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 〈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).