Chaos theory is the field of study in
mathematics that studies the behavior and condition of
dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the
butterfly effect. Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general. This happens even though these systems are
deterministic, meaning that their future behavior is fully determined by their initial conditions, with no
random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as
deterministic chaos, or simply
chaos. The theory was summarized by
Edward Lorenz as:
Chaotic behavior exists in many natural systems, such as weather and climate. This behavior can be studied through analysis of a chaotic
mathematical model, or through analytical techniques such as
recurrence plots and
Poincaré maps. Chaos theory has applications in several disciplines, including
meteorology,
sociology,
physics,
computer science,
engineering,
economics,
biology, and
philosophy. A traffic model was developed showing that the system dynamics can pass under certain conditions to chaos.