Physiological control systems can display a specific type of reversible transition in behavior called bifurcations. Bifurcations can occur between steady states, periodic oscillations and chaotic dynamics. It has been suggested that these transitions in behavior constitute a common dynamical mechanism for several clinically observed failures of physiological regulation. A specific possibility has motivated this study: could a bifurcation be an early event in epileptogenesis? This investigation proposes to continue both theoretical and experimental studies of bifurcations in neural behavior, with specific reference to epileptogenesis. Theoretical work has focused on developing methods for the quantitative characterization of complex dynamical behavior. As the work progressed, the limitations of currently available procedures, especially for dealing with noisy experimental data, became increasingly apparent. Our theoretical work is, therefore, directed to improving these techniques and to constructing alternative measures of dynamical behavior. It includes Lyapunov exponents, correlation dimension and its generalizations to order-q information dimension, topological dimension, metric entropy, topological entropy and complexity. The experimental work will be directed toward establishing a dynamical characterization of focal epileptogenesis in an animal model and to enlarging our data base to include measures under normal (free moving) as well as seizure conditions. To this end we shall record the ECoG and the firing patterns in single cortical neurons. In particular, we wish to identify conditions which can precipitate bifurcations in dynamical behavior that result in seizures.
