- Access by Xinjiang University
Gibbs attractor: A chaotic nearly Hamiltonian system, driven by external harmonic force
Phys. Rev. E 69, 036207 – Published 25 March, 2004
DOI: https://doi.org/10.1103/PhysRevE.69.036207
Abstract
A chaotic autonomous Hamiltonian system, perturbed by small damping and small external force, harmonically dependent on time, can acquire a strange attractor with properties similar to that of the canonical distribution—the Gibbs attractor. The evolution of the energy in such systems can be described as the energy diffusion. For the nonlinear Pullen-Edmonds oscillator with two degrees of freedom, the properties of the Gibbs attractor and their dependence on parameters of the perturbation are studied both analytically and numerically.
References (22)
- V. I. Klyatzkin, Statistical Description of Dynamical Systems with Fluctuating Parameters (Nauka, Moscow, 1975) (in Russian).
- L. D. Landau and E. M. Lifshitz, Statistical Physics: Part 1, 4th ed. (Nauka, Moscow, 1995) (in Russian).
- B. V. Chirikov, Phys. Rep. 52, 263 (1979).
- N. B. Delone, V. P. Krainov, and D. L. Shepelyansky, Sov. Phys. Usp. 26, 551 (1983) [Usp. Fiz. Nauk 140, 355 (1983)].
- G. Casati, B. V. Chirikov, D. L. Shepelyansky, and I. Guarnery, Phys. Rep. 154, 77 (1987).
- C. Jarzynski, Phys. Rev. E 48, 4340 (1993).
- D. Cohen, Phys. Rev. Lett. 82, 4951 (1999).
- R. Mankin, A. Ainsaar, and E. Reiter, Phys. Rev. E 61, 6359 (2000).
- J. Qiang and S. Habib, Phys. Rev. E 62, 7430 (2000).
- R. Mankin, A. Ainsaar, A. Haljas, and E. Reiter, Phys. Rev. E 63, 041110 (2001).
- J.-D. Bao, Phys. Rev. E 63, 061112 (2001).
- I. V. Pogorelov and H. E. Kandrup, Phys. Rev. E 60, 1567 (1999).
- T. Pohl, U. Feudel, and W. Ebeling, Phys. Rev. E 65, 046228 (2002).
- R. A. Pullen and A. R. Edmonds, J. Phys. A 14, L477 (1981).
- H.-D. Meyer, J. Chem. Phys. 84, 3147 (1986).
- P. A. Vorobyev and G. M. Zaslavsky, Zh. Eksp. Teor. Fiz. 92, 1564 (1987) [Sov. Phys. JETP 65, 877 (1987)].
- P. V. Elyutin and V. G. Korolev, Vestn. Mosk. Univ. 3 Fiz. Astron. 30, 87 (1989) [Moscow Univ. Phys. Bull. 44, 106 (1989)].
- P. V. Elyutin and J. Shan, Phys. Rev. Lett. 77, 5043 (1996).
- P. V. Elyutin and A. N. Rogovenko, Phys. Rev. E 63, 026610 (2001).
- J. L. Kaplan and J. A. Yorke, in Functional Differential Equations and the Approximations of Fixed Points, Vol. 730 of Lecture Notes in Mathematics, edited by H. O. Peitgen and H. O. Walther (Berlin, Springer, 1979), pp. 204–227.
- A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics (Springer, Berlin, 1992).
- L. D. Landau and E. M. Lifshitz, Mechanics, 4th ed. (Nauka, Moscow, 1988), Sec. 10 (in Russian).