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Exponential distributed time-delay nonlinear models: Monte Carlo simulations

Author

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  • Cáceres, Manuel O.
  • Rojas R., Christian D.

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).

Suggested Citation

  • Cáceres, Manuel O. & Rojas R., Christian D., 2014. "Exponential distributed time-delay nonlinear models: Monte Carlo simulations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 409(C), pages 61-70.
    • Handle: RePEc:eee:phsmap:v:409:y:2014:i:c:p:61-70
    DOI: 10.1016/j.physa.2014.04.025
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