Exponential distributed time-delay nonlinear models: Monte Carlo simulations

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 〈 t e 〉 M C 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 〈 t e 〉 M C ∼ λ − ν for λ ≪ 1 have also been found in agreement with recent theoretical predictions (Cáceres, 2014).