Chirikov criterion

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

${\displaystyle K\approx S^{2}=(\Delta \omega _{r}/\Delta _{d})^{2}>1.}$

Here ${\displaystyle K}$ is the perturbation parameter, while ${\displaystyle S=\Delta \omega _{r}/\Delta _{d}}$ is the resonance-overlap parameter, given by the ratio of the unperturbed resonance width in frequency ${\displaystyle \Delta \omega _{r}}$ (often computed in the pendulum approximation and proportional to the square-root of perturbation), and the frequency difference ${\displaystyle \Delta _{d}}$ between two unperturbed resonances. Since its introduction, the Chirikov criterion has become an important analytical tool for the determination of the chaos border.

• Chirikov criterion at Scholarpedia
• Chirikov standard map and standard map
• Boris Chirikov and Boris Chirikov at Scholarpedia