Study of singularities in nonsmooth dynamical systems via singular perturbation

SIAM Journal on Applied Dynamical Systems

Volumn 8, Issue 1, 2009, Pages 508-526

  Llibre, Jaume ^a   Da Silva, Paulo R ^b   Teixeira, Marco A ^c  

^a UNIVERSITAT AUTÒNOMA DE BARCELONA   (Spain)

^b SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^c UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

Discontinuous vector fields; Regularizaron; Singular perturbation; Sliding vector fields; Vector fields

Indexed keywords

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; DYNAMICAL SYSTEMS; VECTORS;

DISCONTINUOUS VECTOR FIELDS; REGULARIZARON; SINGULAR PERTURBATION; SLIDING VECTOR FIELDS; VECTOR FIELDS;

PERTURBATION TECHNIQUES;

EID: 63049087849     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/080722886     Document Type: Article

References (14)

1. J. C. ALEXANDER AND T. I. SEIDMAN, Sliding modes in intersecting switching surfaces. I. Blending, Houston J. Math., 24 (1998), pp. 545-569.
2. J. C. ALEXANDER AND T. I. SEIDMAN, Sliding modes in intersecting switching surfaces. II. Hysteresis, Houston J. Math., 25 (1999), pp. 185-211.
3. M. BROUCKE, C. PUGH, AND S. SIMIC, Structural stability of piecewise smooth systems, Comput. Appl. Math., 20 (2001), pp. 51-89.
4. C. BUZZI, P. R. SILVA, AND M. A. TEIXEIRA, A singular approach to discontinuous vector fields on the plane, J. Differential Equations, 231 (2006), pp. 633-655.
5. M. DI BERNARDO, C. BUDD, A. CHAMPNEYS, AND P. KOWALCZYK, Piecewise-Smooth Dynamical Systems. Theory and Applications, Appl. Math. Sci. 163, Springer-Verlag, London, 2008.
6. F. DUMORTIER AND R. ROUSSARIE, Canard cycles and center manifolds, Mem. Amer. Math. Soc., 121 (1996), 132708.
7. N. FENICHEL, Geometric singular perturbation theory for ordinary differential equations, J. Differential Equations, 31 (1979), pp. 53-98.
8. A. F. FILIPPOV, Differential Equations with Discontinuous Righthand Sides, Math. Appl. (Soviet Ser.), Kluwer Academic Publishers, Dordrecht, The Netherlands, 1988.
9. C. JONES, Geometric singular perturbation theory, in Dynamical Systems, C.I.M.E. Lectures (Montecatini Terme, 1994), Lecture Notes in Math. 1609, Springer-Verlag, Heidelberg, 1995, pp. 44-118.
10. J. LLIBRE, P. R. SILVA, AND M. A. TEIXEIRA, Regularization of discontinuous vector fields via singular perturbation, J. Dynam. Differential Equations, 19 (2007), pp. 309-331.
11. J. LLIBRE, P. R. SILVA, AND M. A. TEIXEIRA, Sliding vector fields via slow-fast systems, Bull. Belg. Math. Soc. Simon Stevin, 15 (2008), pp. 851-869.
12. 2, Dyn. Syst., 22 (2007), 133-146.
13. M. A. TEIXEIRA, Stability conditions for discontinuous vector fields, J. Differential Equations, 88 (1990), pp. 15-29.
14. M. A. TEIXEIRA, Perturbation theory for non-smooth dynamical systems, in Encyclopedia of Complexity and Systems Science, G. Gaeta, ed., Springer-Verlag, New York, to appear.