WebWe are interested in finding under what conditions the family has a crossing limit cycle, when the sliding region changes its stability. We call this phenomenon the pseudo-Hopf bifurcation. This class of systems is motivated by piecewise-linear control systems which have not yet been treated in the context of crossing limit cycles. WebJan 1, 2011 · Sliding bifurcations involve sliding motion, for example, a limit cycle may gain or lose a sliding segment. 69 Lastly, the limit cycle may, without additional codimension, …
Bifurcation theory - Wikipedia
WebAbstract In this paper, we analytically consider sliding bifurcations of periodic orbits in the dry-friction oscillator. The system depends on two parameters: F, which corresponds to … WebBifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential … hymn christmas songs
Periodic orbits for double regularization of piecewise
WebJul 15, 2016 · The conjecture is that if the two-dimensional regularized sliding vector field undergoes the Hopf bifurcation at the origin then in the three-dimensional system a sliding limit cycle... WebFeb 1, 2024 · In particular, it has been shown that, in this scenario, the sliding vector field undergoes a saddle–node bifurcation. However, the unfolding dynamics in the crossing regions has not been addressed. We aim to fill this gap, and thus to present complete and detailed results on the unfolding dynamics of a Fold bifurcation of T-singularities. WebMay 15, 2024 · Such a bifurcation occurs in the sliding vector field and creates, in this field, an unstable limit cycle. The limit cycle is connected to the switching manifold and … hymn children of the heavenly father