attractor
Sign in to saveAlso known as attractor state
right|thumb|upright=1.5|Visual representation of a [[#Strange_attractor|strange attractor. Another visualization of the same 3D attractor is this video. Code capable of rendering this is available.]] In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
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~20 min read
Article
17 sectionsContents
- Motivation of attractors
- Mathematical definition
- Types of attractors
- Fixed point
- Finite number of points
- Limit cycle
- Limit torus
- Attractors characterize the evolution of a system
- Basins of attraction
- Linear equation or system
- Nonlinear equation or system
- Partial differential equations
- Numerical localization (visualization) of attractors: self-excited and hidden attractors
- See also
- References
- Further reading
- External links
right|thumb|upright=1.5|Visual representation of a [[#Strange_attractor|strange attractor. Another visualization of the same 3D attractor is this video. Code capable of rendering this is available.]] In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate.