Numerous mathematical models simulating the phenomenon in science and engineering use delay differential equations. In this paper, we focus on semilinear equations, which include a wide range of with time lags, such as reaction-diffusion equation delay, model bacteriophage predation bacteria chemostat, so on. This paper is concerned stability convergence properties exponential Runge–Kutta metho...

The original mathematical model of microbial growth in the Chemostat is modified to describe continuous cultures in which the limiting nutrient is supplied at a rate independent of the dilution rate. The application of this model to continuous Chlorella cultures in which CO(2) is the factor limiting growth is discussed. The conclusions from the model are: (i) at a constant rate of CO(2) supply,...

This paper describes a simple rule-based approach for the state detection in a biological waste water treatment plant. The plant shows bi-stable behaviour that makes its control a challenging and difficult task. The good operating point is difficult to reach and easy to lose. The approach combines the mathematical model of the plant and the available measurement information. After the state det...

We propose a model of chemostat where the bacterial population is individuallybased, each bacterium is explicitly represented and has a mass evolving continuously over time. The substrate concentration is represented as a conventional ordinary differential equation. These two components are coupled with the bacterial consumption. Mechanisms acting on the bacteria are explicitly described (growt...

We apply basic tools of control theory to a chemostat model that describes the growth of one species of microorganisms that consume a limiting substrate. Under the assumption that available measurements of the model have fixed delay t>0, we design a family of feedback control laws with the objective of stabilizing the limiting substrate concentration in a fixed level. Effectiveness of this cont...

The process of oxygenic photosynthesis is robust and ubiquitous, relying centrally on input of light, carbon dioxide, and water, which in many environments are all abundantly available, and from which are produced, principally, oxygen and reduced organic carbon. However, photosynthetic machinery can be conflicted by the simultaneous presence of carbon dioxide and oxygen through a process someti...

A mathematical model of microbial competition for limiting nutrient and wallattachment sites in a chemostat, formulated by Freter et al. in their study of the colonization resistance phenomena associated with the gut microflora, is mathematically analyzed. The model assumes that resident and invader bacterial strains can colonize the fluid environment of the vessel as well as its bounding surfa...

We introduce inhomogeneous, substrate dependent cell division in a time discrete, nonlinear matrix model of size-structured population growth in the chemostat, first introduced by Gage et al. [8] and later analysed by Smith [13]. We show that mass conservation is verified, and conclude that our system admits one non zero globally stable equilibrium, which we express explicitly. Then we run nume...

A mathematical model of competition between two species for two growth-limiting, essential (complementary) resources in the unstirred chemostat is considered. The existence of a positive steady-state solution and some of its properties are established analytically. Techniques include the maximum principle, the fixed point index, and numerical simulations. The simulations also seem to indicate t...