Basic Analysis of Digital Spike Maps

This paper studies digital spike maps that can generate various periodic spike-trains. In order to analyze the maps, we present a simple analysis algorithm to calculate basic feature quantities. We then analyze a typical example of the map given by discretizing the bifurcating neuron. Applying the algorithm to the example, we demonstrate complex dynamics and give basic classification of the dynamics.

[1]  E. Ott Chaos in Dynamical Systems: Contents , 1993 .

[2]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[3]  Shigetoshi Nara,et al.  Completely reproducible description of digital sound data with cellular automata , 2002 .

[4]  Nikolai F. Rulkov,et al.  Chaotic pulse position modulation: a robust method of communicating with chaos , 2000, IEEE Communications Letters.

[5]  Toshimichi Saito,et al.  Digital spiking neuron and its learning for approximation of various spike-trains , 2008, Neural Networks.

[6]  Nabil H. Farhat,et al.  The bifurcating neuron network 3 , 2005, Proceedings. 2005 IEEE International Joint Conference on Neural Networks, 2005..

[7]  Leon O. Chua A Nonlinear Dynamics Perspective Of Wolfram'S New Kind Of Science , 2013 .

[8]  Leon Glass,et al.  Bistability, period doubling bifurcations and chaos in a periodically forced oscillator , 1982 .

[9]  DeLiang Wang,et al.  Synchrony and Desynchrony in Integrate-and-Fire Oscillators , 1999, Neural Computation.

[10]  Toshimichi Saito,et al.  Self-Organizing Digital Spike Maps for Learning of Spike-Trains , 2011, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[11]  Paul L. Rosin Training Cellular Automata for Image Processing , 2006, IEEE Trans. Image Process..

[12]  Hiroyuki Torikai,et al.  Synchronization via multiplex pulse trains , 1999 .

[13]  Hiroyuki Torikai,et al.  An artificial chaotic spiking neuron inspired by spiral ganglion cell: Paralleled spike encoding, theoretical analysis, and electronic circuit implementation , 2009, Neural Networks.

[14]  Toshimichi Saito,et al.  Digital spike maps and learning of spike signals , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[15]  Toshimichi Saito,et al.  Analysis of a Quantized Chaotic System , 2002, Int. J. Bifurc. Chaos.