Chaos Theory
Chaos theory research papers look at the scientific theory in light of another element of research. For example, Paper Masters has written research papers on chaos theory and the philosophy of education, chaos theory and psychology and the science of chaos theory.
Chaos theory is an emerging field of mathematics, one that studies the behavior of various dynamical systems that are frequently subject to random variations. A dynamical system is a mathematical concept in which a fixed rule describes the relationship between space and time for a particular point. Chaos theory is popularly understood by the butterfly effect, in which a small change has the potential to disrupt a large system.
There are chaotic systems in various fields and generally, they depend on the following three things in order to become predictable:
- How much uncertainty can be tolerated
- How accurately its current state is able to measured
- The time scale of the system, called the Lyapunov time
Chaos Theory and Behavior
Chaotic behavior is frequently observed in nature, especially in weather systems. Mathematicians have attempted to construct mathematical models to study such behavior. Chaotic systems are initially predictable and then appear to become random. In order for a system to be defined as chaotic, it must meet three criteria: it must be sensitive to initial conditions, it must be topologically mixing (meaning that is non-constant and will evolve over time), and it must have dense periodic orbits, which means that every point in space can be arbitrarily approached.
The development of the electronic computer was a primary factor in the creation of chaos theory. Edward Lorenz used an early computer in an attempt to predict the weather in the 1960s. Chaos theory has found numerous applications in such diverse fields as physics, meteorology, astrophysics, biology, sociology, and philosophy.