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Baroreflex Physiology Using Koopman Mode Anal- ysis

We propose new methods for the evaluation of eigenvalues λ(t, t0)of the Koopman operator family K(t, t0), t>t0 of the non-autonomous dynamic systems. The first step in the development is a new data-driven method for very accurate evaluation of eigenvalues λ(t, t0), t>t0 in the hybrid linear non-autonomous case. Then, the approach is extended to continuous linear non-autonomous systems and non-autonomous systems in general. We also propose a relationship between eigenvalues λ(t, t0), t>t0 and eigenvalues computed by Arnoldi-like methods on large sets of snapshots. We apply the new approach to baroreflex physiology, i.e. to the resonant breathing which is used in PTSD treatment. For the resonant breathing we have both data and parameterized mathematical model. The model incorporates a delay and thus is infinite dimensional, hybrid, with a stochastic input. Its asymptotic dynamics is close to quasi-periodic. The applied new methods give an improved insight to the eigenvalues of the related Koopman operator family K(t, t0).

Koopman operator, baroreflex physiology, non-autonomous systems

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