The unstable periodic orbits of chaotic dynamics in systems described by delay differential equations are considered. An orbit is stabilized successfully, using a method proposed by Pyragas. The system under investigation is a network of excitatory and inhibitory neurons of moderate size, describing cortical activity. The relevance of the results for synchronized cortical activity is discussed.

A simple mathematical model of cortical tissue is introduced and the system's dynamics is monitored when a small subset of neurons is submitted to oscillatory inputs of various frequency and waveform. In the absence of input, the system shows desynchronized or “turbulent” behavior. The oscillatory input synchronizes the neuronal activity, which is strongest for inputs of low frequency. The increase of spatial coherence is estimated from the spatial autocorrelation function whereas the increase in temporal coherence is evaluated from correlation dimensions. The model accounts qualitatively for some of the features of the thalamocortical system.