Complex dynamical systems, such as financial, ecological, social or other systems of living, interacting agents, spontaneously undergo phase transitions resulting in dramatic regime changes and catastrophic events. Under certain conditions, these events occur in the critical regime of a system's dynamics, resulting in a scale-free distribution of catastrophic event sizes. The implications of such system-size catastrophes may be irreversible in finite systems, leading to collapse and extinction of the entire financial, ecological or social system.

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