Instable Trivial Solution of Autonomous Differential Systems with Quadratic Right-Hand Sides in a Cone
Joint Authors
Šmarda, Zdenĕk
Svoboda, Zdeněk
Khusainov, D. Ya.
Diblík, Josef
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-12-27
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
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 Chetaev's 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.
American Psychological Association (APA)
Khusainov, D. Ya.& Diblík, Josef& Svoboda, Zdeněk& Šmarda, Zdenĕk. 2010. Instable Trivial Solution of Autonomous Differential Systems with Quadratic Right-Hand Sides in a Cone. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-23.
https://search.emarefa.net/detail/BIM-450210
Modern Language Association (MLA)
Khusainov, D. Ya.…[et al.]. Instable Trivial Solution of Autonomous Differential Systems with Quadratic Right-Hand Sides in a Cone. Abstract and Applied Analysis No. 2011 (2011), pp.1-23.
https://search.emarefa.net/detail/BIM-450210
American Medical Association (AMA)
Khusainov, D. Ya.& Diblík, Josef& Svoboda, Zdeněk& Šmarda, Zdenĕk. Instable Trivial Solution of Autonomous Differential Systems with Quadratic Right-Hand Sides in a Cone. Abstract and Applied Analysis. 2010. Vol. 2011, no. 2011, pp.1-23.
https://search.emarefa.net/detail/BIM-450210
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-450210