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Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction

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Abstract.

The nonlinear prediction method based on the interspike interval (ISI) reconstruction is applied to the ISI sequence of noisy pulse trains and the detection of the deterministic structure is performed. It is found that this method cannot discriminate between the noisy periodic pulse train and the noisy chaotic one when noise-induced pulses exist. When the noise-induced pulses are eliminated by the grouping of ISI sequence with the genetic algorithm, the chaotic structure of the chaotic firings becomes clear, and the noisy chaotic pulse train could be discriminated from the periodic one.

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References

  • Davis L (1996) Handbook of genetics algorithms. Van Nostrand Reinhold

  • B Ermentrout (1996) ArticleTitleType I membranes, phase resetting curves, and synchrony Neural Comput 8 979–1001 Occurrence Handle1:STN:280:BymB1M7ntFY%3D Occurrence Handle8697231

    CAS  PubMed  Google Scholar 

  • CW Gardiner (1985) Handbook of stochastic methods Springer Berlin Heidelberg New York

    Google Scholar 

  • EM Izhikevich (1999) ArticleTitleClass 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models IEEE Trans Neural Networks 10 499–507

    Google Scholar 

  • T Kanamaru M Sekine (2003) ArticleTitleAnalysis of the globally connected active rotators with excitatory and inhibitory connections using the Fokker–Planck equation Phys Rev E 67 031916

    Google Scholar 

  • T Kanamaru M Sekine (2004) ArticleTitleAnalysis of globally connected active rotators with excitatory and inhibitory connections having different time constants using the nonlinear Fokker–Planck equations IEEE Trans on Neural Netw 15 1009–1017

    Google Scholar 

  • Kanamaru T, Sekine M (2005) Synchronized firings in the networks of class 1 excitable neurons with excitatory and inhibitory connections and their dependences on the forms of interactions. Neural Comput 17 (in press)

  • Y Kuramoto (1984) Chemical oscillations, waves, and turbulence Springer Berlin Heilderberg New York

    Google Scholar 

  • C Kurrer K Schulten (1995) ArticleTitleNoise-induced synchronous neuronal oscillations Phys Rev E 51 6213–6218 Occurrence Handle1:CAS:528:DyaK2MXmtlKltrc%3D

    CAS  Google Scholar 

  • H Sakaguchi S Shinomoto Y Kuramoto (1988) ArticleTitlePhase transitions and their bifurcation analysis in a large population of active rotators with mean-field coupling Prog Theor Phys 79 600–607

    Google Scholar 

  • T Sauer (1994) ArticleTitleReconstruction of dynamical systems from interspike interval Rhys Rev Lett 72 3811–3814 Occurrence Handle1:CAS:528:DyaK2cXlsFWnsro%3D

    CAS  Google Scholar 

  • Y Shinohara T Kanamaru H Suzuki T Horita K Aihara (2002) ArticleTitleArray-enhanced coherence resonance and forced dynamics in coupled FitzHugh-Nagumo neurons with noise Phys Rev E 65 051906

    Google Scholar 

  • S Shinomoto Y Kuramoto (1986) ArticleTitlePhase transitions in active rotator systems Prog Theor Phys 75 1105–1110

    Google Scholar 

  • H Suzuki K Aihara J Murakami T Shimozawa (2000) ArticleTitleAnalysis of neural spike trains with interspike interval reconstruction Biol Cybern 82 305–311 Occurrence Handle1:STN:280:DC%2BD3c3mtFajtQ%3D%3D Occurrence Handle10804062

    CAS  PubMed  Google Scholar 

  • S Tanabe T Shimokawa S Sato K Pakdaman (1999) ArticleTitleResponce of coupled noisy excitable systems to weak stimulation Phys Rev E 60 2182–2185 Occurrence Handle1:CAS:528:DyaK1MXkvFGktL0%3D

    CAS  Google Scholar 

  • J Theiler S Eubank A Longtin B Galdrikian JD Farmer (1992) ArticleTitleTesting for nonlinearity in time series: the method for surrogate data Physica D 58 77–94

    Google Scholar 

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Correspondence to Takashi Kanamaru.

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Kanamaru, T., Sekine, M. Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction. Biol Cybern 92, 333–338 (2005). https://doi.org/10.1007/s00422-005-0557-z

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  • DOI: https://doi.org/10.1007/s00422-005-0557-z

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