Koopman Mode Analysis (KMA) provides insights into the spatial and temporal dynamics of a wide variety of dynamical systems. Here results are described for an agent-based model (ABM) simulation of urban insurgency and for satellite measurements of sea ice concentration. The ABM work investigates the effect of preferential gathering sites on urban insurgency, where there is a nonlinear tradeoff between the local density of citizens due to the number of preferential gathering sites and the ability of law enforcement officers (LEOs) to adequately patrol that leads to a non-monotonic behavior in the number of large scale outburst of insurgency with respect to the number of gathering sites. This non-monotonicity indicates that a small number of organized units produces a larger insurgency effect than a larger number of distributed units. KMA also shows that the spatial morphology of agents due to the gathering sites gives rise to temporal organization of the model dynamics; there is a prominent quasi-periodic component in the number of active and intimidated citizens and in the spatial distribution of the LEOs. The sea ice work applied KMA to satellite data of sea ice concentration to gain insight into the temporal and spatial dynamics of the sea ice behavior. We discover exponentially decaying spatial modes in both hemispheres and discuss their precise spatial extent. This supports the nonlinear trend of the decline in the sea ice extent suggested in several recent studies. We also perform multi-year precise geographic predictions of future sea ice concentration.
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