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Determination of the number of limit cycles of the second kind for systems of differential equations. (Russian) Zbl 0656.34016

The number of limit cycles of the second kind is considered for the system \[ {\dot \sigma}=c^*x,\quad \dot x=Ax+\alpha_ s\frac{c^*x}{s^ 2+(c^*x)^ 2}b+\phi (\sigma)b, \] where \(x,b,c\in R^ n\); \(\alpha\),s are positive numbers, \(\phi\) (\(\sigma)\) is a periodic function satisfying the Lipschitz’s condition and is an \(n\times n\) matrix. Sufficient conditions for the existence of at least m limit cycles of the second kind are established. The case \(\alpha =0\) is also considered.
Reviewer: I.Foltyńska

MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
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