Dynamics of stochastic microorganism flocculation models

TL;DR

This paper analyzes the complex stochastic dynamics of microorganism flocculation models, incorporating multiple sources of environmental randomness, and provides a comprehensive classification of their long-term behaviors.

Contribution

It introduces a novel stochastic model with layered randomness and develops new analytical techniques to classify asymptotic behaviors, including persistence and extinction.

Findings

Full classification of asymptotic behaviors

Development of new analytical techniques

Insights into persistence and extinction conditions

Abstract

In this paper we study the dynamics of stochastic microorganism flocculation models. Given the strong influence of environmental and seasonal fluctuations that are present in these models, we propose a stochastic model that includes multiple layers of stochasticity, from small Brownian fluctuations, to possibly large changes due to environmental `shifts'. We are able to give a full classification of the asymptotic behavior of these models. New techniques had to be developed to prove the persistence and extinction of the process as the system is not in Kolmogorov form and, as a result, the analysis is significantly more involved.