Analysis of Periodic Attractor in a Simple Hysteresis Network

Kenya JIN'NO  Toshimichi SAITO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.6   pp.873-882
Publication Date: 1996/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Nonlinear Problems
limit cycle,  hysteresis,  piecewise linear system,  synchronization,  stability.,  

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We analyze dynamics of a simple hysteresis network (ab. SHN) which has only two parameters. We classify the periodic orbits and clarify the number of attractors and their domain of attraction. The SHN is a piecewise linear system, and therefore we can calculate the trajectory using exact solutions. We clarify the bifurcation sets on which equilibrium attractors bifurcate to the periodic orbits. We also give a sufficient condition for stability of the periodic orbits, and the stability is verified by laboratory experiment. The results of this paper may contribute to the development of an efficient multi functional artificial neural network.