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Chaotic dynamics in iterated map neutral networks with piecewise linear activation function

Sinha S.

Fundamenta Informaticae

1999

Vol. 37, Nr 1,2

31-50

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibi-tory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair 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, includ-ing 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 applica-tions 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.