Geodesic
On a~method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2016), pp. 12-18

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In this paper we describe the method of attraction domain evaluation for equilibrium states of nonlinear discrete dynamic system based on Lyapunov functions method. Attraction domain evaluation size is equilibrium state neighborhood where the first difference of Lyapunov function is negative. Lyapunov function is chosen as positive quadratic form for which the negativity of its first difference by virtue of linearized system is guaranteed with given supply. We propose the method of attraction domain extension.
Keywords: discrete dynamic system, macro-structure of state space, Lyapunov function method. 
@article{IVM_2016_12_a1,
     author = {O. G. Antonovskaya and V. I. Goryunov},
     title = {On a~method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--18},
     publisher = {mathdoc},
     number = {12},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_12_a1/}
}
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O. G. Antonovskaya; V. I. Goryunov. On a~method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2016), pp. 12-18. http://geodesic.mathdoc.fr/item/IVM_2016_12_a1/