Geodesic
On the Deformation Method of Study of Global Asymptotic Stability
Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 350-358

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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. 
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     author = {G. E. Grishanina and N. G. Inozemtseva and M. B. Sadovnikova},
     title = {On the {Deformation} {Method} of {Study} of {Global} {Asymptotic} {Stability}},
     journal = {Matemati\v{c}eskie zametki},
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     volume = {95},
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     year = {2014},
     language = {ru},
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G. E. Grishanina; N. G. Inozemtseva; M. B. Sadovnikova. On the Deformation Method of Study of Global Asymptotic Stability. Matematičeskie zametki, Tome 95 (2014) no. 3, pp. 350-358. http://geodesic.mathdoc.fr/item/MZM_2014_95_3_a3/