Limit Cycles of One-Dimensional Neural Networks with the Cyclic Connection Matrix

Cheol-Young PARK  Yoshihiro HAYAKAWA  Koji NAKAJIMA  Yasuji SAWADA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.6   pp.752-757
Publication Date: 1996/06/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section of Papers Selected from 1995 Joint Technical Conference on Circuits/Systems, Computers and Communications (JTC-CSCC '95))
neural networks,  continuous-time model,  dynamics,  limit cycles,  equilibrium point,  

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In this paper, a simple method to investigate the dynamics of continuous-time neural networks based on the force (kinetic vector) derived from the equation of motion for neural networks instead of the energy function of the system has been described. The number of equilibrium points and limit cycles of one-dimensional neural networks with the asymmetric cyclic connection matrix has been investigated experimently by this method. Some types of equilibrium points and limit cycles have been theoretically analyzed. The relations between the properties of limit cycles and the number of connections also have been discussed.