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