Expected escape times from attractor basins due to low intensity noise

Gizem D. Acar, Lautaro Cilenti, James A. Yorke, Balakumar Balachandran

Research output: Contribution to journalArticlepeer-review


In this paper, a numerical approach is described to estimate escape times from attractor basins when a dynamical system is subjected to noise or stochastic perturbations. Noise can affect nonlinear system response by driving solution trajectories to different attractors. The changes in physical behavior can be observed as amplitude and phase change of periodic oscillations, initiation or annihilation of chaotic motion, phase synchronization, and so on. Estimating probability of transitions from one attractor to another, and predicting escape times are essential for quantifying the effects of noise on the system response. In this paper, a numerical approach is outlined where probability transition maps are generated between grids. Then, these maps are iterated to find the probability distribution after long durations, wherein, a constant escape rate can be observed between basins. The constant escape rate is then used to estimate the average escape times. The approach is applicable to systems subjected to low-intensity stochastic disturbances and with long escape times, where Monte Carlo simulations are impractical. Escape times up to 10 13 periods are estimated without relying on computationally expensive computations.

Original languageEnglish
Pages (from-to)8935-8946
Number of pages12
JournalNonlinear Dynamics
Issue number10
StatePublished - May 2023

ASJC Scopus subject areas

  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering


  • Cubic maps
  • Duffing oscillators
  • Escape rates
  • Noise

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