Detecting chaotic structures in noisy pulse trains based on interspike interval reconstruction Article First Online: 29 April 2005 Received: 07 July 2003 Accepted: 28 February 2005 DOI:
Cite this article as: Kanamaru, T. & Sekine, M. Biol Cybern (2005) 92: 333. doi:10.1007/s00422-005-0557-z 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.
Davis L (1996) Handbook of genetics algorithms. Van Nostrand Reinhold
Ermentrout, B 1996 Type I membranes, phase resetting curves, and synchrony Neural Comput 8 979 1001 PubMed Google Scholar Gardiner, CW 1985Handbook of stochastic methods Springer Berlin Heidelberg New York Google Scholar Izhikevich, EM 1999 Class 1 neural excitability, conventional synapses, weakly connected networks, and mathematical foundations of pulse-coupled models IEEE Trans Neural Networks 10 499 507 Google Scholar Kanamaru, T, Sekine, M 2003 Analysis of the globally connected active rotators with excitatory and inhibitory connections using the Fokker–Planck equation Phys Rev E 67 031916 Google Scholar Kanamaru, T, Sekine, M 2004 Analysis 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)
Kuramoto, Y 1984Chemical oscillations, waves, and turbulence Springer Berlin Heilderberg New York Google Scholar Kurrer, C, Schulten, K 1995 Noise-induced synchronous neuronal oscillations Phys Rev E 51 6213 6218 Google Scholar Sakaguchi, H, Shinomoto, S, Kuramoto, Y 1988 Phase transitions and their bifurcation analysis in a large population of active rotators with mean-field coupling Prog Theor Phys 79 600 607 Google Scholar Sauer, T 1994 Reconstruction of dynamical systems from interspike interval Rhys Rev Lett 72 3811 3814 Google Scholar Shinohara, Y, Kanamaru, T, Suzuki, H, Horita, T, Aihara, K 2002 Array-enhanced coherence resonance and forced dynamics in coupled FitzHugh-Nagumo neurons with noise Phys Rev E 65 051906 Google Scholar Shinomoto, S, Kuramoto, Y 1986 Phase transitions in active rotator systems Prog Theor Phys 75 1105 1110 Google Scholar Suzuki, H, Aihara, K, Murakami, J, Shimozawa, T 2000 Analysis of neural spike trains with interspike interval reconstruction Biol Cybern 82 305 311 PubMed Google Scholar Tanabe, S, Shimokawa, T, Sato, S, Pakdaman, K 1999 Responce of coupled noisy excitable systems to weak stimulation Phys Rev E 60 2182 2185 Google Scholar Theiler, J, Eubank, S, Longtin, A, Galdrikian, B, Farmer, JD 1992 Testing for nonlinearity in time series: the method for surrogate data Physica D 58 77 94 Google Scholar Copyright information
© Springer-Verlag Berlin Heidelberg 2005