Controlling Populations of Neural Oscillators

Abstract: Deep brain stimulation is a therapeutic treatment for a variety of neurological disorders such as Parkinson’s disease, which is hypothesized to be due to pathological synchronization of neural activity in the motor control region of the brain. This motivates the control objective of desynchronizing neural activity using a single electrical stimulus. Challenges include high-dimensionality, nonlinear effects, underactuation, and constraints on allowable control inputs. Various approaches have been developed to overcome these challenges, including chaotic desynchronization, in which the control is chosen to maximize the Lyapunov exponent associated with phase differences for the neurons, optimal phase resetting in which an input drives the system to the phaseless set where the neurons are particularly sensitive to noise, and phase density control in which an input drives the system toward a desired phase distribution. The presentation will discuss these approaches, recent work which shows how magnitude constraints affect chaotic desynchronization, and that phase resetting can be improved by using the stochastic Hamilton-Jacobi-Bellman equation to calculate optimal inputs.

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Bio: Prof. Jeff Moehlis received a Ph.D. in physics from UC Berkeley in 2000, and was a postdoctoral researcher in the program in Applied and Computational Mathematics at Princeton University from 2000-2003. He joined the Department of Mechanical Engineering at UC Santa Barbara in 2003, and is currently chair of this department. He was also recently the chair of the Program in Dynamical Neuroscience at UC Santa Barbara. He has been a recipient of a Sloan Research Fellowship in Mathematics and a National Science Foundation CAREER Award, and was Program Director of the SIAM Activity Group in Dynamical Systems from 2008-2009. Prof. Moehlis's current research includes applications of dynamical systems and control techniques to neuroscience, cardiac dynamics, collective behavior, and machine learning.