Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations

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Abstract

In the 1960s, L.P. Shilnikov showed that certain homoclinic orbits for smooth families of differential equations imply the existence of chaos, and there are complicated sequences of bifurcations near the parameter value at which the homoclinic orbit exists. We describe how this analysis is modified if the differential equations are piecewise smooth and the homoclinic orbit has a sliding segment. Moreover, we show that the Shilnikov mechanism appears naturally in the unfolding of boundary equilibrium bifurcations in .

Bibliographical metadata

Original languageEnglish
JournalEuropean Journal of Applied Mathematics
Early online date13 Jun 2018
Publication statusPublished - 2018