Journal
NONLINEAR DYNAMICS
Volume 88, Issue 2, Pages 1427-1439Publisher
SPRINGER
DOI: 10.1007/s11071-016-3320-1
Keywords
Piece-wise smooth dynamics; Discontinuous differential equations; Sliding mode (Filippov) solutions; Regularization; Singular perturbations; Asymptotic expansions
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Funding
- Fonds National Suisse [200020_159856]
- Italian INdAM GNCS (Gruppo Nazionale di calcolo Scientifico)
- Swiss National Science Foundation (SNF) [200020_159856] Funding Source: Swiss National Science Foundation (SNF)
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Piece-wise smooth differential equations (their regularization, numerical integration, and classification of solutions) is the topic of the present work. The behaviour close to one discontinuity surface and also the entering into the intersection of two discontinuity surfaces is well understood. Here, we study the solutions that exit a codimension-2 sliding mode. Some results are expected, others come as a surprise. We are able to explain situations, where difficulties in numerical computations are reported in the recent literature. The analysis is based on asymptotic expansions for singularly perturbed problems and on the study of a time-parameterized two-dimensional dynamical system (hidden dynamics). Various situations are illustrated by examples.
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