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.
Statement.
Consider this system of differential equations:
 formula_1
Taking the limit as formula_2, this becomes the "degenerate system":
 formula_3
where the second equation is the solution of the algebraic equation
 formula_4
Note that there may be more than one such function formula_5.
Tikhonov's theorem states that as formula_6 the solution of the system of two differential equations above approaches the solution of the degenerate system if formula_7 is a stable root of the "adjoined system"
 formula_8
References.
 ;templatestyles src="Reflist/styles.css" / ;