Examining the Observability of Emergent Behavior as a Function of Reduced Model Order

Current work on complex systems has been heavily focused on network interactions and network structure, without significant emphasis on the emergent phenomena that characterize such systems. In the included work, the ability to perceive or observe emergent behavior in complex systems has been studied. Specifically, by identifying emergent behavior as the dynamics of reduced-order models of the self-organizing systems, the observability of the emergent phenomena can be studied as a function of the model order. Included analytical results show the relationship between observability metrics of the full- and reduced-order models. Singular perturbation techniques have been used to perform model order reduction for nonlinear systems such as the Hyper Rossler and coupled Hindmarsh-Rose neuron models. Results indicate that accuracy increases and observability decreases with increasing model order. The trade-off between accuracy and observability metrics has been used to propose a predictive metric that identifies the desirable order at which to model emergent behavior.