Zubov's Method

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 .