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Large scale catastrophic shifts have been documented for ecosystems, climate systems, oceanic circulation patterns and socio-economic systems. Such shifts may be related to loss of resilience, in the sense that the basin of attraction of the present state of a system is shrinking and the probability that a small disturbance can tip the system into the basin of attraction of a contrasting state increases. Recent theoretical findings suggest that the shrinking of the basin of attraction has fundamental effects on the dynamical behavior of the system. Such effects appear to change with a consistent way as the system approaches the point where the catastrophic transition takes place. Apparently, being able to decipher these effects into measurable quantities of some sort of leading indicators can enhance our ability to assess the risk of upcoming catastrophic shifts, or to manage systems for enhanced resilience to such transitions.