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Mat. Zametki, 2014, Volume 95, Issue 3, Pages 350–358 (Mi mz10425)  

On the Deformation Method of Study of Global Asymptotic Stability

G. E. Grishaninaa, N. G. Inozemtsevaa, M. B. Sadovnikovab

a Dubna International University for Nature, Society, and Man
b M. V. Lomonosov Moscow State University

Abstract: We consider the one-parameter family of systems
$$ x'=F(x,\lambda),\qquad x\in\mathbb R^n, \quad 0\le\lambda\le1, $$
where $F\colon \mathbb R^n\times[0,1] \to \mathbb R^n$ is a continuous vector field. The solution $x(t)=\varphi(t,y,\lambda)$ is uniquely determined by the initial condition $x(0)=y=\varphi(0,y,\lambda)$ and can be continued to the whole axis $(-\infty,+\infty)$ for all $\lambda\in[0,1]$. We obtain conditions ensuring the preservation of the property of global asymptotic stability of the stationary solution of such a system as the parameter $\lambda$ varies.

Keywords: matrix first-order differential equation, global asymptotic stability of solutions, deformation method, Lyapunov stability.

DOI: https://doi.org/10.4213/mzm10425

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English version:
Mathematical Notes, 2014, 95:3, 316–323

Bibliographic databases:

Document Type: Article
UDC: 517.9
Received: 20.05.2013

Citation: G. E. Grishanina, N. G. Inozemtseva, M. B. Sadovnikova, “On the Deformation Method of Study of Global Asymptotic Stability”, Mat. Zametki, 95:3 (2014), 350–358; Math. Notes, 95:3 (2014), 316–323

Citation in format AMSBIB
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