Predicting potential scenarios for wastewater treatment under unstable physical and chemical laboratory conditions: A mathematical study

Abstract

This research aims to highlight and examine an example of physical complexity. By taking into account the interference between the components of a bio-reactor chemostat, we introduce a mathematical system with a general functional response that describes the wastewater treatment. This model is disturbed by a new class of fluctuations in the hybrid form which simulates certain unstable chemical and environmental variations. We merge between the polynomial white noise and quadratic jumps to offer an excellent overview of the complexity induced in wastewater treatment. Analytically, we present a surrogate framework to get the acute sill between stationarity and bacteria eradication. Our analysis enriches and improves many works by proposing an unfamiliar form of perturbation and unifying the criteria of said asymptotic characteristics. Numerically, we audit the accuracy of our sill in two non-standard cases: quadratic noise and cross perturbation. We demonstrate that the increased order of perturbation has a significant effect on the elimination of bacterial living time. Furthermore, we numerically show that the steady density function modifies its geometric form at some quantities of noise. This result highlights that the sources of complex fluctuations play an active role in the transient dynamics of real-life systems.