleTitleSynchronous firing and higher-order interactions in neural pool Neural Comp 15 127–142 Occurrence Handle10.1162/089976603321043720

    Article  Google Scholar 

  • R Ben-Yishai RL Bar-Or H Sompolinsky (1995) ArticleTitleTheory of orientation tuning in visual cortex Proc Natl Acad Sci USA 92 3844–3948 Occurrence Handle1:CAS:528:DyaK2MXlsVSlu7g%3D Occurrence Handle7731993

    CAS  PubMed  Google Scholar 

  • R Benzi A Sutera A Vulpiani (1981) ArticleTitleThe mechanism of stochastic resonance J Phys A 14 L453–L457

    Google Scholar 

  • C Blakemore R Carpente M Georgeso (1970) ArticleTitleLateral inhibition between orientation detectors in human visual system Nature 228 37–39

    Google Scholar 

  • JJ Collins C Chow A Capela T Imhoff (1995) ArticleTitleAperiodic stochastic resonance Phys Rev E 54 5575–5584 Occurrence Handle10.1103/PhysRevE.54.5575

    Article  Google Scholar 

  • B Doiron B Lindner A Longtin L Maler J Bastian (2004) ArticleTitleOscillatory activity in electrosensory neurons increases with the spatial correlation of the stochastic input stimulus Phys Rev Lett 93 048101

    Google Scholar 

  • JK Douglass L Wilkens E Pantazelou F Moss (1993) ArticleTitleNoise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance Nature 365 337–340

    Google Scholar 

  • J Droulez A Berthoz (1991) ArticleTitleA neural network model of sensoritopic maps with predictive shortterm memory properties Proc Natl Acad Sci USA 88 9653–9657 Occurrence Handle1:STN:280:By2D2M3hsV0%3D Occurrence Handle1946381

    CAS  PubMed  Google Scholar 

  • L Gammaitoni P Hanggi P Jung F Marchesoni (1998) ArticleTitleStochastic resonance Rev Mod Sci 70 223–287 Occurrence Handle10.1103/RevModPhys.70.223 Occurrence Handle1:CAS:528:DyaK1cXhtFCjtLs%3D

    Article  CAS  Google Scholar 

  • Hamaguchi K, Okada M, Aihara K (2004) Theory of localized synfire chain: characteristic propagation speed of stable spike patterns. In: Advances in neural information processing systems 17:553–560

  • K Kitajo D Nozaki L Ward Y Yamamoto (2003) ArticleTitleBehavioral stochastic resonance within the human brain Phys Rev Lett 90 IssueID21 218103 Occurrence Handle10.1103/PhysRevLett.90.218103 Occurrence Handle12786595

    Article  PubMed  Google Scholar 

  • D Lee NL Port W Kruse AP Georgopoulos (1998) ArticleTitleVariability and correlated noise in the discharge of neurons in motor and parietal areas of the primate cortex J Neurosci 18 IssueID3 1161–1170

    Google Scholar 

  • JE Levin JP Miller (1996) ArticleTitleBroadband neural encoding in the cricket cercal sensory system enchanced by stochastic resonance Nature 380 165–168

    Google Scholar 

  • J Lindner S Chandramouli A Bulsara M Locher W Ditto (1998) ArticleTitleNoise enhanced propagation Phys Rev Lett 81 5048–5051 Occurrence Handle10.1103/PhysRevLett.81.5048 Occurrence Handle1:CAS:528:DyaK1cXnsleruro%3D

    Article  CAS  Google Scholar 

  • F Liu B Hu W Wang (2001) ArticleTitleEffects of correlated and independent noise on signal processing in neuronal systems Phys Rev E 63 031907 Occurrence Handle10.1103/PhysRevE.63.031907 Occurrence Handle1:STN:280:DC%2BD38%2FgvVChuw%3D%3D

    Article  CAS  Google Scholar 

  • A Longtin (1993) ArticleTitleStochastic resonance in neuron models J Stat Phys 70 309–327 Occurrence Handle10.1007/BF01053970

    Article  Google Scholar 

  • A Lukashin A Georgopoulos (1993) ArticleTitleA dynamical neural network model for motor cortical activity during movement: Population coding of movement trajectories Biol Cybern 69 517–524 Occurrence Handle10.1007/BF01185423 Occurrence Handle1:STN:280:ByuC3c%2FivFU%3D Occurrence Handle8274549

    Article  CAS  PubMed  Google Scholar 

  • H Nishimura N Katada K Aihara (2000) ArticleTitleCoherent response in a chaotic neural network Neural Processing Letters 12 49–58 Occurrence Handle10.1023/A:1009626028831

    Article  Google Scholar 

  • H Sompolinsky H Yoon K Kang M Shamir (2001) ArticleTitlePopulation coding in neuronal systems with correlated noise Phys Rev E 64 051904 Occurrence Handle10.1103/PhysRevE.64.051904 Occurrence Handle1:STN:280:DC%2BD38%2FjvFWntw%3D%3D

    Article  CAS  Google Scholar 

  • J Teramae D Tanaka (2005) ArticleTitleRobustness of the noise-induced phase synchronization in a general class of limit cycle oscillators Phys Rev Lett 93 204–103

    Google Scholar 

  • MCW Rossum Particlevan GG Turrigiano SB Nelson (2002) ArticleTitleFast propagation of firing rates through layered networks of noisy neurons J Neurosci 22 1956–1966

    Google Scholar 

  • S Wang F Liu W Wang (2004) ArticleTitleImpact of spatially correlated noise on neuronal firing Phys Rev E 69 011909 Occurrence Handle10.1103/PhysRevE.69.011909

    Article  Google Scholar 

  • HR Wilson JD Cowan (1972) ArticleTitleExcitatory and inhibitory interactions in localized population of model neurons Biophys J 12 1–24 Occurrence Handle1:STN:280:CS2D2snltF0%3D Occurrence Handle4332108

    CAS  PubMed  Google Scholar 

  • S Wu S Amari H Nakahara (2002) ArticleTitlePopulation coding and decoding in a neural field: a computational study Neural Comp 14 999–1026 Occurrence Handle10.1162/089976602753633367

    Article  Google Scholar 

  • H Zhonghuai Y Lingfa X Zuo X Houwen (1998) ArticleTitleNoise induced pattern transition and spatiotemporal stochastic resonance Phys Rev Lett 81 2854–2857 Occurrence Handle10.1103/PhysRevLett.81.2854

    Article  Google Scholar 

  • C Zhou J Kurths B Hu (2001) ArticleTitleArray-enhanced coherence resonance: nontrivial effects of heterogeneity and spatial independence of noise Phys Rev Lett 8709 098101 Occurrence Handle10.1103/PhysRevLett.87.098101

    Article  Google Scholar 

  • E Zohary MN Shadlen WT Newsome (1994) ArticleTitleCorrelated neuronal discharge rate and its implications for psychophysical performance Nature 370 140–143

    Google Scholar 

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Authors and Affiliations

  1. RIKEN BSI, 2-1 Hirosawa Wako, Saitama, Japan

    Kosuke Hamaguchi & Masato Okada

  2. Department of Complexity Science and Engineering, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, 277-8561, Japan

    Masato Okada

  3. Department of Bio-System Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa, Yamagata, 992-8510, Japan

    Shigeru Kubota

  4. Institute of Industrial Science, University of Tokyo and ERATO Aihara Complexity Modeling Project JST, 4-6-1 Komaba, Meguro, Tokyo, 153-8505, Japan

    Kazuyuki Aihara

Authors
  1. Kosuke Hamaguchi
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  2. Masato Okada
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  3. Shigeru Kubota
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  4. Kazuyuki Aihara
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Correspondence to Kosuke Hamaguchi.

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Hamaguchi, K., Okada, M., Kubota, S. et al. Stochastic resonance of localized activity driven by common noise. Biol Cybern 92, 438–444 (2005). https://doi.org/10.1007/s00422-005-0570-2

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  • DOI: https://doi.org/10.1007/s00422-005-0570-2

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