the chaos theory
In: Physics
The study of *dynamical systems* is, loosely speaking, the mathematical study of things that interact and change over time. These include things like pendulums, planets, animal populations, as well as many other mathematical models.
Chaos theory deals with the study of how such dynamical systems can be sensitive to their initial conditions, among other (less well-known) characteristics of chaos like repelling periodic orbits and mixing within the state space. How a system evolves over time can be fixed (it is deterministic with a specified formula and there is no randomness), but if we even very slightly change our starting position, the outcome after a while can be drastically different. We want to examine when systems become chaotic (in terms of model parameters), “how chaotic” they are, if spontaneous order can arise, among other things.
You can look up videos of a *double pendulum*, which is one of the most well-known chaotic systems. And you would have heard of the *butterfly effect*, which is a metaphor of the sensitivity to initial conditions.
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