Chaotic Dynamics in Iterated Map Neural Networks with Piecewise Linear Activation Function

Article type: Research Article

Authors: Sinha, Sitabhra

Affiliations: Machine Intelligence Unit, Indian Statistical Institute, Calcutta 700035, India

Note: [] Current affiliation and the address for correspondence: Department of Physics, Indian Institute of Science, Bangalore 560 012, India, [email protected].

Abstract: The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the other inhibitory) connected with each other, is studied in detail. Even such a simple system shows a rich variety of behavior, including high-period oscillations and chaos. Border-collision bifurcations and multifractal fragmentation of the phase space is also observed for a range of parameter values. Extension of the model to a larger number of neurons is suggested under certain restrictive assumptions, which makes the resultant network dynamics effectively one-dimensional. Possible applications of the network for information processing are outlined. These include using the network for auto-association, pattern classification, nonlinear function approximation and periodic sequence generation.

Keywords: excitatory-inhibitory neural networks, chaos, nonlinear dynamics

DOI: 10.3233/FI-1999-371202

Journal: Fundamenta Informaticae, vol. 37, no. 1-2, pp. 31-50, 1999