Abstract

The exponentially small splitting of separatrix, standard and whisker map approaches. Chirikov overlap criterion, renormalization group technique, incremental energy method are surveyed herein for the analytic modeling of stochastic layers caused by the interaction of nonlinear resonance in nonlinear dynamics. For verification of the analytic modeling, the numerical method to predict the onset of resonance in the stochastic layer through its minimum and maximum energy spectra is also presented. Illustrations of stochastic layers are given by the Poincare mapping section of the Duffing oscillator and periodically-driven pendulum.

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