Instable Trivial Solution of Autonomous Differential Systems with Quadratic Right-Hand Sides 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 Chetaev's method, assuming that the matrix of linear terms has a...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/154916 |
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| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |