Synchronization and desynchronization in a network of locally coupled Wilson-Cowan oscillators

Abstract

A network of Wilson-Cowan (WC) oscillators is constructed, and its emergent properties of synchronization and desynchronization are investigated by both computer simulation and formal analysis. The network is a 2D matrix, where each oscillator is coupled only to its neighbors. We show analytically that a chain of locally coupled oscillators (the piecewise linear approximation to the WC oscillator) synchronizes, and we present a technique to rapidly entrain finite numbers of oscillators. The coupling strengths change on a fast time scale based on a Hebbian rule. A global separator is introduced which receives input from and sends feedback to each oscillator in the matrix. The global separator is used to desynchronize different oscillator groups. Unlike many other models, the properties of this network emerge from local connections that preserve spatial relationships among components and are critical for encoding Gestalt principles of feature grouping. The ability to synchronize and desynchronize oscillator groups within this network offers a promising approach for pattern segmentation and figure/ground segregation based on oscillatory correlation.

From neural oscillations to variational problems in the visual cortex

“…It is then natural to ask if the functional (10) obtained in [12] as Γ-limit in a Riemannian space can be extended to subriemannian spaces. In this case indeed it would be possible to find a solution of the difference equation (7), as steepest descent flow of a functional formally written as in (8). A natural expression of the subriemannian Mumford and Shah would be:…”

“…As suggested by Wang [54,8], these equations can represent global activity of neural groups, which play a pivotal role in signal processing of the brain [51]. Each neural group is described by means of a two-variable system, representing populations of excitatory and inhibitory neurons (Figure 1),left).…”

“…Our main convergence result in [12] is the study of the Γ-limit of the familŷ F introduced in (8). The limit functional is defined in a new space, which is the analogous of P C in a continuous setting, the set of special bounded variation functions SBV (Ω).…”

“…From the neurological point of view, the more accreditated hypothesis is that grouping is represented in the brain with a temporal coding, meaning that semantically homogeneous areas in the image would be encoded in the synchronization (phase locking) of oscillatory neural responses [20]. Several connessionist models have been proposed to describe such characteristics of neural activity, see for example [54,8,47,48].…”

Visual Selection and Shifting Mechanisms Based on a Network of Chaotic Wilson-Cowan Oscillators

“…A natural way of encoding temporal correlation is by using synchronization of oscillators where each oscillator encodes some features of an object [16,20,22]. Inspired from the biological findings and von der Masburg's brain correlation theory, Wang and his collaborators have developed oscillatory correlation theory for scene segmentation [3,4,16,23], which can be described by the following rule: the neurons which process different features of the same object are synchronized, while neurons which code different objects are desynchronized. There are two basic mechanisms working simultaneously in each oscillatory correlation model: synchronization and desynchronization.…”