ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Malyshev A. I., Chizhova L. A. Arnol’d diffusion in a simple nonlinear system: analytical estimations and numerical simulation. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 1, pp. 46-56. DOI: 10.18500/0869-6632-2009-17-1-46-56

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon 2009no1p046.pdf
(downloads: 312)
Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
534.014, 530.182
DOI: 
10.18500/0869-6632-2009-17-1-46-56

Arnol’d diffusion in a simple nonlinear system: analytical estimations and numerical simulation

Autors: 
Malyshev Aleksandr Igorevich, Lobachevsky State University of Nizhny Novgorod
Chizhova Larisa Aleksandrovna, Lobachevsky State University of Nizhny Novgorod
Abstract: 

We consider the Arnol’d diffusion in a system with 2.5 degrees of freedom along a resonance with an external oscillating field. The analytical estimation of the diffusion coefficient we made is in a good agreement with numerical results. It’s also shown that both the amplitude of external field and the parameter of weak interaction between two spatial degrees of freedom have an influence on Arnol’d diffusion manifestation and its rate.

Key words: 
Nonlinear resonance
Arnol’d diffusion
Reference: 
  1. Arnol'd VI. Instability of dynamical systems with many degrees of freedom. Dokl. Akad. Nauk SSSR. 1964;156(1): 9–12.
  2. Lichtenberg A, Lieberman M. Regular and stochastic dynamics. Cherepovets: Mercury-PRESS; 2000. 527 p. (In Russian).
  3. Chirikov BV. A Universal instability of many dimensional oscillator systems. Phys. Rep. 1979;52(5):263–379. DOI: 10.1016/0370-1573(79)90023-1.
  4. Milczewski J von, Diercksen GHF, Uzer T. Computation of the Arnol’d web for the hydrogen atom in crossed electric and magnetic fields. Phys. Rev. Lett. 1996;76(16):2890–2893. DOI: 10.1103/PhysRevLett.76.2890.
  5. Demikhovskii VYa, Izrailev FM, Malyshev AI. Manifestation of Arnol’d diffusion in quantum systems. Phys. Rev. Lett. 2001;88(15):154101. DOI: 10.1103/PhysRevLett.88.154101.
  6. Demikhovskii VYa, Malyshev AL. Quantum Arnold Diffusion In Rippled Channel At The Presence Of Alternating Electric Field. Izvestiya VUZ. Applied Nonlinear Dynamics. 2004;12(5):3–15.
  7. Zaslavsky GM. Physics of chaos in Hamiltonian systems. Izhevsk-Moscow: Institute of Computer Sciences; 2004. 288 p. (In Russian).
Received: 
01.08.2008
Accepted: 
21.10.2008
Published: 
30.04.2009
Short text (in English):
PDF icon a2009no1p046.doc_.pdf
(downloads: 58)
  • 1963 reads