Chaos theory is the study of nonlinear dynamic systems. This system can be described with a simple initial value problem. In the former, there is only one solution for every state, and in the latter, there are many possible solutions that can be chosen from a probability distribution.
Chaotic systems are deterministic, yet they are unpredictable.
One consequence of this sensitivity is that seemingly insignificant adjustments to a system will be compounded over a time and can dramatically change the overall behavior of a system. In other words, initial points will diverge exponentially as time passes. Nevertheless, it should be noted that if the initial conditions were to be chosen precisely, a system is completely predictable. Our ability to choose exact numerical values for conditions is limited since computers deal with a finite set of numbers. Hence, initial conditions can never be chosen with infinite precision.