Construct · 1 fields · 1 citations

basin: a standalone construct

One name. One construct. A landmark on the map.

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basin1 CONSTRUCTBasin of attractionMILNOR · STATE-SPACE SET

A single standalone construct; nearby constructs are located against it in the Collider. Tap a field for its definition, unit, and measures.

Dynamical systems and mathematics

the set of initial states whose trajectories converge over time to a given attractor.

In a dynamical system, the set of initial states whose trajectories converge over time to a given attractor: every starting point in the basin is eventually drawn toward the same long-run behaviour, and the boundary between basins separates states that end up at different attractors. Milnor's 1985 On the concept of attractor gave a careful definition of an attractor in terms of the probable asymptotic behaviour of orbits and of the set of points attracted to it, which he called the realm of attraction and which is more commonly called the basin. The referent is a subset of a system's state space defined purely by long-run dynamics, with no length, depth, or material, and it shares only a metaphor with a catchment, a depocentre, or an ocean floor.[1]

Unit
A set of initial states in a system's phase space that converge to one attractor
Recovery means
A state displaced within the basin is drawn back toward the attractor, and that convergence is what marks it as belonging to the basin
Measured by
Mapped by integrating trajectories from many initial conditions and locating the boundaries that separate one attractor's basin from another's

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Nearby constructs

equilibrium4 fields · 4 citationsjingle · one word, four constructsstability4 fields · 5 citationsjingle · one word, four constructssink3 fields · 3 citationsjingle · one word, three constructs

References

  1. Milnor, J. (1985). On the concept of attractor. Communications in Mathematical Physics, 99(2), 177–195. https://doi.org/10.1007/BF01212280

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