Minimum constituents of chaos neural network composed of conventional neurons

Abstract

AbstractMany studies of the neural network with chaotic output have been presented. In most of these, however, a neuron model or a network model is specially prepared to realize the chaotic response, and few studies have been based on the conventional model. This paper considers a neural network based on the conventional neuron model, such as is used in the Hopfield and other neural networks, and discusses the oscillation phenomenon. It is shown theoretically and experimentally that the behavior of the network composed of two neurons is either convergence or periodic oscillation. Then the network composed of three neurons is examined experimentally, and it is shown that convergence, periodic oscillation, quasi‐periodic oscillation, or chaos can occur. In other words, it is shown that the minimum configuration of a neural network based on the conventional neuron model that can generate chaos is a network composed of three neurons. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(7): 62–71, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1152