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Catastrophe Theory

TL;DR

Section titled “TL;DR”
  • Describes how small changes in conditions can produce sudden, large changes in a system’s behavior.
  • Centers on bifurcations: parameter values where system behavior shifts qualitatively (stable or unstable).
  • Applied across physics, engineering, economics, and social sciences to explain events like market crashes and revolutions.

Definition

Section titled “Definition”

Catastrophe theory is a branch of mathematics that deals with the sudden, drastic changes in the behavior of systems. It is based on the concept of bifurcations, which refers to the sudden changes in a system’s behavior when certain conditions are met.

Explanation

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  • Origin: Catastrophe theory was first developed by mathematician Rene Thom in the 1960s.
  • Core concept: Bifurcations occur when changes in system conditions cause the system’s behavior to change suddenly. These bifurcations can be stable or unstable and can produce either gradual or sudden transitions.
  • Interpretation in the source: Some phenomena are characterized as stable bifurcations (where a small event sets off a chain reaction) and others as unstable bifurcations (where behavior changes suddenly and unpredictably).

Examples

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Butterfly effect

Section titled “Butterfly effect”

The so-called “butterfly effect” is presented as an example: the flapping of a butterfly’s wings can cause a tornado thousands of miles away. In the source this is described as an example of a stable bifurcation, where the butterfly’s action does not directly cause the tornado but sets off a chain reaction of events that eventually lead to it.

Tipping point

Section titled “Tipping point”

A tipping point is described as the moment when a small change in conditions causes a system to suddenly change its behavior. The source identifies this as an example of an unstable bifurcation, characterized by sudden and unpredictable change.

”Black Monday” (1987) — market crash

Section titled “”Black Monday” (1987) — market crash”

Catastrophe theory is applied to market crashes. The stock market crash of 1987, known as “Black Monday,” is cited: a combination of factors such as high levels of leverage, computerized trading, and investor psychology reached a tipping point and the market suddenly crashed, causing widespread panic and losses.

Arab Spring (2011) — social upheaval

Section titled “Arab Spring (2011) — social upheaval”

In social systems, catastrophe theory is used to study sudden changes such as revolutions and political upheaval. The Arab Spring (2011) is given as an example: revolutions and protests in the Middle East and North Africa were triggered by factors such as corruption, poverty, and political repression that reached a tipping point and led to widespread unrest and political change.

Use cases

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  • Physics
  • Engineering
  • Economics
  • Social sciences
Section titled “Related terms”
  • Bifurcations
  • Tipping point
  • “Butterfly effect”
  • Rene Thom