Zubov's method

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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.[1] 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 .


  1. ^ Vladimir Ivanovich Zubov, Methods of A.M. Lyapunov and their application, Izdatel'stvo Leningradskogo Universiteta, 1961. (Translated by the United States Atomic Energy Commission, 1964.) ASIN B0007F2CDQ.