Asymptotic methods in singularly perturbed systems:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
Consultants Bureau
1994
|
| Series: | Monographs in contemporary mathematics
|
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 281 S. |
| ISBN: | 0306110342 |
Staff View
MARC
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| 245 | 1 | 0 | |a Asymptotic methods in singularly perturbed systems |c E. F. Mishchenko... |
| 264 | 1 | |a New York [u.a.] |b Consultants Bureau |c 1994 | |
| 300 | |a XI, 281 S. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Monographs in contemporary mathematics | |
| 700 | 1 | |a Miščenko, Aleksandr S. |e Sonstige |4 oth | |
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Record in the Search Index
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| adam_text | Contents
Introduction. Relaxation oscillations 1
I. Regular and singular dependence of solutions on
a parameter 1
II. Second-order relaxation systems 7
III. Arbitrary-order relaxation systems 15
Chapter 1. Theorem on the C1-proximity of the solutions
of a relaxation and a relay system and the asymptotics
of relaxation oscillations 28
1. Statement of the problem, preliminary information,
and heuristic arguments 29
2. Proof of the theorem on the C1-proximity 40
3. Principle of reduction in the neighborhood of a junction
point 54
4. Asymptotics of multidimensional relaxation oscillations
in the neighborhood of a junction point 57
5. Uniqueness, asymptotics, and stability of a relaxation cycle ... 77
6. Stochastic character of the behavior of trajectories
in three-dimensional relaxation systems 80
7. Pontryagin s problem on the tori of singularly perturbed
systems 82
8. Stable relaxation tori in three-dimensional systems 87
ix
x Contents
Chapter 2. Relaxation oscillations in a medium
with diffusion 91
9. On a certain class of parabolic relay systems 92
10. Theorem on the C1-proximity for relaxation parabolic
systems 95
11. Criterion of stability of a homogeneous relaxation cycle 99
12. Analysis of some mathematical models of biophysics 105
Chapter 3. Structure of the neighborhood of a relaxation
cycle 108
13. Normal form of mapping 108
14. Intrinsic resonance upon the loss of stability by
a homogeneous cycle of a relay system 114
15. Bifurcation of a relaxation cycle 117
Chapter 4. Duck-trajectories of relaxation systems 120
16. Origination of duck-trajectories upon the violation of
the normal switching condition 121
17. Destruction of an invariant torus of van der Pol s system
with harmonic input 136
18. Pontryagin delay phenomenon and stable duck-cycles 143
19. Instability of duck-cycles of multidimensional relaxation
systems 156
Chapter 5. Nonclassical relaxation auto-oscillations 162
20. Systems of Lotka-Volterra type 162
21. Relaxation cycles of systems of Lotka-Volterra type 172
22. Construction of complete asymptotics of trajectories 174
23. Multidimensional systems of Lotka-Volterra type 191
24. A new type of relaxation oscillations 199
Contents xi
Chapter 6. Autowave processes in singularly perturbed
systems of reaction-diffusion type 206
25. Exponential dichotomy of solutions of linear parabolic
equations 207
26. Estimates of bounded solutions of linear differential
equations 210
27. Stability of solutions of linear parabolic equations 216
28. Bifurcation of invariant tori of parabolic systems with
small diffusion 228
29. Applications of bifurcation theorems 250
30. Diffusion chaos 259
31. Dynamics of systems with a terminal turn point 263
References 273
|
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| dewey-ones | 515 - Analysis |
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| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV024974219 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:24:51Z |
| institution | BVB |
| isbn | 0306110342 |
| language | English |
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| physical | XI, 281 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Consultants Bureau |
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| series2 | Monographs in contemporary mathematics |
| spelling | Asymptotic methods in singularly perturbed systems E. F. Mishchenko... New York [u.a.] Consultants Bureau 1994 XI, 281 S. txt rdacontent n rdamedia nc rdacarrier Monographs in contemporary mathematics Miščenko, Aleksandr S. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641793&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Asymptotic methods in singularly perturbed systems |
| title | Asymptotic methods in singularly perturbed systems |
| title_auth | Asymptotic methods in singularly perturbed systems |
| title_exact_search | Asymptotic methods in singularly perturbed systems |
| title_full | Asymptotic methods in singularly perturbed systems E. F. Mishchenko... |
| title_fullStr | Asymptotic methods in singularly perturbed systems E. F. Mishchenko... |
| title_full_unstemmed | Asymptotic methods in singularly perturbed systems E. F. Mishchenko... |
| title_short | Asymptotic methods in singularly perturbed systems |
| title_sort | asymptotic methods in singularly perturbed systems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019641793&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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