Detail publikačního výsledku

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

DIBLÍK, J.; ŠMARDA, Z.; SVOBODA, Z.; KHUSAINOV, D.

Originální název

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

Anglický název

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

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

instability, general n-dimensional system of ordinary differential equations with quadratic right-hand sides, the zero solution, cone, Chetaevs method

Klíčová slova v angličtině

instability, general n-dimensional system of ordinary differential equations with quadratic right-hand sides, the zero solution, cone, Chetaevs method

Autoři

DIBLÍK, J.; ŠMARDA, Z.; SVOBODA, Z.; KHUSAINOV, D.

Rok RIV

2012

Vydáno

15.03.2011

ISSN

1085-3375

Periodikum

Abstract and Applied Analysis

Svazek

2011

Číslo

Article ID 15491

Stát

Spojené státy americké

Strany od

1

Strany do

23

Strany počet

23

BibTex

@article{BUT49861,
  author="Denys {Khusainov} and Josef {Diblík} and Zdeněk {Svoboda} and Zdeněk {Šmarda}",
  title="Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone",
  journal="Abstract and Applied Analysis",
  year="2011",
  volume="2011",
  number="Article ID 15491",
  pages="1--23",
  issn="1085-3375"
}