“Tikhonov's theorem (dynamical systems)”的意思、由来-开放百科全书

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Tikhonov's theorem (dynamical systems)

释义

Statement
References

In applied mathematics, Tikhonov's theorem on dynamical systems is a result on stability of solutions of systems of differential equations. It has applications to chemical kinetics.^[1]^[2] The theorem is named after Andrey Nikolayevich Tikhonov.

Statement

Consider this system of differential equations:

Taking the limit as , this becomes the "degenerate system":

where the second equation is the solution of the algebraic equation

Note that there may be more than one such function .

Tikhonov's theorem states that as the solution of the system of two differential equations above approaches the solution of the degenerate system if is a stable root of the "adjoined system"

References

1. ^{{cite journal |first=Wlodzimierz |last=Klonowski |authorlink=Wlodzimierz Klonowski |title=Simplifying Principles for Chemical and Enzyme Reaction Kinetics |journal=Biophysical Chemistry |volume=18 |issue=2 |year=1983 |pages=73–87 |doi=10.1016/0301-4622(83)85001-7 }}
2. ^{{cite paper |first=Marc R. |last=Roussel |title=Singular perturbation theory |date=October 19, 2005 |work=Lecture notes |url=http://people.uleth.ca/~roussel/nld/singpert.pdf }}

3 : Differential equations|Perturbation theory|Theorems in dynamical systems

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