About: Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The present investigation deals with global instability of a general n-dimensional system of ordinary differential equations with quadratic right-hand sides. The global instability of the zero solution in a given cone is proved by Chetaevs method, assuming that the matrix of linear terms has a simple positive eigenvalue and the remaining eigenvalues have negative real parts. The sufficient conditions for global instability obtained are formulated by inequalities involving norms and eigenvalues of auxiliary matrices. In the proof, a result is used on the positivity of a general third-degree polynomial in two variables to estimate the sign of the full derivative of an appropriate function in a cone. The present investigation deals with global instability of a general n-dimensional system of ordinary differential equations with quadratic right-hand sides. The global instability of the zero solution in a given cone is proved by Chetaevs method, assuming that the matrix of linear terms has a simple positive eigenvalue and the remaining eigenvalues have negative real parts. The sufficient conditions for global instability obtained are formulated by inequalities involving norms and eigenvalues of auxiliary matrices. In the proof, a result is used on the positivity of a general third-degree polynomial in two variables to estimate the sign of the full derivative of an appropriate function in a cone. (en)
Title	Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone (en)
skos:prefLabel	Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone (en)
skos:notation	RIV/00216305:26220/11:PU91522!RIV12-GA0-26220___
http://linked.open...avai/predkladatel	Fakulta elektrotechniky a komunikačních technologií
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GAP201/10/1032), P(GAP201/11/0768), Z(MSM0021630503), Z(MSM0021630519)
http://linked.open...iv/cisloPeriodika	Article ID
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Svoboda, Zdeněk Šmarda, Zdeněk Diblík, Josef Khusainov, Denys
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoké učení technické v Brně / Fakulta elektrotechniky a komunikačních technologií
http://linked.open...dnocenehoVysledku	205052
http://linked.open...ai/riv/idVysledku	RIV/00216305:26220/11:PU91522
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	instability, general n-dimensional system of ordinary differential equations with quadratic right-hand sides, the zero solution, cone, Chetaevs method (en)
http://linked.open.../riv/klicoveSlovo	instability Chetaevs method cone general n-dimensional system of ordinary differential equations with quadratic right-hand sides the zero solution
http://linked.open...odStatuVydavatele	FK - Falklandské ostrovy
http://linked.open...ontrolniKodProRIV	[EF7D7EB9B061]
http://linked.open...i/riv/nazevZdroje	Abstract and Applied Analysis
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	4 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales III Qualitative properties of solutions of differential equations and their applications
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	2011
http://linked.open...iv/tvurceVysledku	Diblík, Josef Khusainov, Denys Svoboda, Zdeněk Šmarda, Zdeněk
http://linked.open...n/vavai/riv/zamer	Nové trendy v mikroelektronických systémech a nanotechnologiích (MIKROSYN) Progressive reliable and durable civil engineering structures
issn	1085-3375
number of pages	23 (xsd:int)
http://localhost/t...ganizacniJednotka	26220
is http://linked.open...avai/riv/vysledek of	Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone

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