"692117" . . . . "Use of central variety theorem for investigation of stability of equilibrium states of nonlinear dynamic systems."@en . "0"^^ . "1"^^ . "0"^^ . "In\u017Een\u00FDrsk\u00E1 mechanika - Engineering Mechanics" . "4" . . "RIV/00216305:26210/01:PU34725" . . "8" . . . . "26210" . "241-254" . "Proch\u00E1zka, Franti\u0161ek" . "1"^^ . "Pou\u017Eit\u00ED v\u011Bty o centr\u00E1ln\u00ED variet\u011B k vy\u0161et\u0159ov\u00E1n\u00ED stability rovnov\u00E1\u017En\u00FDch stav\u016F neline\u00E1rn\u00EDch dynamick\u00FDch soustav." . . . "Pou\u017Eit\u00ED v\u011Bty o centr\u00E1ln\u00ED variet\u011B k vy\u0161et\u0159ov\u00E1n\u00ED stability rovnov\u00E1\u017En\u00FDch stav\u016F neline\u00E1rn\u00EDch dynamick\u00FDch soustav." . . . "P\u0159edkl\u00E1dan\u00FD p\u0159\u00EDsp\u011Bvek se zab\u00FDv\u00E1 problematikou stability rovnov\u00E1\u017En\u00FDch stav\u016F neline\u00E1rn\u00EDch dynamick\u00FDch sou-stav na hranic\u00EDch oblast\u00ED stability jejich p\u0159idru\u017Een\u00FDch line\u00E1rn\u00EDch matematick\u00FDch model\u016F (hranici oblasti stability odpov\u00EDd\u00E1 vlastn\u00ED \u010D\u00EDslo s nulovou re\u00E1lnou \u010D\u00E1st\u00ED), co\u017E znamen\u00E1, \u017Ee soustava diferenci\u00E1ln\u00EDch rovnic popisuj\u00EDc\u00EDch chov\u00E1n\u00ED neline\u00E1rn\u00ED dynamick\u00E9 soustavy nen\u00ED lok\u00E1ln\u011B struktur\u00E1ln\u011B stabiln\u00ED v okol\u00ED sv\u00E9ho rovnov\u00E1\u017En\u00E9ho stavu, tak\u017Ee m\u016F\u017Ee doch\u00E1zet k bifurkaci (kvalitativn\u00ED zm\u011Bn\u011B f\u00E1zov\u00E9ho portr\u00E9tu). K \u0159e\u0161en\u00ED dan\u00E9 problematiky bylo pou\u017Eito v\u011Bty o invariantn\u00EDch variet\u00E1ch a v\u011Bty o redukci na centr\u00E1ln\u00ED varietu, p\u0159i\u010Dem\u017E bude uk\u00E1z\u00E1no, \u017Ee jejich pou\u017Eit\u00EDm se n\u00E1m podstatn\u011B redukuje dimenze \u0159e\u0161en\u00E9ho probl\u00E9mu, tak\u017Ee doch\u00E1z\u00ED k v\u00FDrazn\u00E9mu zjednodu\u0161en\u00ED v\u00FDpo\u010Dt\u016F." . "Pou\u017Eit\u00ED v\u011Bty o centr\u00E1ln\u00ED variet\u011B k vy\u0161et\u0159ov\u00E1n\u00ED stability rovnov\u00E1\u017En\u00FDch stav\u016F neline\u00E1rn\u00EDch dynamick\u00FDch soustav."@cs . "RIV/00216305:26210/01:PU34725!RIV/2003/MSM/262103/N" . . "14"^^ . "Use of central variety theorem for investigation of stability of equilibrium states of nonlinear dynamic systems."@en . "Pou\u017Eit\u00ED v\u011Bty o centr\u00E1ln\u00ED variet\u011B k vy\u0161et\u0159ov\u00E1n\u00ED stability rovnov\u00E1\u017En\u00FDch stav\u016F neline\u00E1rn\u00EDch dynamick\u00FDch soustav."@cs . "CZ - \u010Cesk\u00E1 republika" . . . . "Bifurcation, dynamic system, structural stability, phase portrait, topological orbital equivalence, hyper-bolic equivalent state, invariant variaties \u2013 stabil, central and unstabil variety, central variety dimension, Ljapunovian stability."@en . "1210-2717" . . . . . "[0BEF940FDA7D]" . . . "In this article problems of stability of equilibrium states of nonlinear dynamic systems have been solved by means of two basic theorems of qualitative theory of differential equations i.e. inva-riant varieties theorem and the theorem of reduction to central variety. It has shown that by use of those two theorems it is possible to tak\u00E9 decision regarding stability of the equilibrium state also in such cases when the proper figures of the linearisation matrix have real parts null, i.e. when diffe-rentiall equations describing behaviour of a nonlinear dynamic syst\u00E9m are in vicinity of the equili-brium state structurally unstabil, due to which a bifurcation takes place (change in quality of the phase portrait). A close analysis has shown that in course of investigation of the conditions on the bounds of stability (when at least a single proper figure of the linearisation matrix is null) the di-mension of the task substantially reduces in many cases, since the dimension agrees with the central variety dim"@en . "Z(MSM 262100024)" .