The moving equilibrium theorem, suggested by Alfred J. Lotka, concerns dynamical systems with a fast-moving variable and a slow-moving variable, where the fast variable's own subsystem settles to an asymptotically stable equilibrium for any fixed value of the slow variable. The theorem states that if that fast subsystem is heavily damped, meaning it settles quickly, the solutions of the full two-variable system can be closely approximated by substituting the fast variable's equilibrium value into the equation governing the slow variable, reducing a higher-dimensional dynamical problem to a lower-dimensional one; the result has been proved rigorously for linear systems. The theorem underlies Alfred Marshall's method of temporary equilibrium in economics, where markets that adjust quickly are treated as always in equilibrium relative to more slowly changing conditions.
Facts
StatementThe theorem permits reducing high-dimensional dynamical problems to lower dimensions and underlies Alfred Marshall's temporary equilibrium method. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Moving equilibrium theorem - Wikipedia
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It permits reducing high-dimensional dynamical problems to lower dimensions and underlies Alfred Marshall's temporary equilibrium method.
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