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

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.