Bacterial growth presents many beautiful phenomena that pose new theoretical challenges
to statistical physicists, and are also amenable to laboratory experimentation. This review …

Dynamical system theory has developed rapidly over the past fifty years. It is a subject upon
which the theory of limit cycles has a significant impact for both theoretical advances and …

We develop a perturbation argument based on existing results on asymptotic autonomous
systems and the Fredholm alternative theory that yields the persistence of traveling …

We study the qualitative properties of population cycles in a predator–prey system where
genetic variability allows contemporary rapid evolution of the prey. Previous numerical …

In this paper, a stochastic delayed chemostat model with nutrient storage and Lévy jumps is
proposed. Firstly, the existence and uniqueness of the positive global solution of the model …

In this article, we consider a 4-dimensional predator–prey chemostat model of nitrogen-
phytoplankton-rotifer interactions with staged structure proposed by Blasius et al.(2020) …

We consider a stochastic chemostat model involving two obligate mutualistic species
feeding on a limiting substrate. It is shown that the spatial arrangement of the random states …

Sustained and transient oscillations are frequently observed in clinical data for immune
responses in viral infections such as human immunodeficiency virus, hepatitis B virus, and …

Competitive exclusion is frequently observed in the chemostat when multiple species
compete exploitatively for a single growth-limiting nutrient. However, rigorous mathematical …

A chemostat model with general nonmonotone response functions is considered. The
nutrient conversion process involves time delay. We show that under certain conditions …