Investigation of asymptotic stability of equilibria by localization of the invariant compact sets
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The method of localization of invariant compact sets was proposed to study for asymptotic stability the equilibrium points of an autonomous system of differential equations. This approach relies on the necessary and sufficient conditions for asymptotic stability formulated in terms of positive invariant sets and invariant compact sets, and enables one to study the equilibrium points for asymptotic stability in the cases where it is impossible to use the first approximation or the method of Lyapunov functions. The possibilities of the method were illustrated by examples.
Keywordsequilibrium point asymptotic stability invariant compact set positive invariant set localizing set
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- 1.Shil’nikov, L.P., Shil’nikov, A.L., Turaev, D.V., and Chua, L., Methods of Qualitative Theory in Nonlinear Dynamics, Moscow–Izhevsk: Inst. Komp’yut. Issled., 2003.Google Scholar
- 2.Khalil, H.K., Nonlinear Systems, Upper Saddle River: Prentice Hall, 2002, 3rd ed. Translated under the title Nelineinye sistemy, Moscow–Izhevsk: NITs “Regulyarnaya i Khaoticheskaya Dinamika,” Inst. Komp’yut. Issled., 2009.Google Scholar
- 3.Kanatnikov, A.N. and Krishchenko, A.P., Invariantnye kompakty dinamicheskikh sistem (Invariant Compact Sets of Dynamic Systems), Moscow: Bauman MGTU, 2011.Google Scholar
- 10.Krishchenko, A.P. and Starkov, K.E, Dynamical Analysis of Raychaudhuri Equations Based on the Localization Method of Compact Invariant Sets, Int. J. Bifurcat. Chaos, 2014, vol. 24, no. 11.Google Scholar