Coupled Catastrophes

I ran across this cool article on network dynamics, and thought the model would be an interesting application for Ventity:

Coupled catastrophes: sudden shifts cascade and hop among interdependent systems

Charles D. Brummitt, George Barnett and Raissa M. D’Souza


An important challenge in several disciplines is to understand how sudden changes can propagate among coupled systems. Examples include the synchronization of business cycles, population collapse in patchy ecosystems, markets shifting to a new technology platform, collapses in prices and in confidence in financial markets, and protests erupting in multiple countries. A number of mathematical models of these phenomena have multiple equilibria separated by saddle-node bifurcations. We study this behaviour in its normal form as fast–slow ordinary differential equations. In our model, a system consists of multiple subsystems, such as countries in the global economy or patches of an ecosystem. Each subsystem is described by a scalar quantity, such as economic output or population, that undergoes sudden changes via saddle-node bifurcations. The subsystems are coupled via their scalar quantity (e.g. trade couples economic output; diffusion couples populations); that coupling moves the locations of their bifurcations. The model demonstrates two ways in which sudden changes can propagate: they can cascade (one causing the next), or they can hop over subsystems. The latter is absent from classic models of cascades. For an application, we study the Arab Spring protests. After connecting the model to sociological theories that have bistability, we use socioeconomic data to estimate relative proximities to tipping points and Facebook data to estimate couplings among countries. We find that although protests tend to spread locally, they also seem to ‘hop’ over countries, like in the stylized model; this result highlights a new class of temporal motifs in longitudinal network datasets.

Ventity makes sense here because the system consists of a network of coupled states. Ventity makes it easy to represent a wide variety of network architectures. This means there are two types of entities in the system: “Nodes” and “Couplings.”

The Node entitytype contains a single state (X), with local feedback, as well as a remote influence from Coupling and a few global parameters referenced from the Model entity:

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Climate, the Bailout, and the Blame Game

I’ve been watching a variety of explanations of the financial crisis. As a wise friend noticed, the only thing in short supply is acceptance of responsibility. I’ve seen theories that place the seminal event as far back as the Carter administration. Does that make sense, causally?

In a formal sense, it might in some cases. I could have inhaled a carcinogen a decade ago that only leads to cancer a decade from now, without any outside triggers. But I think that sort of system is a rarity. As a practical matter, we have to look elsewhere.

Socioeconomic systems are at a constant slow boil, with many potential threats existing below the threshold of imminent danger at any given time. Occasionally, one grows exponentially and emerges as a real catastrophe. It seems like a surprise, because of the hockey stick behavior of growth (the French riddle of the lily pond again). However, most apparent low-level threats never emerge from the noise. They don’t have enough gain to grow fast, or they get shut down by some unsuspected negative feedback.

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