Dynamic bifurcations: Hysteresis, scaling laws and feedback control

Progress of Theoretical Physics Supplement

Volumn , Issue 139, 2000, Pages 325-336

  Berglund, N ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034375471     PISSN: 03759687     EISSN: None     Source Type: Journal    
DOI: 10.1143/PTPS.139.325     Document Type: Article

References (42)

1. E. F. Mishchenko, Yu. S. Kolesov, A. Yu. Kolesov and N. Kh. Rozov, Asymptotic Methods in Singularly Perturbed Systems (Consultants Bureau, New York, 1994).
2. A. B. Vasil'eva, V. F. Butusov and L. V. Kalachev, The Boundary Function Method for Singular Perturbation Problems (SIAM, Philadelphia, 1995).
3. E. Benoît (ed.), Dynamic Bifurcations, Proc. (Luminy, 1990) Lecture Notes in Math. 1493 (Springer, Berlin, 1991).
4. C. K. R. T. Jones, Dynamical Systems, Proc. (Montecatini Terme, 1994), ed. R. Johnson (ed.) Lecture Notes in Math. 1609 (Springer, Berlin, 1995).
5. E. F. Mishchenko and N. Kh. Rozov, Differential Equations with Small Parameters and Relaxations Oscillations (Plenum, New York, 1980).
6. N. Berglund and H. Kunz, J. of Phys. A32 (1999), 15.
7. N. Berglund, Adiabatic Dynamical Systems and Hysteresis, Thesis EPFL no 1800 (1998). Available at http://dpwww.epfl.ch/instituts/ipt/berglund/these.html
8. A. I. Neishtadt, Diff. Equ. 23 (1987), 1385; 24 (1988), 171.
9. A. I. Neishtadt, Diff. Equ. 23 (1987), 1385; 24 (1988), 171.
10. th International Congress of Mathematical Physics, ed. D. Jacobnitzer (International Press, Boston, 1995).
11. N. Berglund, to appear in Nonlinearity 13 (January 2000).
12. N. Berglund and K. S. Schneider, Stability and Stabilization of Nonlinear Systems, ed. D. Aeyels, F. Lamnabhi-Lagarrigue and A. van der Schaft Lecture Notes in Contr. and Inform. Sciences 246 (Springer, Berlin, 1999).
13. A. N. Tihonov, Mat. Sbornik N.S. 31 (1952), 575.
14. I. S. Gradšteǐn, Mat. Sbornik N.S. 32 (1953), 263.
15. N. Fenichel, J. Diff. Eq. 31 (1979), 53.
16. C. Baesens, Nonlinearity 8 (1995), 179.
17. L. S. Pontryagin and L. V. Rodygin, Dokl. Akad. Nauk SSSR 131 (1960), 237.
18. M. V. Berry, Proc. R. Soc. London A429 (1990), 61.
19. A. Joye, H. Kunz and C.-E. Pfister, Ann. of Phys. 208 (1991), 299.
20. L. S. Pontryagin, Izv. Akad. Nauk SSSR. Ser. Mat. 21 (1957), 605.
21. R. Haberman, SIAM J. Appl. Math. 37 (1979), 69.
22. N. R. Lebovitz and R. J. Schaar, Stud. in Appl. Math. 54 (1975), 229.
23. N. N. Nefedov and K. R. Schneider, Zeitschr. Angewandte Mathematik und Mechanik (ZAMM) 78 (1998), 199.
24. N. R. Lebovitz and R. J. Schaar, Stud. in Appl. Math. 56 (1977), 1.
25. T. Erneux and P. Mandel, SIAM J. Appl. Math. 46 (1986), 1.
26. N. Berglund and H. Kunz, Phys. Rev. Lett. 78 (1997), 1691.
27. P. Jung, G. Gray, R. Roy and P. Mandel, Phys. Rev. Lett. 65 (1990), 1873.
28. A. Hohl, H. J. C. van der Linden, R. Roy, G. Goldsztein, F. Broner and S. H. Strogatz, Phys. Rev. Lett. 74 (1995), 2220
29. G. H. Goldsztein, F. Broner and S. H. Strogatz, SIAM J. Appl. Math. 57 (1997), 1163.
30. M. Rao, H. K. Krishnamurthy and R. Pandit, Phys. Rev. B42 (1990), 856.
31. J.-S. Suen and J. L. Erskine, Phys. Rev. Lett. 78 (1997), 3567.
32. M. A. Shishkova, Dokl. Akad. Nauk SSSR 209 (1973), 576 [English transl.: Soviet Math. Dokl. 14 (1973), 384].
33. M. A. Shishkova, Dokl. Akad. Nauk SSSR 209 (1973), 576 [English transl.: Soviet Math. Dokl. 14 (1973), 384].
34. S. M. Baer, T. Erneux and J. Rinzel, SIAM J. Appl. Math. 49 (1989), 55.
35. L. Holden and T. Erneux, SIAM J. Appl. Math. 53 (1993), 1045.
36. D. Aeyels, Systems Control Lett. 5 (1985), 289.
37. E. H. Abed, Systems and control theory for power systems, ed. J. H. Chow (Springer, New York, 1995).
38. W. Müller and K. R. Schneider, J. Differ. Equations Appl. 4 (1998), 579.
39. A. I. Khibnik, B. Krauskopf and C. Rousseau, Nonlinearity 11 (1998), 1505.
40. W. Wasow, Asymptotic expansions for ordinary differential equations (Krieger, New York, 1965, 1976).
41. R. Bellman, Introduction to Matrix Analysis (McGraw-Hill, New York, 1960).
42. S. G. Krein, Linear Differential Equations in Banach Spaces (American Mathematical Society, Providence, Rhode Island, 1971).