Bifurcation analysis of zero-dispersion nonlinear resonance

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 4, 1998, Pages 701-712

  Mannella, R ^a,b   Soskin, S M ^a,c   McClintock, P V E ^a  

^a LANCASTER UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF PISA   (Italy)

^c INSTITUTE OF SEMICONDUCTOR PHYSICS   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039572408     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498000498     Document Type: Article

References (34)

1. Barone, R. & Paterno, G. [1982] Physics and Applications of the Josephson Effect (Wiley, New York).
2. Berman, G. P. & Zaslavsky, G. M. [1977] "Theory of quantum nonlinear resonance," Phys. Lett. A61, 295-296.
3. Berman, G. P. & Kolovsky, A. R. [1992] "Quantum chaos in interactions of multilevel quantum systems with a coherent radiation field," Sov. Phys. Uspekhi 162, 95-142.
4. Bogolyubov, N. N. & Mitropolsky, Yu. A. [1961] Asymptotic Methods in the Theory of Nonlinear Oscillations (Gordon and Breach, New York).
5. del-Castillo-Negrete, D. & Morrison, P. J. [1993] "Chaotic transport by Rossby waves in shear flow," Phys. Fluids A5, 948-965.
6. Del-Castillo-Negrete, D., Greene, J. M. & Morrison, P. J. [1996] "Area-preserving nontwist maps: Periodic orbits and transition to chaos," Physica D61, 1-23.
7. Chirikov, B. V. [1979] "A universal instability of many-dimensional oscillator systems," Phys. Rep. 52, 263-379.
8. Dykman, M. I. & Krivoglaz, M. A. [1979] "Theory of fluctuational transitions between stable states of a nonlinear oscillator," Sov. Phys. JETP 50, 30-37.
9. Dykman, M. I., Mannella, R. M., McClintock, P. V. E., Soskin, S. M. & Stocks, N. G. [1990] "Noise-induced narrowing of peaks in the power spectra of underdamped nonlinear oscillators," Phys. Rev. A42, 7041-7049.
10. Gerasimov, A., Israilev, F. M., Tennyson, J. L. & Temnykh, A. B. [1986] "The dynamics the beam-beam interaction," in Nonlinear Dynamics Aspects of Particle Accelerators, eds. Jowett, J. M., Month, M. & Turner, S., Springer Lecture Notes in Physics, Vol. 247, pp. 154-175.
11. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, New York).
12. Hayashi, C. [1964] Nonlinear Oscillations in Physical Systems (McGraw-Hill, New York).
13. Howard, J. E. & Hohs, S. M. [1984] "Stochasticity and reconnection in Hamiltonian systems," Phys. Rev. A29, 418-421.
14. Howard, J. E. & Humpherys, J. [1995] "Nonmonotonic twist maps," Physica D80, 256-276.
15. Kautz, R. L. [1988] "Thermally induced escape: The principle of minimum available noise energy," Phys. Rev. A38, 2066-2080.
16. Kim, J. H. & Lee, H. W. [1995] "Nonlinear resonance and chaos in the relativistic phase space for driven nonlinear systems," Phys. Rev. E52, 473-480.
17. Korn, G. A. & Korn, T. M. [1961] Mathematical Handbook for Scientists and Engineers (McGraw-Hill, New York).
18. Landau, L. D. & Lifshitz, E. M. [1976] Mechanics (Pergamon, London).
19. Lichtenberg, A. J. & Liebermann, M. A. [1990] Regular and Stochastic Motion (Springer, New York).
20. Likharev, K. K. [1986] Dynamics of Josephson Junctions and Circuits (Gordon and Breach, Philadelphia).
21. Luchinsky, D. G., McClintock, P. V. E., Soskin S. M. & Mannella, R. [1995] "Fluctuations in zero-dispersion nonlinear resonance," in Noise in Physical Systems and 1/f Fluctuations, eds. Bareikis, V. & Katilius, R. (World Scientific, Singapore), pp. 705-708.
22. Luchinsky, D. G., McClintock, P. V. E., Soskin, S. M., Stein, N. D. & Neiman, A. B. [1996a] "Comment on 'Nonlinear resonance and chaos in the relativistic phase space for driven nonlinear systems'," Phys. Rev. E53, 4240-4241.
23. Luchinsky, D. G., Mannella, R. M., McClintock, P. V. E. & Soskin, S. M. [1996b] "Zero-dispersion nonlinear resonance in dissipative systems," Phys. Rev. Lett. 76, 4453-4456.
24. McClintock, P. V. E., Soskin, S. M., Stein, N. D. & Stocks, N. G. [1993] "Universality of zero-dispersion peaks in the fluctuation spectra of underdamped nonlinear oscillators," Phys. Rev. E48, 147-156.
25. Neiman, A. B., Soskin, S. M. & McClintock, P. V. E. [1995] "Dynamical chaos in zero-dispersion nonlinear resonance," in Noise in Physical Systems and 1/f Fluctuations, eds. Bareikis, V. & Katilius, R. (World Scientific, Singapore), pp. 701-704.
26. Politi, A. & Oppo, G. L. [1986] "Coexistence of conservative and dissipative behavior in reversible dynamical systems," Phys. Rev. A33, 4055-4060.
27. Soskin, S. M. [1989] "Fluctuation spectrum peaks for systems where the oscillator frequency dependence on energy has an extremum," Physica A155, 401-429.
28. Soskin, S. M. [1994] "Nonlinear resonance for the oscillator with a nonmonotonic dependence of eigenfrequency on energy," Phys. Rev. E50, R44-R46.
29. Soskin, S. M. & Luchinsky, D. G. [1995] "Zero-dispersion nonlinear resonance," Nuovo Cimento D17, 915-924.
30. Soskin, S. M., Luchinsky, D. G., Mannella, R., Neiman, A. B. & McClintock, P. V. E. [1997] "Zero-dispersion nonlinear resonance," Int. J. Bifurcation and Chaos 7, 923-936.
31. Symon, K. R. & Sessler, A. M. [1956] "Methods of radio frequency acceleration in fixed field accelerators with applications to high current and intersecting beam accelerators," in Proc. CERN Symp. High Energy Accelerators and Pion Physics, CERN Report 56-25 (CERN, Geneva), pp. 44-58.
32. Weiss, J. B. [1991] "Transport and mixing in traveling waves," Phys. Fluids A3, 1379-1384.
33. Wiggins, S. [1988] Global Bifurcations and Chaos: Analytical Methods (Springer, New York).
34. Zaslavsky, G. M., Sagdeev, R. Z., Usikov, D. A. & Chernikov A. A. [1991] Weak Chaos and Quasi-Regular Patterns (Cambridge Univ. Press).