Analysis of bifurcation phenomena in a 3-cells hysteresis neural network

Author

Jin´no, Kenya ; Nakamura, Takahiko ; Saito, Toshimichi

Author_Institution

Dept. of Electr. & Electron. Eng., Nippon Inst. of Technol., Saitama, Japan

Volume

46

Issue

7

fYear

1999

fDate

7/1/1999 12:00:00 AM

Firstpage

851

Lastpage

857

Abstract

This paper considers bifurcation phenomena in a simplified hysteresis neural network. The network consists of three cells and has three control parameters. We have discovered that the simple system exhibits various attractors: stable equilibria, periodic orbits, and chaos. Since the system is piecewise linear, the return map and Lyapunov exponents are calculated by using the piecewise exact solution. Using the mapping procedure, the bifurcation mechanism of stable equilibria and three kinds of bifurcation mechanisms of periodic orbits have been clarified. In addition, chaos has been analyzed by using Lyapunov exponents of the return map

Keywords

Lyapunov methods; bifurcation; chaos; hysteresis; neural nets; nonlinear network analysis; piecewise linear techniques; 3-cells hysteresis neural network; Lyapunov exponents; attractors; bifurcation phenomena; chaos; control parameters; mapping procedure; periodic orbits; piecewise exact solution; piecewise linear system; return map; stable equilibria; Artificial neural networks; Associative memory; Bifurcation; Chaos; Circuits; Hysteresis; Intelligent networks; Neural networks; Orbits; Piecewise linear techniques;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.774231

Filename

774231