Opuscula Math. 40, no. 6 (2020), 685-702
https://doi.org/10.7494/OpMath.2020.40.6.685

Opuscula Mathematica

# A note on attractivity for the intersection of two discontinuity manifolds

Fabio V. Difonzo

Abstract. 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.

Keywords: piecewise smooth systems, sliding motion, co-dimension 2, discontinuity manifold, attractivity.

Mathematics Subject Classification: 34A36.

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• Fabio V. Difonzo
• https://orcid.org/0000-0003-0101-3391
• Czech Technical University in Prague, Department of Computer Science, Faculty of Electrical Engineering, Karlovo nám. 13, 120 00 Nové Město, Prague, Czech Republic
• Code Architects Srl, Via Campania 1, 70029 Santeramo in Colle (BA), Italy
• Communicated by Paweł Przybyłowicz.
• Revised: 2020-10-03.
• Accepted: 2020-10-05.
• Published online: 2020-12-01.