Tikhonov's theorem (dynamical systems)
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. The theorem is named after Andrey Nikolayevich Tikhonov.
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"