A Method for Detecting Possible Non-determinism in a Time Series

Abstract

A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase space trajectory of the system may jump from one solution to another. This discontinous change implies divergence of the second derivative of the solution whenever it passes near the singular point. A time series can be examined for such divergences, which may indicate non-determinism in the dynamical system. Examples with both simulated and actual data are given.