Biomedical subjects

F M Atay

Publications and source records attributed to F M Atay.

2 recordsLinked to original sources

PubMed1999

Recovering smooth dynamics from time series with the aid of recurrence plots.

A graphical method based on recurrence plots is used in the reconstruction of the phase space from a time series of measurements. It is demonstrated that if the embedding delay and dimension are correctly chosen, the recurrence plot of a smooth dynamical system has a particularly simple form. It is shown how to use recurrence plots to determine the correct embedding parameters so that reliable quantitative information can be drawn about the system generating the time series. The average line length in the plot is shown to be directly related to the prediction horizon. Furthermore, it is a numerical characteristic of the embedded series independent of the threshold used in the plot.

Journal Article↗

PubMed1998

Modeling reflex asymmetries with implicit delay differential equations.

Neuromuscular reflexes with time-delayed negative feedback, such as the pupil light reflex, have different rates depending on the direction of movement. This asymmetry is modeled by an implicit first-order delay differential equation in which the value of the rate constant depends on the direction of movement. Stability analyses are presented for the cases when the rate is: (1) an increasing and (2) a decreasing function of the direction of movement. It is shown that the stability of equilibria in these dynamical systems depends on whether the rate constant is a decreasing or increasing function. In particular, when the asymmetry has the shape of an increasing step function, it is possible to have stability which is independent of the value of the time delay or the steepness (i.e., gain) of the negative feedback.

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