DETECTION OF CHAOTIC DETERMINISM IN TIME-SERIES FROM RANDOMLY FORCED MAPS

Time series from biological systems often display fluctuations in the measured variables. Much effort has been directed at determining wheth er this variability reflects deterministic chaos, or whether it is mer ely ''noise''. Despite this effort, it has been difficult to establish the presence of chaos in time series from biological systems. The out put from a biological system is probably the result of both its intern al dynamics, and the input to the system from the surroundings. This i mplies that the system should be viewed as a mixed system with both st ochastic and deterministic components. We present a method that appear s to be useful in deciding whether determinism is present in a time se ries, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditio ns. The method relies on fitting a nonlinear autoregressive model to t he time series followed by an estimation of the characteristic exponen ts of the model over the observed probability distribution of states f or the system. The method is tested by computer simulations, and appli ed to heart rate variability data.