Stochastic Resonance in a Bacterium Growth System with Time Delay and Colored Noise

Abstract

The phenomenon of stochastic resonance in a bacterium growth system that is with two different kinds of time delays and is driven by colored noises is investigated. Based on the extended unified colored noise theory and the method of the probability density approximation, the Fokker-Planck equation and the stationary probability density function are derived. Then via the theory of adiabatic limit, the analytical expression of the signal-to-noise ratio (SNR) is obtained. The different effects of the time delays existed in the nonlinear system and the noise correlation times on the stationary probability density and the signal-to-noise rate are discussed respectively. Finally, numerical simulations are offered and are consistent with approximate analytical results.

Mean First Passage Time and Stochastic Resonance in a Transcriptional Regulatory System with Non-Gaussian Noise

“…The mean first passage time (MFPT), or the statistical mean of the FPT, is an important quantity in stochastic processes and statistical mechanics, with wide applications ranging from the lifespan of electron devices [3] and neural firing dynamics [4] to the spread of diseases [5] and stochastic resonance (SR) [6,7].…”

Overflow oscillations free implementation of state-delayed digital filter with saturation arithmetic and external disturbance

“…The time-delay is generally encountered due to transport lags, measurement lags, finite speed of information processing, etc. As time-delay is inherent in many applications, it has been addressed for bacterium growth systems (Li and Wu, 2015), tension-leg platform (Kiamini et al, 2018), cancer development systems (Wang et al, 2017), chemical reactor systems (Liu et al, 2017c), congestion analysis in high speed networks (Liu et al, 2008), communication delays in web transactions (Bhargava, 2001), and so forth. Many dynamical systems are stable in the absence of delay but become unstable in the presence of delay; on the contrary there are systems that are stable under nonzero delay but unstable with zero delay conditions (Gu et al, 2001).…”