Construct · 2 fields · 3 citations

Where does perturbation collide?

One name. Different field. Different construct. One map.

● jingle · one word, two constructs Nearest construct by meaning·not indexed
perturbation2 CONSTRUCTSPerturbation theoryRAYLEIGH · SMALL PARAMETERPerturbation experimentBENDER · PRESS & PULSE

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1877Perturbation theory1984Perturbation experiment
2026

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Physics and applied mathematics

A small term added to a solvable problem

In physics and applied mathematics, perturbation theory is a method for solving a problem that is close to one already solved by adding a small term and expanding the answer as a series in that small parameter, so the hard problem is approximated by corrections to the easy one. Rayleigh's The Theory of Sound developed the systematic perturbation method for the vibration frequencies of a system disturbed from a known one, and Bender and Orszag's Advanced Mathematical Methods for Scientists and Engineers is the standard modern treatment. The referent is an approximation technique built around a small parameter in an equation, judged by how fast the resulting series converges. It is a way of solving equations, not an experimental push to a living community or a mechanical jolt to a person's balance.[1][2]

Unit
A series expansion of a solution in powers of a small parameter added to a solvable problem
Recovery means
Not applicable
Measured by
Assessed by the order of the expansion retained and how quickly the perturbation series converges

Community ecology

A deliberate disturbance to an ecosystem

In community ecology, a perturbation is a deliberate disturbance to an ecosystem, such as removing or adding a species, used to reveal the web of interactions by watching how the other populations respond. Bender, Case, and Gilpin's 1984 Perturbation experiments in community ecology distinguished a lasting press perturbation, which holds one species at a new level, from a brief pulse perturbation, and showed what each can and cannot reveal about interaction strengths. The referent is an experimental disturbance imposed on a network of interacting populations and the community's response to it, measured by shifts in abundances. It is an intervention on an ecosystem, not a small parameter in an equation or a jolt to a person's balance.[3]

Unit
A press or pulse disturbance to species abundances and the community's response
Recovery means
Not applicable
Measured by
Observed as changes in population abundances following a press or pulse disturbance to one species

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Nearby collisions

balance4 fields · 5 citationsjingle · one word, four constructsbody2 fields · 3 citationsjingle · one word, two constructscommunity5 fields · 7 citationsjingle · one word, five constructs

References

  1. Rayleigh, J. W. S. (1976). The theory of sound, Volume One. Dover. (Original work published 1877) ISBN 9780486602929
  2. Bender, C. M., & Orszag, S. A. (1999). Advanced mathematical methods for scientists and engineers: Asymptotic methods and perturbation theory. Springer. (Original work published 1978) ISBN 9780387989310
  3. Bender, E. A., Case, T. J., & Gilpin, M. E. (1984). Perturbation experiments in community ecology: Theory and practice. Ecology, 65(1), 1–13. https://doi.org/10.2307/1939452

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