Determination of limit cycles using stroboscopic set-valued maps
Résumé
Given a dynamical system $Σp$ with a parameter $p$ taking its values in a fixed interval $\mathcal{Q}$, we present a simple criterion of set inclusion which guarantees that the Euler approximate solutions of $Σp_0$ for some value $p_0$ $∈$ $\mathcal{Q}$ converge to a limit cycle $\mathcal{E}$. Moreover, we characterize a compact set $\mathcal{I}$ containing $\mathcal{E}$ which is invariant for the exact solutions of $Σp$ whatever the value of $p$∈ $\mathcal{Q}$. We illustrate the application of our method on the example of a parametric Van der Pol system driven by a periodic input.
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