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On deferring the loss of stability for dynamic bifurcations. II. (English. Russian original) Zbl 0677.58035
Differ. Equations 24, No. 2, 171-176 (1988); translation from Differ. Uravn. 24, No. 2, 226-233 (1988).
[For part I, cf. 23, No.12, 2066-2067 (1987; Zbl 0646.34068).]
The system \(\dot x=f(x,y,\epsilon)\), \(\dot y=\epsilon g(x,y,\epsilon)\), \(x\in R^ n\), \(y\in R^ m\) with a small parameter \(\epsilon\) is considered. For fixed slow variables y, the system for the fast variable x has an equilibrium. With drifting the slow variables a dynamic bifurcation occurs, when a pair of conjugate eigenvalues of this equilibrium is crossing the imaginary axis from the left to the right. For analytic systems the loss of stability is delayed for a time of order 1/\(\epsilon\) after the moment of bifurcation. \(\epsilon\) is the small parameter characterizing the speed of the drift. A lower estimate for the time of the delay of the loss of stability is derived.
Reviewer: Št.Schwabik

37G99 Local and nonlocal bifurcation theory for dynamical systems