Moving equilibrium theorem

Consider a dynamical system (1)..........

with the state variables

is slow.

Assume that the system (1) gives, for any fixed

, an asymptotically stable solution

to indicate that the solution

to (3) differs from the solution for

obtainable from the system (1), (2).

The Moving Equilibrium Theorem suggested by Lotka states that the solutions

obtainable from (3) approximate the solutions

obtainable from (1), (2) provided the partial system (1) is asymptotically stable in

and heavily damped (fast).

The theorem has been proved for linear systems comprising real vectors

It permits reducing high-dimensional dynamical problems to lower dimensions and underlies Alfred Marshall's temporary equilibrium method.