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Krasnow Institute > Monday Seminars > Abstracts Applying Periodic Orbit Theory Steven J. Schiff Neurons and their networks are highly nonlinear, but tools from nonlinear dyamics have had little impact so far in increasing our understanding of the nervous system. In dynamical systems theory, an efficient, perhaps optimal means to describe a system is through the periodic orbits which form a skeleton for the dynamics in a space representing the state of the system. Such orbit information can also provide a means to control such systems with minimal perturbations, exploiting the natural dynamics of the system to increase or decrease its periodicity. We have developed rigorous algorithms for the extraction of periodic orbits from noisy experimental data, and here describe in a comprehensive fashion the prevalence of such orbits in a broad range of hierarchical neuronal organization - from single cells to human cortex. The prospect to perform parametric control of such networks using electric fields as a control parameter is discussed
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