Zubov's method is a technique for computing the basin of attraction for a set of ordinary differential equations (a dynamical system). The domain of attraction is the set, where is the solution to a partial differential equation known as the Zubov equation. 'Zubov's method' can be used in a number of ways.
Zubov's theorem states that:
- If is an ordinary differential equation in with, a set containing 0 in its interior is the domain of attraction of zero if and only if there exist continuous functions such that:
- , for, on
- for every there exist such that, if
- for or
If f is continuously differentiable, then the differential equation has at most one continuously differentiable solution satisfying .
Famous quotes containing the word method:
“The method of scientific investigation is nothing but the expression of the necessary mode of working of the human mind. It is simply the mode in which all phenomena are reasoned about, rendered precise and exact.”
—Thomas Henry Huxley (1825–95)