A complex-valued version of Nagumo--Sato model of a single neuron and its behavior

Authors:
Iku Nemoto;Kei Saito
Affiliations:
School of Information Environment, Tokyo Denki University, Muzai-Gakuendai, Inzai, Chiba 270-1382, Japan;NHK Computer Service, Inc., 4-14, Kamiyamacho, Shibuya, Tokyo 150-0047, Japan
Venue:
Neural Networks
Year:
2002

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The behavior of the network consisting of two complex-valued Nagumo-Sato neurons

ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing

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Abstract

The Nagumo-Sato model of a single neuron was extended so that it can handle complex numbers and the behavior of the complex-valued model was investigated. The model neuron receives its past outputs through a complex-valued weight and fires when the absolute value of the membrane potential exceeds a threshold. Some of the basic features of the model, such as associated with fixed points and period-two orbits, were derived. The main purpose of the paper is to show the model's chaotic behavior which is the result of the extension to the complex numbers and different from that of the original real-valued model. The apparently chaotic orbits were numerically shown to have positive Lyapunov exponents and high sensitivity to the initial conditions. Some of the chaotic orbits seem to be related to the saddles of period-two and their associated stable and unstable manifolds.