Complexity in the Role of Noise in Stochastic Systems

摘要

The role of noise in stochastic system could be constructive or destructive depending on the topology of the biochemical network, interaction mechanism and strength of the noise. The noise in genetic and chemical oscillators is studied using chemical Langevin equation and numerically using stochastic simulation algorithm to study the role of noise. The temporal behaviors of the variables in genetic oscillator are found to maintain their oscillatory nature at small system size limit (V ≤ 13 ± 3), but above this the oscillatory behaviors get start destroying by getting transition from fluctuated limit cycle to no oscillation limit as V → ∞. However, in chemical oscillator case, in the limit V → ∞ the oscillatory behaviors of the variables get transition from fluctuated limit cycle (tending destroy oscillatory behavior) to normal limit cycle (maintain sustain oscillations). The noise parameter calculated as a function of V for genetic oscillator first slowly decrease and increases as V increases. However the noise parameter in chemical oscillator decreases first (V ≤ 50 ± 5) and then remains constant as V increases. The calculated noise parameter via stochastic simulation algorithm is always found to be larger than that is obtained via chemical Langevin equation.