Statistical Patterns of Non-Equilibrium Systems1

Abstract Most applied models assume the system under study is in equilibrium or moving-equilibrium. Recent theoretical work has considered chaotic behavior or sustained-bounded-motion (SBM) of systems. We show how to determine the necessary conditions for SBM. We establish, in some cases, the patterns of covariation or the bounds on variance. It is possible to use the data to identify sources of external perturbation to a SBM system. Alternative measures of stability, resiliency and rates of change of systems are provided. Theoretical models help explain variable time-series data collected for environmental assessment or monitoring.