Báo Cáo Báo cáo hóa học DETERMINATION AND APPROXIMATION OF THE DOMAIN OF ATTRACTION IN THE CASE OF AUTONOMOU

METHODS FOR DETERMINATION AND APPROXIMATION OF THE DOMAIN OF ATTRACTION IN THE CASE OF AUTONOMOUS DISCRETE DYNAMICAL SYSTEMS ST. BALINT, E. KASLIK, A. M. BALINT, AND A. GRIGIS Received 15 October 2004; Accepted 18 October 2004 A method for determination and two methods for approximation of the domain of attraction Da (0) of the asymptotically stable zero steady state of an autonomous, R-analytical, discrete dynamical system are presented. The method of determination is based on the construction of a Lyapunov function V , whose domain of analyticity is Da (0). The first method of approximation uses a sequence of Lyapunov functions V p , which converge to the Lyapunov function V on Da (0). Each V p defines an estimate N p of Da (0). For any x ∈ Da (0), there exists an estimate N px which contains x. The second method of approximation uses a ball B(R) ⊂ Da (0) which generates the sequence of estimates M p = f ư p (B(R)). For any x ∈ Da (0), there exists an estimate M px which