Optimal Chaotic Desynchronization for Neural Populations

A procedure is developed for finding an energy-optimal stimulus which gives a positive Lyapunov exponent, and hence desynchronization, for a neural population. The procedure is illustrated for three different neural models. Not only does it achieve desynchronization for each model, but it also does so using less energy than recently proposed methods, suggesting a powerful alternative to pulsatile stimuli for deep brain stimulation. Furthermore, we calculate error bounds on the optimal stimulus which will guarantee a minimum Lyapunov exponent. Also, a related control strategy is developed for desynchronizing neurons based on the population's phase distribution.