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Our Center studies systems like economies, the brain, ecosystems, political systems, social networks, and the Internet that consist of many interacting individuals, nodes, or parts and that produce collective behaviors that exceed and even transcend the capabilities of the constituent parts. The behaviors of interest include:

SELF-ORGANIZATION into patterns, as occurs with flocks of birds, periodicity in disease outbreaks, or residential segregation.

EMERGENCE of functionalities, such as cognition in the brain or the robustness of networks.

CHAOS, where small changes in initial conditions ("the flapping of a butterfly's wings in Argentina") produce large later changes ("a hurricane in the Caribbean").

"FAT-TAIL" BEHAVIOR, where rare events (e.g. mass extinctions, market crashes, and epidemics) occur much more often than would be predicted by a normal (bell-curve) distribution.

ADAPTIVE INTERACTION, where interacting agents (as in markets or the Prisoner's Dilemma) modify their strategies in diverse ways as experience accumulates to produce cooperative behavior.

Note that these emergent behaviors need not align with the goals of the individual parts. This complex of unintuitive relationships between the micro and the macro makes these systems difficult to analyze, explain, and predict.

Scientific progress in complex systems often requires cross-disciplinary techniques that combine mathematics with computational models and simulations. Scholars in our Center use a variety of quantitative tools including differential equations, statistical mechanics, information theory, graph and network theory, agent based models, cellular automata, Markov processes, matrix algebra, generated systems (e.g., logics and generated groups), and game theory. We often incorporate models, measures, and insights from traditional disciplines -- physics, biology, computer science, economics, and mathematics -- but we do so in novel ways with the hope of identifying properties that hold across a wide range of complex systems.