Catastrophe and Pestilence

If a large number of real systems exhibit dynamics that bear the potential for chaos, why do we not see more chaos in real-world processes? Fortunately, the domains over which stability of the system occurs can be relatively large. But once in a while, systems may move “toward the edge of stability” and little nudges to the system may move it from stability to instability—that is, into a catastrophe. Subsequently, reorganization of system components may occur to bring the system back into a stable domain—a kind of evolutionary process. This stable domain, however, may not be the same as the one prior to the disturbance.

The system undergoes a catastrophic event in the sense that it is moved from an initial state of stability through a dramatic phase of reorganization and back to some degree of stability. Examples for such catastrophic events include landslides, avalanches, earthquakes, and pest outbreaks in ecosystems. In each case, small changes in the system occur that individually may not be critical to the system’s behavior. Collectively, however, they lead to the evolution of the system toward a critical state. This is apparent, for example, in the case of avalanches. Each individual snowflake potentially adds to the instability of the system. When a critical point is reached, the next snowflake may trigger an avalanche that affects a large part of the system. Temporary stability is quickly reached if the avalanche is not too dramatic. Even if not of a large scale, the avalanche adds to the “stress” of the system downhill, making it more susceptible to further avalanches as more snow falls at those regions or as additional small avalanches are received from higher on the hill. Ultimately, a large-scale, catastrophic event may occur, which affects the entire system, not just individual regions. The system components re-group and finally enter a phase of new, temporary stability.