Using Information Flow for Whole System Understanding From Component Dynamics

Complex systems that exhibit emergent behaviors arise as a result of nonlinear interdependencies among multiple components. Characterizing how such whole system dynamics are sustained through multivariate interaction remains an open question. In this study, we propose an information flow-based framework to investigate how the present state of any component arises as a result of the past interactions among interdependent variables, which is termed as causal history. Using a partitioning time lag, we divide this into immediate and distant causal history components and then characterize the information flow-based interactions within these as self- and cross-feedbacks. Such a partition allows us to characterize the information flow from the two feedbacks in both histories by using partial information decomposition as unique, synergistic, or redundant interactions. We employ this casual history analysis approach to investigate the information flows in a short-memory coupled logistic model and a long-memory observed stream chemistry dynamics. While the dynamics of the short-memory system are mainly maintained by its recent historical states, the current state of each stream solute is sustained by self-feedback-dominated recent dynamics and cross-dependency-dominated earlier dynamics. The analysis suggests that the observed 1/f signature of each solute is a result of the interactions with other variables in the stream. Based on high-density data streams, the approach developed here for investigating multivariate evolutionary dynamics provides an effective way to understand how components of dynamical system interact to create emergent whole system behavioral patterns such as long-memory dependency.