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Calculation of eigen values and idiosyncratic dynamical systems

Lagkonakis Emmanouil

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Summary

Stability analysis of dynamic systems is of great importance because loss of stabilityoften leads to sudden, drastic effects on a system. For example, when the electricalwave propagating in the heart is destabilized, abnormal heartbeats occur, leading tovarious cardiac arrhythmias.This paper illustrates a technique that overcomes these problems and can estimate the most dominant eigenvalues and their standard errors from a time series of one or more measurable quantities.The purpose is to improve these techniques and focus on more efficient ways tomaximize the likelihood function once the appropriate error model has beendetermined, as well as to consider a richer class of error models than a vectorautoregressive process of order one.Methodology The method that will be used is the literature review where with the keywords stability analysis? maximum likelihood, state space, empirical method, dynamical systems on the pages pubmed, elsevier, doabooks, google, google scholar, articles from the last five years will be requested.Expected ResultsThe results we expect are a new method that imposes a statistical model (eg, amultivariate autoregressive time series) that combines the effects of measurement error and model misspecification error (arising from ignoring nondominant eigenvalues and assuming a linear projection) in time series. Using standard maximum likelihood techniques, one can obtain both point estimates and approximate standard errors for the dominant eigenvalues.

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