Publication detail
Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone
DIBLÍK, J. ŠMARDA, Z. SVOBODA, Z. KHUSAINOV, D.
Original Title
Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone
English Title
Instable trivial solution of autonomous differential systems with quadratic right-hand sides in a cone
Type
journal article - other
Language
en
Original Abstract
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.
English abstract
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.
Keywords
instability, general n-dimensional system of ordinary differential equations with quadratic right-hand sides, the zero solution, cone, Chetaevs method
RIV year
2011
Released
15.03.2011
ISBN
1085-3375
Periodical
Abstract and Applied Analysis
Year of study
2011
Number
Article ID 15491
State
US
Pages from
1
Pages to
23
Pages count
23
Documents
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",
annote="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.",
chapter="49861",
journal="Abstract and Applied Analysis",
number="Article ID 15491",
volume="2011",
year="2011",
month="march",
pages="1--23",
type="journal article - other"
}