SARI , Tewfik

The Rosenzweig-MacArthur model is a system of two ODEs used in population dynamics to modelize the predator-prey relationship. For certain values of the parameters the differential system exhibits a unique stable limit cycle. When the dynamics of the prey is faster than the dynamics of the predator, during oscillations along the limit cycle,...

The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been completely analyzed. Here, we complete this analysis and we...

We study the probability of extinction of a population modelled by a linear birth-and-death process with several types in a periodic environment when the period is large compared to other time scales. This probability depends on the season and may present a sharp jump in relation to a "canard" in a slow-fast dynamical system. The point of...

The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been completely analysed. Here, we complete this analysis and we...

We study the probability of extinction of a population modelled by a linear birth-and-death process with several types in a periodic environment when the period is large compared to other time scales. This probability depends on the season and may present a sharp jump in relation to a "canard" in a slow-fast dynamical system. The point of...

The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been fully analyzed. Here, we complete this analysis and we delineate...

This paper deals with a two-microbial species model in competition for a single-resource in the chemostat including general intra-and interspecific density-dependent growth rates with distinct removal rates for each species. In order to understand the effects of intra-and interspecific competition, this general model is first studied by...

Invented by J. Monod, and independently by A. Novick and L. Szilard, in 1950, the chemostat is both a micro-organism culturing device and an abstracted ecosystem managed by a controlled nutrient flow. This book studies mathematical models of single species growth as well as competition models of multiple species by integrating recent work in...

We consider populations with time-varying growth rates living in sinks. Each population, when isolated, would become extinct. Dispersal-induced growth (DIG) occurs when the populations are able to persist and grow exponentially when dispersal among the populations is present. We provide a mathematical analysis of this surprising phenomenon, in...

Optimal control is a branch of applied mathematics that engineers need in order to optimize the operation of systems and production processes. Its application to concrete examples is often considered to be difficult because it requires a large investment to master its subtleties.The purpose of Optimal Control in Bioprocesses is to provide a...

L'application de la théorie de la commande optimale sur des exemples concrets est souvent considérée comme une tâche difficile car elle demande un investissement important pour en maîtriser les subtilités. Optimisation des bioprocédés apporte un éclairage pédagogique sur les fondements de la théorie. Pour l'appliquer, il accompagne le lecteur...

We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, 1 − ε > 0 or −(1 + ε) < 0. We study the specific case where the growth rate is positive in one habitat and negative in the other one for the first half of the period, and conversely for the...

Inventé par J. Monod, et indépendamment par A. Novick et L. Szilard en 1950,le chémostat est à la fois un dispositif de laboratoire de culture en continu de micro-organismes et une abstraction d'écosystème traversé par un flux nutritif. Cet ouvrage est consacré à l'étude des modèles mathématiques de croissance d'une espèce isolée ainsi que des...

In a recent paper [Asymptotic of the largest Floquet multiplier for cooperative matrices Annales de la Faculté des Sciences de Toulouse, Tome XXXI, no 4 (2022)] P. Carmona gives an asymptotic formulae for the top Lyapunov exponent of a linear T-periodic cooperative differential equation, in the limit T goes to infinity. This short note...

We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, 1 − ε > 0 or −(1 + ε) < 0. We study the specific case where the growth rate is positive in one habitat and negative in the other one for the first half of the period, and conversely for the...

Inventado por J. Monod, e independientemente por A. Novick y L. Szilard, en 1950, el quimiostato es a la vez un dispositivo de cultivo de microorganismos y un ecosistema abstraído, gestionado por un flujo controlado de nutrientes.Este libro estudia modelos matemáticos de crecimiento de una sola especie, así como modelos de competencia de...

This paper is a follow-up to a previous work where we considered populations with time-varying growth rates living in patches and irreducible migration matrix between the patches. Each population, when isolated, would become extinct. Dispersal-induced growth (DIG) occurs when the populations are able to persist and grow exponentially when...

We consider a population spreading across a finite number of sites. Individuals can move from one site to the other according to a network (oriented links between the sites) that vary periodically over time. On each site, the population experiences a growth rate which is also periodically time varying. Recently, this kind of models have been...

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Cultivation of microalgae in wastewater and digestate has received special attention during the last years due to the potential for nutrient, CO2 and/or heat recovery and recycling. However, understanding microalgae-bacteria interactions remains a major concern for process operation and control. This paper aims to develop a new mathematical...