Chaotic oscillators: theory and applications
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Singapore u.a.
World Scientific
1992
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 650 S. Ill., graph. Darst. |
| ISBN: | 9810206534 |
Internformat
MARC
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| 245 | 1 | 0 | |a Chaotic oscillators |b theory and applications |c ed. by Tomasz Kapitaniak |
| 264 | 1 | |a Singapore u.a. |b World Scientific |c 1992 | |
| 300 | |a XV, 650 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Chaos |2 gtt | |
| 650 | 7 | |a Dynamische systemen |2 gtt | |
| 650 | 7 | |a Niet-lineaire dynamica |2 gtt | |
| 650 | 4 | |a Chaotic behavior in systems | |
| 650 | 0 | 7 | |a Chaostheorie |0 (DE-588)4009754-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Schwingungssystem |0 (DE-588)4180568-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Schwingungssystem |0 (DE-588)4180568-9 |D s |
| 689 | 0 | 1 | |a Chaostheorie |0 (DE-588)4009754-7 |D s |
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| 700 | 1 | |a Kapitaniak, Tomasz |d 1959- |e Sonstige |0 (DE-588)115857982 |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804122541839613952 |
|---|---|
| adam_text | _^_____ ix
Contents
Introduction v
I. Chaos before Chaos
1.1. Frequency Demultiplication (.Nature 120, (1927) 363 364)
B. Van der Pol and J. Van der Mark 4
1.2. On Nonlinear Differential Equations of the Second Order:
I. The Equation y Ml y2)y + y = bXkcos( t + a), k
Large (J. London Math. Soc. 20, (1945) 180 189)
M.L. Cartwright and J.E. Littlewood 6
1.3. Nonlinear Vibrations of a Buckled Beam under Harmonic
Excitation (ASME J. Appl. Mech. 38,(1971) 467 476)
W. Y. Tseng and J. Dugundji 16
1.4. Random Phenomena Resulting from Nonlinearity in the
System Described by Duffing s Equation (Int. J. Non Linear
Mech. 20, (1985) 481 491)
Y. Ueda 26
II. Description and Quantification of Chaotic Behavior
11.1. Strange Attractors (Math. Intelligencer 2, (1980) 126 137)
D. Ruelle 40
11.2. Geometry from a Time Series (Phys. Rev. Lett. 45, (1980)
712 716)
N.H. Packard, J.P. Crutchfield, J.D. Farmer and R.S. Shaw 52
11.3. Deterministic Representation of Chaos in Classical Dynamics
(Phys. Lett. 107A, (1985) 125 128)
M. Zak 57
II. 4. Determining Lyapunov Exponents from a Time Series
(Physica 16D, (1985) 285 317)
A. Volf, J.B. Swift, H.L. Swinney and J.A. Vastano 61
X
III. Analytical Methods
111.1. A Partial Differential Equation with Infinitely Many
Periodic Orbits: Chaotic Oscillations of a Forced Beam
{Arch. Rat. Mech. Anal. 76, (1981) 135 165)
P. Holmes and J. Marsden 98
111.2. Second Order Averaging and Bifurcations to Subharmonics
in Duffing s Equation (J. Sound Vib. 78, (1981) 161 174)
C. Holmes and P. Holmes 129
111.3. Subharmonic and Homoclinic Bifurcations in a Parametrically
Forced Pendulum (Physica 16D, (1985) 1 13)
B.P. Koch and R.W. Leven 143
111.4. Power Spectra of Strange Attractors near Homoclinic Orbits
(Phys. Rev. Lett. 58, (1987) 1699 1702)
V. Brunsden and P. Holmes 156
111.5. The Mel nikov s Technique for Highly Dissipative Systems
(SIAM J. Appl. Math. 47, (1987) 232 243)
F. Salam 160
III. 6. The Variational Approach to the Theory of Subharmonic
Bifurcations (Physica 26D, (1987) 251 276)
N. Takimoto and H. Yamashida 172
111.7. The Refined Approximate Criterion for Chaos in a Two State
Mechanical Oscillator (Ingenieur Archiv 58, (1988) 354 366)
W. Szemplinska Stupnicka 198
111.8. Analytical Condition for Chaotic Behaviour of
the Duffing Oscillator (Phys. Lett. A144, (1990) 322 324)
T. Kapitaniak 211
IV. Classical Nonlinear Oscillators:
Duffing, Van der Pol and Pendulum
IV.1. Universal Scaling Property in Bifurcation Structure of
Duffing s and of Generalized Duffing s Equations
{Phys. Rev. A28, (1983) 1654 1658)
S. Sato, H. Sano and Y. Sawada 219
xi
IV. 2. Superstructure In the Bifurcation Set of the
Duffing s Equation, x+dx+x+x=f cos(ut)
(Phys. Lett. A107, (1985) 351 355)
U. Parlitz and W. Lauterborn 224
IV.3. On the Understanding of Chaos in Duffing s Equation
Including a Comparison with Experiment
(ASME J. Appl. Mech. 53, (1986) 5 9)
E. Dowel 1 and C. Pezeshki 229
IV. 4. Chaotically Transitional Phenomena in the Forced
Negative Resistance Oscillator
(IEEE Trans. Circuits Syst. CAS 28, (1981) 217 224)
Y. Ueda and N. Akamatsu 234
IV. 5. Period Doubling Cascades and Devil s Staircases of the
Driven Van der Pol Oscillator
(Phys. Rev. A36, (1987) 1428 1434)
U. Parlitz and W. Lauterborn 242
IV.6. Chaotic States and Routes to Chaos in the Forced
Pendulum (Phys. Rev. A26, (1982) 3483 3496)
D. D Humieres, N.R. Beasley, B.A. Huberman
and A. Libchaber 249
IV. 7. Josephson Junctions and Circle Maps
(Solid State Commun. 51, (1984) 231 234)
P. Bak, T. Bohr, H.H. Jensen and P. Christiansen 263
IV.8. Resonance and Symmetry Breaking for the Pendulum
(Physica 31D, (1988) 252 268)
J. Miles 267
V. Other Oscillatory Systems
V.I. Experiments on Chaotic Motions of a Forced Nonlinear
Oscillator: Strange Attractors (ASME J. Appl. Mech. 47,
(1980) 638 644)
F.C. Moon 289
xii
V.2. Chaos after Period Doubling Bifurcations in the Resonance
of an Impact Oscillator (Phys. Lett. A91, (1982) 5 8)
J.M.T. Thompson and R. Ghaffari 296
V.3. Devil s Attractors and Chaos of a Driven Impact Oscillator
(Phys. Lett. A107, (1985) 343 346)
H.M. Isomaki, J. von Boehm and J. Raty 300
V.4. A Periodically Forced Piecewise Linear Oscillator
(J. Sound Vib. 90, (1983) 129 155)
S.W. Shaw and P. Holmes 304
V.5. Complex Dynamics of Compliant Off Shore Structures
(Proc. R. Soc. London A387, (1983) 407 427)
J.M.T. Thompson 331
V.6. Chaos Generated by the Cutting Process
(Phys. Lett. A117, (1986) 384 386)
I. Grabec 352
V.7. The Stability of Modes at Rest in a Chaotic System
(J. Sound Vib. 138, (1990) 421 431)
S. R. Hsieh and S.W. Shaw 355
V.8. Chaotic Motion of an Elastic Plastic Beam
(ASME J. Appl. Mech. 55, (1988) 185 189)
B. Poddar, F.C. Moon and S. Mukherjee 366
V.9. Chua s Circuit Family (Proc. IEEE 75, (1987) 1022 1032)
S. Wu 371
V.10. Chaos via Torus Breakdown (IEEE Trans. Circuits Syst.
CAS 34, (1987) 240 253)
T. Matsumoto, L.O. Chua and R. Tokunaga 382
VI. Chaos in Noisy Systems
VI.1. Fluctuations and the Onset of Chaos
(Phys. Lett. ATT, (1980) 407 410)
J.P. Crutchfield and B.A. Huberman 401
xiu
VI.2. Noise versus Chaos in Acousto optic Bistability
(Phys. Rev. A30, (1984) 336 342)
R. Vallee, C. Delisle and J. Chrostowski 405
VI.3. Generalized Multistability and Noise Induced Jumps in a
Nonlinear Dynamical System (Phys. Rev. A32, (1985) 402 408)
F.T. Arecchi, R. Badii and A. Pol iti 412
VI.4. Chaotic Distribution of Non Linear Systems Perturbed by
Random Noise (Phys. Lett. A116, (1986) 251 254)
T. Kapitaniak 419
VI. 5. Influence of Perturbations on Period Doubling Bifurcation
(.Phys. Rev. A36, (1987) 2413 2417)
H. Svensmark and M. Samuel sen 423
VI.6. Chaos in a Noisy Mechanical System with Stress Relaxation
(J. Sound Vib. 123, (1988) 391 396)
T. Kapitaniak 428
VI. 7. Homoclinic Chaos in Systems Perturbed by Weak Langevin Noise
(Phys. Rev. A41, (1990) 668 681)
A.R. Bulsara, W.C. Schieve and E.W. Jacobs 434
VII. Strange Nonchaotic Attractors
VII. 1. Quasiperiodically Forced Dynamical Systems with Strange
Nonchaotic Attractors (Physica 26D, (1987) 277 294)
F.J. Romeiras, A. Bondeson, E. Ott, T.M. Antonsen, Jr.
and C. Grebogi 452
VII.2. Dimensions of Strange Nonchaotic Attractors
(Phys. Lett. A137, (1989) 167 172)
N. Ding, C. Grebogi and E. Ott 470
VII.3. Route to Chaos via Strange Non chaotic Attractors
(J. Phys. A23, (1990) L383 L387)
T. Kapitaniak, E. Ponce and J. Wojewoda 476
xiv
VIII. Spatial Chaos
VIII. 1. Chaos as a Limit in a Boundary Value Problem
(Z. Naturforsch. A39, (1984) 1200 1203)
C. Kahlert and O.E. Rossler 484
VI11.2. On the Connection between Statical and Dynamical Chaos
(Z. Naturforsch. A44, (1989) 645 650)
M.S. El Naschie and S. Al Athel 488
VI11.3. Spatially Complex Equilibria of Buckled Rods
(Arch. Rat. Mech. Anal. 101, (1988) 319 348)
A. Mielke and P. Holmes 494
VI11.4. Spatial Chaos and Localization Phenomena in Nonlinear
Elasticity (Phys. Lett. A126, (1988) 491 496)
J.M.T. Thompson and L.N. Virgin 524
VIII.5. Soliton Chaos Models for Mechanical and Biological
Elastic Chains (Phys. Lett. A147, (1990) 275 281)
M.S. El Naschie and T. Kapitaniak 530
VI11.6. Spatiotemporal Dynamics in a Dispersively Coupled Chain of
Nonlinear Oscillators (Phys. Rev. A39, (1989) 4835 4842)
D.K. Umberger, C. Grebogi, E. Ott and B. Afeyan 537
IX. Fractal Basin Boundaries
IX.1. Fractal Basin Boundaries (Physica 17D, (1985) 125 153)
S.W. McDonald, C. Grebogi, E. Ott and J.A. Yorke 548
IX.2. Fractal Basin Boundaries and Homoclinic Orbit for
Periodic Motion in a Two Well Potential
(Phys. Rev. Lett. 55, (1985) 1439 1442)
F.C. Moon and G. H. Li 577
IX. 3. Fractal Basin Boundaries of an Impacting Particle
(Phys. Lett. A126, (1988) 484 490)
H.M. Isomaki, J. von Boehm and R. Raty 581
XV
IX. 4. Integrity Measures Quantifying the Erosion of Smooth and
Fractal Basins of Attraction (J. Sound Vib. 135, (1989)
453 475)
M.S. Soliman and J.M.T. Thompson 588
References 611
|
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| isbn | 9810206534 |
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| spelling | Chaotic oscillators theory and applications ed. by Tomasz Kapitaniak Singapore u.a. World Scientific 1992 XV, 650 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chaos gtt Dynamische systemen gtt Niet-lineaire dynamica gtt Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd rswk-swf Schwingungssystem (DE-588)4180568-9 gnd rswk-swf Schwingungssystem (DE-588)4180568-9 s Chaostheorie (DE-588)4009754-7 s DE-604 Kapitaniak, Tomasz 1959- Sonstige (DE-588)115857982 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005383398&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chaotic oscillators theory and applications Chaos gtt Dynamische systemen gtt Niet-lineaire dynamica gtt Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd Schwingungssystem (DE-588)4180568-9 gnd |
| subject_GND | (DE-588)4009754-7 (DE-588)4180568-9 |
| title | Chaotic oscillators theory and applications |
| title_auth | Chaotic oscillators theory and applications |
| title_exact_search | Chaotic oscillators theory and applications |
| title_full | Chaotic oscillators theory and applications ed. by Tomasz Kapitaniak |
| title_fullStr | Chaotic oscillators theory and applications ed. by Tomasz Kapitaniak |
| title_full_unstemmed | Chaotic oscillators theory and applications ed. by Tomasz Kapitaniak |
| title_short | Chaotic oscillators |
| title_sort | chaotic oscillators theory and applications |
| title_sub | theory and applications |
| topic | Chaos gtt Dynamische systemen gtt Niet-lineaire dynamica gtt Chaotic behavior in systems Chaostheorie (DE-588)4009754-7 gnd Schwingungssystem (DE-588)4180568-9 gnd |
| topic_facet | Chaos Dynamische systemen Niet-lineaire dynamica Chaotic behavior in systems Chaostheorie Schwingungssystem |
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