|
|
| Line 1: |
Line 1: |
| Consider a dynamical system
| | Greetings. The writer's name is Phebe and she feels comfy when individuals use [http://riddlesandpoetry.com/?q=node/19209 over the counter std test] full title. For many years he's been working as a meter reader and it's some thing he really appreciate. What I love doing is performing ceramics but I haven't produced a dime with it. Years ago we moved to North Dakota. |
| | |
| (1)..........<math>\dot{x}=f(x,y)</math>
| |
| | |
| (2)..........<math>\qquad \dot{y}=g(x,y)</math>
| |
| | |
| with the state variables <math>x</math> and <math>y</math>. Assume that <math>x</math> is ''fast'' and <math>y</math> is ''slow''. Assume that the system (1) gives, for any fixed <math>y</math>, an asymptotically stable solution <math>\bar{x}(y)</math>. Substituting this for <math>x</math> in (2) yields
| |
| | |
| (3)..........<math>\qquad \dot{Y}=g(\bar{x}(Y),Y)=:G(Y).</math>
| |
| | |
| Here <math>y</math> has been replaced by <math>Y</math> to indicate that the solution <math>Y</math> to (3) differs from the solution for <math>y</math> obtainable from the system (1), (2).
| |
| | |
| The '''Moving Equilibrium Theorem''' suggested by [[Alfred J. Lotka | Lotka]] states that the solutions <math>Y</math> obtainable from (3) approximate the solutions <math>y</math> obtainable from (1), (2) provided the partial system (1) is asymptotically stable in <math>x</math> for any given <math>y</math> and heavily damped (''fast'').
| |
| | |
| The theorem has been proved for linear systems comprising real vectors <math>x</math> and <math>y</math>. It permits reducing high-dimensional dynamical problems to lower dimensions and underlies [[Alfred Marshall]]'s [[temporary equilibrium method]].
| |
| | |
| ==References==
| |
| *{{cite book | author=Schlicht, E. | title=Isolation and Aggregation in Economics | year=1985 | publisher = Springer Verlag | isbn = 0-387-15254-7 | url=http://epub.ub.uni-muenchen.de/archive/00000003/}}
| |
| *{{cite journal | author=Schlicht, E. | title=The Moving Equilibrium Theorem again | journal=Economic Modelling | year=1997 | volume=14 | pages=271–278 | doi=10.1016/S0264-9993(96)01034-6 | issue=2}}
| |
| | |
| [[Category:Economics theorems]]
| |
Latest revision as of 04:36, 9 March 2014
Greetings. The writer's name is Phebe and she feels comfy when individuals use over the counter std test full title. For many years he's been working as a meter reader and it's some thing he really appreciate. What I love doing is performing ceramics but I haven't produced a dime with it. Years ago we moved to North Dakota.