Quantized Dynamics from an Integrate-and-Fire Circuit with Pulse-Train Stimulation

Yoshinobu KAWASAKI  Hiroyuki TORIKAI  Toshimichi SAITO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A    No.10    pp.2547-2552
Publication Date: 2001/10/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
integrate-and-fire circuit,  pulse-train stimulation,  quantization,  return map,  firing pulse-train,  

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We present a novel kind of integrate-and-fire circuit (IFC) with two periodic inputs: a pulse-train stimulation input and a base input. We clarify that the system state is quantized by the pulse-train stimulation input. Then the system dynamics is described by a return map with quantized state (Qmap). By changing the shape of the base input, various Qmaps can be obtained. The Qmap exhibits co-existence state of various super-stable periodic orbits, and the IFC outputs one of corresponding super-stable periodic pulse-trains depending on the initial state. For a typical case, we clarify the number of co-existing periodic pulse-trains theoretically for the stimulation frequencies. Constructing a simple test circuit, typical phenomena can be verified in the laboratory.