DYNAMICAL SYSTEM ANALYSER

摘要

A dynamical system analyser (10) incorporates a computer (22) to perform a singular value decom- position 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 fi- nite impulse response filter (34). The time series is formed into Tak- ens' vectors each of which is pro- jected onto each of the singular vec- tors by the filter (34). Each Takens' vector thereby provides the co-ordi- nates of a respective point on a tra- jectory of the system (14) in a phase space. A heuristic processor (44) is used to transform delayed co-ordi- nates by QR decomposition and least squares fitting so that they are fitted to non-delayed co-ordinates. The heuristic processor (44) gen- erates a mathematical model to implement this transformation, which predicts future system states on the basis of respective current states. A trial system is em- ployed to generate like co-ordinates for transformation in the heuristic processor (44). This produces estimates of the trial sys- tem's future states predicted from the comparison system's model. Alternatively, divergences between such estimates and actual behaviour may be obtained. As a further alternative, mathematical models derived by the analyser (10) fromdifferent dynamical systems may be compared.