# Chaos Theory

Chaos theory is a field of study in mathematics; however, it has applications in several disciplines, including sociology and other social sciences. In the social sciences, chaos theory is the study of complex non-linear systems of social complexity. It is not about disorder but rather about very complicated systems of order.

Nature, including some instances of social behavior and social systems, is highly complex, and the only prediction you can make is that it is unpredictable. Chaos theory looks at this unpredictability of nature and tries to make sense of it.

Chaos theory aims to find the general order of social systems and particularly social systems that are similar to each other. The assumption here is that the unpredictability in a system can be represented as overall behavior, which gives some amount of predictability, even when the system is unstable. Chaotic systems are not random systems. Chaotic systems have some kind of order, with an equation that determines overall behavior.

The first chaos theorists discovered that complex systems often go through a kind of cycle, even though specific situations are rarely duplicated or repeated. For example, say there is a city of 10,000 people. In order to accommodate these people, a supermarket is built, two swimming pools are installed, a library is erected, and three churches go up. In this case, these accommodations please everybody and equilibrium are achieved. Then a company decides to open a factory on the outskirts of town, opening jobs for 10,000 more people. The town then expands to accommodate 20,000 people instead of 10,000. Another supermarket is added, as are two more swimming pools, another library, and three more churches. The equilibrium is thus maintained. Chaos theorists study this equilibrium, the factors that affect this type of cycle, and what happens (what the outcomes are) when the equilibrium is broken.

## Qualities of a Chaotic System

A chaotic system has three simple defining features:

• Chaotic systems are deterministic. That is, they have some determining equation ruling their behavior.
• Chaotic systems are sensitive to initial conditions. Even a very slight change in the starting point can lead to significantly different outcomes.
• Chaotic systems are not random, nor disorderly. Truly random systems are not chaotic. Rather, chaos has a send of order and pattern.

## Concepts

There are several key terms and concepts used in chaos theory:

• Butterfly effect (also called sensitivity to initial conditions): The idea that even the slightest change in the starting point can lead to greatly different results or outcomes.
• Attractor: Equilibrium within the system. It represents a state to which a system finally settles.
• Strange attractor: A dynamic kind of equilibrium which represents some kind of trajectory upon which a system runs from situation to situation without ever settling down.

## Applications in Real-Life

Chaos theory, which emerged in the 1970s, has impacted several aspects of real-life in its short life thus far and continues to impact all sciences. For instance, it has helped answer previously unsolvable problems in quantum mechanics and cosmology. It has also revolutionized the understanding of heart arrhythmias and brain function. Toys and games have also developed from chaos research, such as the Sim line of computer games (SimLife, SimCity, SimAnt, etc.).

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