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Tame semiflows for piecewise linear vector fields

Daniel Panazzolo (2002)

Annales de l’institut Fourier

Let be a disjoint decomposition of n and let X be a vector field on n , defined to be linear on each cell of the decomposition . Under some natural assumptions, we show how to associate a semiflow to X and prove that such semiflow belongs to the o-minimal structure an , exp . In particular, when X is a continuous vector field and Γ is an invariant subset of X , our result implies that if Γ is non-spiralling then the Poincaré first return map associated Γ is also in an , exp .

The existence of limit cycle for perturbed bilinear systems

Hanen Damak, Mohamed Ali Hammami, Yeong-Jeu Sun (2012)

Kybernetika

In this paper, the feedback control for a class of bilinear control systems with a small parameter is proposed to guarantee the existence of limit cycle. We use the perturbation method of seeking in approximate solution as a finite Taylor expansion of the exact solution. This perturbation method is to exploit the “smallness” of the perturbation parameter ε to construct an approximate periodic solution. Furthermore, some simulation results are given to illustrate the existence of a limit cycle for...

The period of a whirling pendulum

Hana Lichardová (2001)

Mathematica Bohemica

The period function of a planar parameter-depending Hamiltonian system is examined. It is proved that, depending on the value of the parameter, it is either monotone or has exactly one critical point.

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