In this paper we review some principles for information storage and retrieval based on oscillations in dynamical systems.
1. Introduction
Oscillations and chaos are present in both biological and artificial neurons.
A single biological neuron has oscillatory dynamics and can generate chaos. At a macroscopic level however, chaos is not created by the dynamics of individual neurons but by the interaction of large groups of neurons. These macroscopic oscillations are measured by EEG (electroencephalogram) recordings that indicate the presence of chaotic attractors in the brain, i.e. in the olfactory cortex I or in the brain of epileptic patients.* Also in the visual cortex, neurons have been found to oscillate in a coherent way depending on the global stimulus.'
On the other hand, since recurrent artificial neural networks are non linear dynamical systems, it is possible to get different behaviours by adjusting their parameters: convergence towards equilibrium points, towards periodic solutions (e.g. Reference 4) or chaotic trajectories (e.g. References 5 and 6). In this case the study of oscillations is more a scientific activity than a goal for storing and processing information. In this paper, however, we explore the possibilities of making use of chaos for information storage.
Although the essential mode of operation of a CNN is based on the convergence of the state variables to equilibrium points, a future trend of the field will also include arrays made of oscillators. It is therefore useful to analyse and review what advantages this feature could bring if the goal of the CNN is to store and retrieve information.
Section 2 recalls the definition of an associative memory and its desired properties. It is typically implemented as a dynamical system, whose general structure is described in Section 3. Conventional systems based on stable equilibrium points are briefly recalled in Section 4, while Sections 5 and 6 present systems storing patterns as respectively stable and unstable periodic solutions. Section 7 finally gives some concluding remarks.
2. ASSOCIATIVE MEMORY
An associative memory is a device in which some number p of patterns r, 1 G p d p , is stored during a learning process. In a second phase, the recall step, one of these p patterns (possibly corrupted by noise) is i Pan of this research has been reported in the