Seasonal footprints on ecological time series and jumps in dynamic states of protein configurations from a nonlinear forecasting method characterization

Abstract We have analyzed phenology data and protein configurations from molecular dynamics simulations with the nonlinear forecasting method proposed by May and Sugihara. Our primary focus in this work is to characterize the dynamic state of a system by quantifying prediction quality from data. Full plots of prediction quality as a function of dimensionality E and forecasting time T p , the two basic parameters of the method, give fast and valuable information about complex systems dynamics. We detect changes in protein dynamics due to mutations and, regarding ecology data, we show how cycles and rhythms of the environment manifests in parameter space <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>E</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> for some species.