sharing insights that are particular to a given field and that, by analogy, might apply to other fields. This is the approach taken in this chapter.


At the conference, ecologist Simon Levin of Princeton University identified a range of concepts that have proved helpful in understanding complex systems in ecology and that might also apply to financial systems. One useful conceptual model of an ecosystem is a “trophic web,” which represents how species are interconnected. At a coarse level, a trophic web in an ecosystem might be thought of as a set of predator-prey relationships. In this case, sets of differential equations can be successful in modeling the rise and fall of populations as the ecosystem fluctuates around an equilibrium or becomes unstable. More generally, however, “trophic” refers to the flow of energy, so the trophic web for an ecosystem is a framework for representing how the primary source of nutrition (say, sunlight or geothermal vents) is transmitted between levels in the food chain. This interpretation of the trophic web is more applicable to financial systems, in which the interactions are usually less extreme than those in predator-prey relationships; we simply have to interpret “energy” as anything of value that is transmitted through the system. Because of this analogy, it is not surprising that we would find similar, if not identical, phenomena in these two systems, and therefore similar insights might be brought to bear in analyzing them. Complex systems of any sort are characterized by non-linearities, multiple stable states, hysteresis, contagion, and synchrony, all of which have relevance to the problem of systemic risk.

Nonlinear relationships are a key characteristic of virtually any complex system. They can lead to multiple stable states, such that the system can exist in one configuration (basin of attraction) for a period of time but then be knocked into a different configuration by a perturbation or shock. This transition can be accompanied by hysteresis, meaning that if the system is to return to its original configuration, it must take a different path. Often, pain and other costs are associated with that recovery pathway.

Nonlinear feedbacks, which can be either positive or negative, can drive a complex system away from a given equilibrium state;1 the stability of any complex system is determined by the nature of these feedbacks. Feedbacks can result from the low-level processes in the system (for example, the behaviors or individuals in a food chain, traders in a market, or components of an engineered system), from an explicit top-down


“State” is used here as a shorthand to mean either a single state or a set of dynamically (possibly stochastically) related states in a common basin of attraction, not something static.

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