TY - JOUR
T1 - Expected escape times from attractor basins due to low intensity noise
AU - Acar, Gizem D.
AU - Cilenti, Lautaro
AU - Yorke, James A.
AU - Balachandran, Balakumar
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2023/5
Y1 - 2023/5
N2 - 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.
AB - 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.
KW - Cubic maps
KW - Duffing oscillators
KW - Escape rates
KW - Noise
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U2 - 10.1007/s11071-023-08330-z
DO - 10.1007/s11071-023-08330-z
M3 - Article
AN - SCOPUS:85148610173
SN - 0924-090X
VL - 111
SP - 8935
EP - 8946
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
IS - 10
ER -