A biologically plausible, stochastic, neural network model that exhibits spontaneous transitions between a low-activity (normal) state and a high-activity (epileptic) state is studied by computer simulation. Brief excursions of the network to the high-activity state lead to spontaneous population bursting similar to the behavior observed in hippocampal slices bathed in a high-potassium medium. Although the variability of interburst intervals in this model is due to stochasticity, first return maps of successive interburst intervals show trajectories that resemble the behavior expected near unstable periodic orbits (UPOs) of systems exhibiting deterministic chaos. Simulations of the effects of the application of chaos control, periodic pacing, and anticontrol to the network model yield results that are qualitatively similar to those obtained in experiments on hippocampal slices. Estimation of the statistical significance of UPOs through surrogate data analysis also leads to results that resemble those of similar analysis of data obtained from slice experiments and human epileptic activity. These results suggest that spontaneous population bursting in hippocampal slices may be a manifestation of stochastic bistable dynamics, rather than of deterministic chaos. Our results also question the reliability of some of the recently proposed, UPO-based, statistical methods for detecting determinism and chaos in experimental time-series data.

• Received 19 June 2002

DOI:https://doi.org/10.1103/PhysRevE.66.051908