Complex Webs: Mostly linear dynamics

One strategy for predicting an improbable but potentially catastrophic future event is to construct a faithful model of the dynamics of the complex web of interest and study its extremal properties. But we must also keep in mind that the improbable is not the same as the impossible. The improbable is something that we know can happen, but our experience tells us that it probably will not happen, because it has not happened in the past. Most of what we consider to be common sense or probable is based on what has happened either to us in the past or to the people we know. In this and subsequent chapters we explore the probability of such events directly, but to set the stage for that discussion we examine some of the ways webs become dynamically complex, leading to an increase in the likelihood of the occurrence of improbable events. The extremes of a process determine the improbable and consequently it is at these extremes that failure occurs. Knowing a web's dynamical behavior can help us learn the possible ways in which it can fail and how long the recovery time from such failure may be. It will also help us answer such questions as the following. How much time does the web spend in regions where the likelihood of failure is high? Are the extreme values of dynamical variables really not important or do they actually dominate the asymptotic behavior of a complex web?