Chaos theory

In mathematics, chaos theory is the field which studies the behavior of dynamical systems that are highly sensitive to initial conditions -- a response popularly referred to as the butterfly effect.

Description

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 Norton Lorenz as:

Chaos: When the present determines the future, but the approximate present does not approximately determine the future.

Chaos in natural systems

Chaotic behavior exists in many natural systems, such as weather and climate.

Analytical techniques

This behavior can be studied through analysis of a chaotic mathematical model, or through analytical techniques such as recurrence plots and Poincaré maps.

Disciplines

Chaos theory has applications in several disciplines, including:

• Computer science
• Database management
• Meteorology
• Sociology
• Physics
• Engineering
• Economics
• Biology
• Philosophy

See also

• Complex dynamics
• Deterministic Nonperiod Flow
• Deterministic system
• Fractal
• Mandelbrot set
• Lorenz, Edward Norton
• Numerical computation
• Poincaré section
• Recursion
• Rounding errors
• Strange attractor

External links

• Chaos theory @ Wikipedia