Effects of Nonlinear Time-Delay on a Stochastic Asymmetric System

We numerically investigate the effects of nonlinear time-delay on the stochastic system. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, and the normalized variance and the normalized autocorrelation function is rapidly decreased for large delay time.