Deterministic systems are main subject of chaos theory. Chaos theory holds a great concern about these deterministic systems.
Especially those systems, this behavior can be predicted that is within the scope of principle, and related concepts. In the beginning, such chaotic systems tend to be predictable. Later on, they turn out to be random. It means that chaotic systems are predictable until a specific amount of time from their generation. This amount of time can be derived from three aspects:
Level of expected uncertainty in the forecast or simply prediction
Accuracy in the measurement of the current or last available stage
Lyapunov time, which is the time scale fully dependant on system dynamics
Following are some examples of Lyapunov time:
Chaotic electric circuits [1 millisecond, almost ] Weather system [several days, yet unproven]
The great solar system [50 million years, most accurate since we cannot test it]
In chaotic systems, uncertainty in the forecast keeps increasing exponentially. The increment level keeps rising as the time flows on. The more time is passed the more uncertainty should be expected. Thus, according to mathematical prospective, if the forecast time is doubled the uncertainty will increase more than square value of its current level. According to this concept, chaos theory says that accurate prediction is hard to achieve if it is made after a time interval, which is double or triple than Lyapunov time value. A system is said to be random if any meaningful prediction cannot be made.
According to this description, anyone can understand that chaos theory is all about predictions and its accuracy. Many concepts in chaos theory describe how technical predictions can be made, some other describes how inaccuracy can be reduced and accuracy can be increased in those predictions. This is the main base for each concept of the theory. The learner of this theory will study how this concept is applied in various subjects and fields. Sources, for chaos theory can be found in many other theories. Such as pure mathematics, pure physics, theory of computer science, theory of environmental science, economic theory, biology and many other concepts and fields.
Would you like to read more about this topic? This book might interest you: Chaos Theory.