Chaos theory
From The Art and Popular Culture Encyclopedia
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In mathematics, chaos theory describes the behavior of certain dynamical systems – that is, systems whose state evolves with time – that may exhibit dynamics that are highly sensitive to initial conditions (popularly referred to as the butterfly effect). As a result of this sensitivity, which manifests itself as an exponential growth of perturbations in the initial conditions, the behavior of chaotic systems appears to be random. This happens even though these systems are deterministic, meaning that their future dynamics are fully defined by their initial conditions, with no random elements involved. This behavior is known as deterministic chaos, or simply chaos.
Chaotic behaviour is also observed in natural systems, such as the weather. This may be explained by a chaos-theoretical analysis of a mathematical model of such a system, embodying the laws of physics that are relevant for the natural system.
See also
- Examples of chaotic systems
- Advected contours
- Arnold's cat map
- Bouncing ball dynamics
- Chua's circuit
- Cliodynamics
- Coupled map lattice
- Double pendulum
- Duffing equation
- Dynamical billiards
- Economic bubble
- Gaspard-Rice system
- Hénon map
- Horseshoe map
- List of chaotic maps
- Logistic map
- Rössler attractor
- Standard map
- Swinging Atwood's machine
- Tilt A Whirl
- Other related topics
- Amplitude death
- Anosov diffeomorphism
- Bifurcation theory
- Catastrophe theory
- Chaos theory in organizational development
- Chaotic mixing
- Chaotic scattering
- Complexity
- Control of chaos
- Edge of chaos
- Emergence
- Fractal
- Kolmogorov–Arnold–Moser theorem
- Ill-conditioning
- Ill-posedness
- Nonlinear system
- Patterns in nature
- Predictability
- Quantum chaos
- Santa Fe Institute
- Synchronization of chaos
- Unintended consequence
- People
- Ralph Abraham
- Michael Berry
- Leon O. Chua
- Ivar Ekeland
- Doyne Farmer
- Mitchell Feigenbaum
- Martin Gutzwiller
- Brosl Hasslacher
- Michel Hénon
- Andrey Nikolaevich Kolmogorov
- Edward Lorenz
- Aleksandr Lyapunov
- Ian Malcolm (Jurassic Park character)
- Benoît Mandelbrot
- Norman Packard
- Henri Poincaré
- Otto Rössler
- David Ruelle
- Oleksandr Mikolaiovich Sharkovsky
- Robert Shaw
- Floris Takens
- James A. Yorke
- George M. Zaslavsky
