Random Perturbations of a Periodically Driven Nonlinear Oscillator:\n Escape from a resonance zone

2015/10/29 by Nishanth Lingala, Lingala, Nishanth, N. Sri Namachchivaya +3
Computer Science · Physics and Astronomy · #34C15 #34C46 #60F10 #70K65 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #Quantum chaos and dynamical systems #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1510.08919

openalex publication_date 2015/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The phase space for a periodically driven nonlinear oscillator consists of\nmany resonance zones. Let the strength of periodic excitation and the strength\nof the damping be indexed by a small parameter \ε. It is well known\nthat, as \ε \→ 0, the measure of the set of initial conditions\nwhich lead to 'capture in a resonance zone' goes to zero. In this paper we\nstudy the effect of weak noise on the escape from a resonance zone.\n

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