Open AccessA note on attractivity for the intersection of two discontinuity manifolds
Author(s) -
Fabio V. Difonzo
Publication year - 2020
Publication title -
rocznik akademii górniczo-hutniczej im. stanisława staszica. opuscula mathematica/opuscula mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 16
eISSN - 2300-6919
pISSN - 1232-9274
DOI - 10.7494/opmath.2020.40.6.685
Subject(s) - mathematics , discontinuity (linguistics) , bifurcation , manifold (fluid mechanics) , sign (mathematics) , intersection (aeronautics) , piecewise , mathematical analysis , nonlinear system , mechanical engineering , physics , quantum mechanics , engineering , aerospace engineering
In piecewise smooth dynamical systems, a co-dimension 2 discontinuity manifold can be attractive either through partial sliding or by spiraling. In this work we prove that both attractivity regimes can be analyzed by means of the moments solution, a spiraling bifurcation parameter and a novel attractivity parameter, which changes sign when attractivity switches from sliding to spiraling attractivity or vice-versa. We also study what happens at what we call attractivity transition points, showing that the spiraling bifurcation parameter is always zero at those points.