Where does attractor collide?

In dynamical systems theory an attractor is a set of states toward which a system settles over time, so that a wide range of starting conditions end up evolving into it. Auslander, Bhatia, and Seibert's 1964 Attractors in dynamical systems gave an early formal definition of such a set, and Ruelle and Takens's 1971 On the nature of turbulence added the strange attractor, a fractal set that captures chaotic long-term behaviour. The referent is an abstract region in the space of a system's possible states, defined by the convergence of trajectories, and it is not a lump of matter in the sky or a word inside a sentence.[1][2]

Unit

A closed set in a system's state space that nearby trajectories approach as time grows

Recovery means

A perturbation decays and the trajectory relaxes back onto the attractor, provided it stays within the basin of attraction

Measured by

Identified from the governing equations or an observed time series by finding the invariant set trajectories converge to, using tools like Lyapunov exponents and reconstructed phase portraits

In the study of subject-verb agreement the attractor is an intervening noun that lures a verb into agreeing with it rather than with the true subject, as in the key to the cabinets are missing, where cabinets pulls the verb to plural. Bock and Miller's 1991 Broken agreement established the modern experimental account of this agreement attraction, in which the closest but grammatically wrong noun captures the verb's number. The referent is a word inside a sentence that disturbs grammatical marking during language production, and it is unrelated to a set in state space or a mass concentration between galaxies.[3]

Unit

A single noun phrase that intervenes between the subject head and the verb

Recovery means

Not applicable

Measured by

Quantified by rates of agreement errors in elicited sentence production, or by reading-time disruption in comprehension experiments