To help realize the potential of complex systems models we need new measures
appropriate for capturing processes that exhibit feedback, nonlinearity, heterogeneity, and
emergence. As part of a larger research project encompassing several categories of
dynamical properties this paper provides formal and general definitions of tipping point-
related phenomena. For each tipping concept this paper provides a probabilistic definition
derived from a Markov model representation. We start with the basic features of Markov …

Complex systems are characterized by processes that exhibit feedback, nonlinearity,
heterogeneity, and path dependencies, and accurately modeling such systems is becoming
increasing important. To help realize the potential of complex systems modeling we need
new methods that are capable of capturing the dynamical properties of such processes
across disciplines and modeling frameworks. This chapter presents a portion of the
methodology development that includes formal and domain-agnostic definitions of …