In mathematics, a strange nonchaotic attractor (SNA) is a form of

attractor 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 ...

which, while converging to a limit, is

strange Strange may refer to: Fiction * Strange (comic book), a comic book limited series by Marvel Comics * Strange (Marvel Comics), one of a pair of Marvel Comics characters known as The Strangers * Adam Strange, a DC Comics superhero * The title cha ...

, because it is not

piecewise differentiable In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. ...

, and also non-

chaotic Chaotic was originally a Danish trading card game. It expanded to an online game in America which then became a television program based on the game. The program was able to be seen on 4Kids TV (Fox affiliates, nationwide), Jetix, The CW4Kids ...

, in that its Lyapunov exponents are non-positive. SNAs were introduced as a topic of study by Grebogi et al. in 1984. SNAs can be distinguished from periodic, quasiperiodic and chaotic attractors using the 0-1 test for chaos. Periodically driven damped nonlinear systems can exhibit complex dynamics characterized by strange chaotic attractors, where strange refers to the fractal geometry of the attractor and chaotic refers to the exponential sensitivity of orbits on the attractor. Quasiperiodically driven systems forced by incommensurate frequencies are natural extensions of periodically driven ones and are phenomenologically richer. In addition to periodic or quasiperiodic motion, they can exhibit chaotic or nonchaotic motion on strange attractors. Although quasiperiodic forcing is not necessary for strange nonchaotic dynamics (e.g., the period doubling accumulation point of a period doubling cascade), if quasiperiodic driving is not present, strange nonchaotic attractors are typically not robust and not expected to occur naturally because they exist only when the system is carefully tuned to a precise critical parameter value. On the other hand, it was shown in the paper of Grebogi et al. that SNAs can be robust when the system is quasiperiodically driven. The first experiment to demonstrate a robust strange nonchaotic attractor involved the buckling of a magnetoelastic ribbon driven quasiperiodically by two incommensurate frequencies in the golden ratio. Strange nonchaotic attractors have been robustly observed in laboratory experiments involving magnetoelastic ribbons, electrochemical cells, electronic circuits, a neon glow discharge and most recently detected in the dynamics of the pulsating

RR Lyrae variables RR Lyrae variables are periodic variable stars, commonly found in globular clusters. They are used as standard candles to measure (extra) galactic distances, assisting with the cosmic distance ladder. This class is named after the prototype and ...

KIC 5520878 (as obtained from the

Kepler Space Telescope The Kepler space telescope is a disused space telescope launched by NASA in 2009 to discover Earth-sized planets orbiting other stars. Named after astronomer Johannes Kepler, the spacecraft was launched into an Earth-trailing heliocentric orbi ...

) which may be the first strange nonchaotic

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

observed in the wild.

References

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