Predicting Complex Behavior in Sparse Asymmetric Networks

Abstract

Recurrent networks of threshold elements have been studied intensively as associative memories and pattern-recognition devices. While most research has concentrated on fully-connected symmetric networks, which relax to stable fixed points, asymmetric networks show richer dynamical behavior, and can be used as sequence generators or flexible pattern-recognition devices. In this paper, we approach the problem of predicting the complex global behavior of a class of random asymmetric networks in terms of network parameters. These networks can show fixed-point, cyclical or effectively aperiodic behavior, depending on parameter values, and our approach can be used to set parameters, as necessary, to obtain a desired complexity of dynamics. The approach also provides qualitative insight into why the system behaves as it does and suggests possible applications.