Английская Википедия:Chirikov criterion
The Chirikov criterion or Chirikov resonance-overlap criterion was established by the Russian physicist Boris Chirikov. Back in 1959, he published a seminal article,[1] where he introduced the very first physical criterion for the onset of chaotic motion in deterministic Hamiltonian systems. He then applied such a criterion to explain puzzling experimental results on plasma confinement in magnetic bottles obtained by Rodionov at the Kurchatov Institute.
Description
According to this criterion a deterministic trajectory will begin to move between two nonlinear resonances in a chaotic and unpredictable manner, in the parameter range
- <math mylabel1>
K \approx S^2 = (\Delta \omega_r/\Delta_d)^2 > 1 . </math> Here <math> K</math> is the perturbation parameter, while <math> S = \Delta \omega_r/\Delta_d</math> is the resonance-overlap parameter, given by the ratio of the unperturbed resonance width in frequency <math> \Delta \omega_r</math> (often computed in the pendulum approximation and proportional to the square-root of perturbation), and the frequency difference <math> \Delta_d</math> between two unperturbed resonances. Since its introduction, the Chirikov criterion has become an important analytical tool for the determination of the chaos border.
See also
- Chirikov criterion at Scholarpedia
- Chirikov standard map and standard map
- Boris Chirikov and Boris Chirikov at Scholarpedia
References
- B.V.Chirikov, "Research concerning the theory of nonlinear resonance and stochasticity", Preprint N 267, Institute of Nuclear Physics, Novosibirsk (1969), (Engl. Trans., CERN Trans. 71-40 (1971))
- B.V.Chirikov, "A universal instability of many-dimensional oscillator systems", Phys. Rep. 52: 263 (1979)
- Шаблон:Cite book Springer link
References
External links
- website dedicated to Boris Chirikov
- Special Volume dedicated to 70th of Boris Chirikov: Physica D 131:1-4 vii (1999) and arXiv
