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,
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
Here is the perturbation parameter,
while

is the resonance-overlap parameter, given by the ratio of the
unperturbed resonance width in frequency

,
and the frequency difference

between two unperturbed resonances. Since its introduction, the Chirikov criterion has become an important analytical tool for the determination of the chaos border.