Resonant-separatrix webs in stochastic layers of the twin-well Duffing oscillator

Nonlinear Dynamics

Volumn 19, Issue 1, 1999, Pages 37-48

  Luo, Albert C J ^a   Gu, Keqin ^a   Han, Ray P S ^b  

^a SOUTHERN ILLINOIS UNIVERSITY EDWARDSVILLE   (United States)

^b IA United States   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

RANDOM PROCESSES; RESONANCE;

ENERGY SPECTRUM; RESONANT-SEPARATRIX WEBS; TWIN-WELL DUFFING OSCILLATOR;

OSCILLATIONS;

EID: 0032668353     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008383030507     Document Type: Article

References (24)

1. Feng, K. and Qin, M. Z., 'Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study', Computational Physical Communication 65, 1991, 173-187.
2. McLachlan, R. and Atela, P., 'The accuracy of symplectic integrators', Nonlinearity 5, 1992, 541-562.
3. Luo, A. C. J. and Han, R. P. S., 'The mechanism of stochastic layers characterized by inherent resonance in the vicinity of a separatrix', Philosophical Proceedings of the Royal Society of London, 1998, submitted.
4. Poincaré, H., 'Sur la problème des trois corps et les équations de la dynamique', Acta Mathematica 13, 1890, 1-271.
5. Melnikov, V. K., 'On the behavior of trajectories of system near to autonomous Hamiltonian systems', Soviet Mathematics-Doklady 3, 1962, 109-112.
6. Melnikov, V. K., 'On the stability of the center for time periodic perturbations', Transactions Moscow Mathematics Society 12, 1963, 1-57.
7. Chirikov, B. V., 'A universal instability of many-dimensional oscillator systems', Physics Report 52, 1979, 263-379.
8. Reichl, L. E. and Zheng, W. M., 'Field-induced barrier penetration in the quadratic potential', Physical Review 29A, 1984, 2186-2193.
9. Reichl, L. E. and Zheng, W. M., 'Perturbed double-well system: The pendulum approximation and low-frequency effect', Physical Review 30A, 1984, 1068-1077.
10. Abdullaev, S. S. and Zaslavsky, G. M., 'Self-similarity of stochastic magnetic field lines near the X-Point', Physical Plasmas 2, 1995, 4533-4541.
11. Zaslavsky, G. M. and Abdullaev, S. S., 'Scaling properties and anomalous transport of particles inside the stochastic layer', Physical Review 51E, 1995, 3901-3910.
12. Abdullaev, S. S. and Zaslavsky, G. M., 'Application of the separatrix map to study perturbed magnetic field lines near the separatrix', Physical Plasmas 3, 1996, 516-528.
13. Zaslavsky, G. M. and Filonenko, N. N., 'Stochastic instability of trapped particles and conditions of application of the quasi-linear approximation', Soviet Physics JETP 27, 1968, 851-857.
14. Arnold, V. I., 'Instability of dynamical systems with several degrees of freedom', Soviet Mathematics-Doklady 5, 1964, 581-585.
15. Lichtenberg, A. J. and Lieberman, M. A., Regular and Chaotic Dynamics, 2nd edn., Springer-Verlag, New York, 1992.
16. Reichl, L. E., The Transition to Chaos in Conservative Classic System: Quantum Manifestations, Springer-Verlag, New York, 1992.
17. Rom-Kedar, V, 'Transport rates of a class of two-dimensional maps and flow', Physica D 43, 1990, 229-268.
18. Rom-Kedar, V, 'Homoclinic tangles-classification and applications', Nonlinearity 7, 1994, 441-473.
19. Rom-Kedar, V, 'Secondary homoclinic bifurcation theorems', Chaos 5, 1995, 385-401.
20. Ahn, T., Kim, G., and Kim, S., 'Analysis of the separatrix map in Hamiltonian systems', Physica D 89, 1996, 315-328.
21. Iomin, A. and Fishman, S., 'Semiclassical quantization of a separatrix map', Physical Review 54E, 1996, R1-R5.
22. Luo, A. C. J., 'Analytical modeling of bifurcations, chaos, and multifractals in nonlinear dynamics', Ph.D. Dissertation, University of Manitoba, Winnipeg, Manitoba, Canada, 1995.
23. Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
24. Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, 1990.