Dynamical system analyzer

Abstract

A dynamical system analyzer (10) incorporates a computer (22) to perform a singular value decomposition of a time series of signals from a nonlinear (possibly chaotic) dynamical system (14). Relatively low-noise singular vectors from the decomposition are loaded into a finite impulse response filter (34). The time series is formed into Takens' vectors each of which is projected onto each of the singular vectors by the filter (34). Each Takens' vector thereby provides the co-ordinates of a respective point on a trajectory of the system (14) in a phase space. A heuristic processor (44) is used to transform delayed co-ordinates by QR decomposition and least squares fitting so that they are fitted to non-delayed co-ordinates. The heuristic processor (44) generates a mathematical model to implement this transformation, which predicts future system states on the basis of respective current states. A trial system is employed to generate like co-ordinates for transforation in the heuristic processor (44). This produces estimates of the trial system's future states predicted from the comparison system's model. Alternatively, divergences between such estimates and actual behavior may be obtained. As a further alternative, mathematical models derived by the analyzer (10) from different dynamical systems may be compared.

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