  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.
