Chaos and fractals from a forced artificial neural cell

Author

Saito, Toshimichi ; Oikawa, Masami

Author_Institution

Dept. of Electr. Eng., Hosei Univ., Tokyo, Japan

Volume

4

Issue

1

fYear

1993

fDate

1/1/1993 12:00:00 AM

Firstpage

43

Lastpage

52

Abstract

Chaos and fractal responses from an artificial neural cell stimulated by a periodic square wave are discussed. The dynamics are described by an autonomous equation, and the one-dimensional return map is derived explicitly. The relation between the exciting pulse-width τ₁, and the excited rate γ_e which is the number ratio of input pulses and output pulses investigated. Mathematical evidence for γ_e to be Cantor function for τ₁ is given. It corresponds to fractal responses. A condition for observable chaos generation in responses from the cell is proved. This condition is described only by parameters. Some of the theoretical results are verified by laboratory experiments

Keywords

chaos; fractals; neural nets; 1D return map; Cantor function; dynamics; fractal responses; neural nets; observable chaos generation; periodic square wave; Associative memory; Biological systems; Chaos; Equations; Fractals; Hysteresis; Laboratories; Limit-cycles; Space vector pulse width modulation; Sufficient conditions;

fLanguage

English

Journal_Title

Neural Networks, IEEE Transactions on

Publisher

ieee

ISSN

1045-9227

Type

jour

DOI

10.1109/72.182694

Filename

182694