Nonstationarity signatures in the dynamics of global nonlinear models

Abstract

The aim of this paper is to learn how to recognize a posteriori signatures that nonstationarity leaves on global models obtained from data. To this end the effects of nonstationarity on the dynamics of such models are reported for two benchmarks. Parameters of the Rössler and Lorenz models are varied to produce nonstationary data. It is shown that not only the rate of change of the varying parameter but also which recorded variable is used to estimate global models may have visible effects on the results, which are system-dependent and therefore difficult to generalize. Although the effects of nonstationarity are not necessarily obvious from the phase portraits, the first-return map to a Poincaré section is a much more adequate tool to recognize such effects. Three examples of models previously obtained from experimental data are analyzed in the light of the concepts discussed in this paper.