Using Synchronization of Dynamical Systems for Verification and Validation of Neurobiological Models: Experiment and Theory

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In this project the PI will develop a nonlinear dynamical method for the estimation of states and parameters in models of neurobiological systems using experimental data. Utilizing this method the PI will analyze models of individual neurons in the crustacean Pyloric central pattern generator (CPG) and models of sub-circuits of neurons within this CPG. The general problem of determining the parameters of mathematical models of individual neurons and networks of neurons will be addressed using a novel method called dynamical parameter estimation (DPE), which is based on the classical problem of optimal tracking of a desired trajectory. In this case the DPE is known in the control theory literature as a Luenberger observer with adaptive gain: a filter in the sense of Kalman. Using this approach the PI will apply the new technique to the analysis of experimental data from CPG neurons and CPG sub-circuits. Two graduate students will be involved in this efforts. The research group of the PI will also work each summer with Research Experience for Undergraduates (REU) undergraduate students program at UCSD.