Nearly Optimal Chaotic Desynchronization of Neural Oscillators

Motivated by deep brain stimulation treatment of neural disorders such as Parkinson's disease, it has been proposed that desynchronization of neural oscillators can be achieved by maximizing the Lyapunov exponent of the phase difference between pairs of oscillators. Here we consider two approximations to optimal stimuli for chaotic desynchronization of neural oscillators. These approximations are based on the oscillators' phase response curve, and unlike previous approaches do not require numerical solution of a two-point boundary value problem. It is shown that these approximations can achieve nearly optimal desynchronization, and can be used with an event-based control scheme to desynchronize populations of noisy, coupled neurons.