Dynamical bifurcation of a sewage treatment model with general higher-order perturbation

Abstract

In this research, we expose new results on the dynamics of a high disturbed chemostat model for industrial wastewater. Due to the complexity of heavy and erratic environmental variations, we take into consideration the polynomial perturbation. We scout the asymptotic characterization of our proposed system with a general interference response. It is demonstrated that the long-run characteristics of the chemostat process are classified by using the threshold classification approach. If the critical sill is strictly negative, the bacteria will disappear exponentially, indicating that the chemostat wastewater process is not running (excluded scenario), otherwise, the stationarity and ergodicity properties of our model are verified (practical scenario). The theoretical arsenal of this work offers a comprehensive overview of the industrial wastewater behavior under general hypotheses and introduces novel technical aspects to deal with other perturbed systems in biology. Numerically, we audit the accuracy of our threshold in three particular situations: linear, quadratic and cubic perturbations. We establish that the increasing order of disturbance has a passive influence on the extinction time of bacteria. This finding highlights that complex noise sources fulfill a significant role in the transient dynamics of chemostat systems.

Keywords

• Chemostat model
• Stochastic process
• Dynamics
• Wastewater
• Higher-order perturbation