Exponential distributed time-delay nonlinear models: Monte Carlo simulations

Manuel O. Cáceres and Christian D. Rojas R.

Physica A: Statistical Mechanics and its Applications, 2014, vol. 409, issue C, 61-70

Abstract: The stochastic dynamics toward the final attractor in an exponential distributed time-delay nonlinear model is studied, in the small noise approximation. The passage time statistic for this non-Markovian type of system has been worked out using Monte Carlo simulations. We report the mean first passage time 〈te〉MC from the unstable state as a function of the mean time-delay ϵ≡λ−1. We have compared our Monte Carlo simulations for λ≫1 against previous results (Cáceres, 2008) and we have found excellent agreement in the adiabatic regime. The crossover for λ∼1 and a power-law behavior 〈te〉MC∼λ−ν for λ≪1 have also been found in agreement with recent theoretical predictions (Cáceres, 2014).

Keywords: Distributed time-delay; Non-linear population models; Non-adiabatic approach; Non-Markov process; Relaxation from unstable states; Anomalous fluctuations (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:409:y:2014:i:c:p:61-70

DOI: 10.1016/j.physa.2014.04.025

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