Role of Noise in the Fairen-Velarde model of bacterial respiration

Abstract

Following our recent study (S. Kundu and M. Acharyya, International Journal of Modern Physics C, 35 (2024) 2450094), we have introduced stochasticity (random noise) in the Fairen-Velarde deterministic differential equations. The role of such noise on time scales is studied. The probability of reaching the domain of fixed points in a given interval is also calculated. The probability is studied as a function of the width of the noise, and a hyperbolic tangent fitting is proposed. The noise reduces the time scale for bringing the bacteria into an inactive state. The area of the fixed-point domain was found to be asympotically linear with noise. The time to reach the fixed-point domain is fitted to a Gaussian function with noise intensity.