On the deformation method of study of global asymptotic stability

We consider the one-parameter family of systems where F : ℝ n × [0, 1] → ℝ n is a continuous vector field. The solution x ( t ) = φ ( t, y, λ ) is uniquely determined by the initial condition x (0) = y = φ (0, y, λ ) and can be continued to the whole axis (−∞, +∞) for all λ ∈ [0, 1]. We obtain condi...

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Bibliographic Details
Published in:Mathematical Notes 2014-03, Vol.95 (3-4), p.316-323
Main Authors: Grishanina, G. É., Inozemtseva, N. G., Sadovnikova, M. B.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We consider the one-parameter family of systems where F : ℝ n × [0, 1] → ℝ n is a continuous vector field. The solution x ( t ) = φ ( t, y, λ ) is uniquely determined by the initial condition x (0) = y = φ (0, y, λ ) and can be continued to the whole axis (−∞, +∞) for all λ ∈ [0, 1]. We obtain conditions ensuring the preservation of the property of global asymptotic stability of the stationary solution of such a system as the parameter λ varies.
ISSN:0001-4346
1573-8876
DOI:10.1134/S0001434614030043