On the deformation method of study of global asymptotic stability
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- 作者：G. é. Grishanina (1) <br> N. G. Inozemtseva (1) <br> M. B. Sadovnikova (2) <br>
- 关键词：matrix first ; order differential equation ; global asymptotic stability of solutions ; deformation method ; Lyapunov stability
- 刊名：Mathematical Notes
- 出版年：2014
- 出版时间：March 2014
- 年：2014
- 卷：95
- 期：3-4
- 页码：316-323
- 全文大小：
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- 作者单位：G. é. Grishanina (1) <br> N. G. Inozemtseva (1) <br> M. B. Sadovnikova (2) <br><br>1. International University of Nature, Society, and Mankind, Dubna, Moscow Region, Russia <br> 2. Moscow State University, Moscow, Russia <br>
- ISSN：1573-8876
文摘
We consider the one-parameter family of systems $$x' = F(x,\lambda ), x \in \mathbb{R}^n , 0 \leqslant \lambda \leqslant 1,$$ where F: ?sup class="a-plus-plus"> n × [0, 1] ??sup class="a-plus-plus"> 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.