On singularly perturbed Filippov systems. (English) Zbl 1320.34022
Summary: We study singularly perturbed Filippov systems. More specifically, our main question is to know how the dynamics of Filippov systems is affected by singular perturbations. We extend the Fenichel theory developed by N. Fenichel [J. Differ. Equations 31, 53–98 (1979; Zbl 0476.34034)] to these systems. In addition, the study of non-smooth constrained systems is considered.
MSC:
34A36 | Discontinuous ordinary differential equations |
34E15 | Singular perturbations for ordinary differential equations |
34A26 | Geometric methods in ordinary differential equations |
Citations:
Zbl 0476.34034References:
[1] | Physica D. Nonlinear Phenom. 239 pp 44– (2009) |
[2] | DOI: 10.1006/jmaa.1994.1033 · Zbl 0803.34004 · doi:10.1006/jmaa.1994.1033 |
[3] | DOI: 10.1023/A:1025161101223 · Zbl 1086.34036 · doi:10.1023/A:1025161101223 |
[4] | Differential Equations with Discontinuous Righthand Sides, Mathematics and Its Applications (Soviet Series) (1988) |
[5] | J. Differ. Equ. 92 pp 252– (1990) |
[6] | Asymptotic Analysis II pp 449– (1983) |
[7] | SIAM Rev. 50 pp 629– (2005) |
[8] | DOI: 10.1007/s11856-011-0169-3 · Zbl 1258.34021 · doi:10.1007/s11856-011-0169-3 |
[9] | DOI: 10.1007/BF01237678 · Zbl 0799.58071 · doi:10.1007/BF01237678 |
[10] | DOI: 10.1016/0022-0396(79)90152-9 · Zbl 0476.34034 · doi:10.1016/0022-0396(79)90152-9 |
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