Propagating structures in globally coupled systems with time delays

We consider an ensemble of globally coupled phase oscillators whose interaction is transmitted at finite speed. This introduces time delays, which make the spatial coordinates relevant in spite of the infinite range of the interaction. In the limit of short delays, we show that the ensemble approaches a state of frequency synchronization, where all the oscillators have the same frequency, and can develop a nontrivial distribution of phases over space. Numerical calculations on one-dimensional arrays with periodic boundary conditions reveal that, in such geometry, the phase distribution is a propagating structure.

Competing neural networks: finding a strategy for the game of matching pennies

The ability of a deterministic, plastic system to learn to imitate stochastic behavior is analyzed. Two neural networks-actually, two perceptrons-are put to play a zero-sum game one against the other. The competition, by acting as a kind of mutually supervised learning, drives the networks to produce an approximation to the optimal strategy, that is to say, a random signal.

Dynamical clustering in large populations of Rossler oscillators under the action of noise

The effects of noise on the dynamical clustering of globally coupled chaotic Rossler oscillators are numerically investigated. Stable clusters and intermittent clustering regimes are found, depending on the coupling intensity and the noise level. Our results agree with the first experimental observations of dynamical clustering recently reported for globally coupled electrochemical oscillators.