Role of Noise in the Fairen–Velarde Model of Bacterial Respiration

Bacterial respiration, a fundamental biological process, plays a crucial role in ecological systems. The Fairen–Velarde model provides a theoretical framework to study the interplay between oxygen and nutrient concentrations in bacterial populations, representing a system of coupled nonlinear differential equations. In this work, how the introduction of noise affects the stability and behavior of bacterial respiration is investigated. Biological systems are inherently stochastic, with noise arising from environmental fluctuations and molecular-level randomness. Through numerical simulations, how random fluctuations in oxygen and nutrient concentrations influence the system's stability is analyzed, particularly, the transition between limit cycles and fixed points. These results demonstrate that noise can induce a reduction in time scales, pushing the system toward a domain of fixed points, which contrasts with the noiseless case where the system exhibits a stable limit cycle. By employing statistical analysis across varying noise intensities, the likelihood of reaching the fixed domain is quantified and the area of this domain is examined under different noise conditions. These insights contribute to the broader understanding of how stochastic factors affect bacterial population dynamics, offering implications for microbial ecology and the management of bacterial processes in natural and engineered environments.