Stability in the presence of singular perturbations. (English) Zbl 0948.34029

Artstein, Zvi

Nonlinear Anal., Theory Methods Appl. 34, No. 6, 817-827 (1998).

The author examines the Lypapunov asymptotic stability of a solution \(x(t)\) to the coupled autonomous system \(dx/dt= f(x,y)\), \(\varepsilon(dy/dt)= g(x,y)\), where \(\varepsilon> 0\) is a small real parameter and \(x\in\mathbb{R}^n\) and \(y\in\mathbb{R}^m\). The dynamics of \(x\) are coupled through \(y\) to a singularly perturbed fast motion. Proofs of results used the theory of invariant measures.

Reviewer: P.Smith (Keele)

MSC:

34D15	Singular perturbations of ordinary differential equations
34E15	Singular perturbations for ordinary differential equations

Keywords:

singular perturbations; asymptotic stability; invariant measures

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