scholarly journals Operating diagram of a flocculation model in the chemostat

2020 ◽  
Vol Volume 31 - 2019 - CARI 2018 ◽  
Author(s):  
Radhouane Fekih-Salem ◽  
Tewfik Sari
Keyword(s):  
Local Stability ◽  
Stability Region ◽  
Steady States ◽  
Complete Analysis ◽  
Stable Limit ◽  
Control Parameters ◽  
Coexistence Region ◽  
Microbial Ecosystem ◽  
International Audience ◽  
Stable Limit Cycles

International audience The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species. L'objectif de cette étude est d'analyser un modèle du chémostat impliquant la dynamique d'attachement et de détachement de la biomasse planctonique et agrégée en présence d'une seule ressource. En considérant la mortalité des espèces, nous donnons une analyse complète de l'existence et de la stabilité locale de tous les équilibres pour des taux de croissance monotones. Le modèle pré-sente un ensemble riche de comportements avec multiplicité d'équilibres de coexistence, bi-stabilité et apparition des cycles limites stables. De plus, nous déterminons le diagramme opératoire qui dé-crit le comportement asymptotique du système par rapport aux paramètres de contrôle. Il montre l'émergence d'une région de bi-stabilité via une bifurcation noeud col et l'occurrence d'une région de coexistence via une bifurcation transcritique. Enfin, nous illustrons l'importance de la mortalité sur la déstabilisation de l'écosystème microbien en favorisant le lessivage des espèces.

TUMOR-IMMUNE SYSTEM INTERACTION: MODELING THE TUMOR-STIMULATED PROLIFERATION OF EFFECTORS AND IMMUNOTHERAPY

2006 ◽  
Vol 16 (08) ◽  
pp. 1375-1401 ◽  
Author(s):  
A. D'ONOFRIO
Keyword(s):  
Immune System ◽  
Tumor Cells ◽  
Local Stability ◽  
Tumor Burden ◽  
Stable Limit ◽  
Asymptotically Stable ◽  
Proliferation Response ◽  
Interaction Modeling ◽  
Stable Limit Cycles ◽  
Competing Populations

Tumoral dynamics and antitumor immunotherapies are likely to be influenced by the modalities of interaction between tumor cells and immune system effectors, and by the inter-effectors interactions. Within the framework of the theory of competing populations, we study here the influence of the proliferation response of effectors to tumor burden, and of cooperation and/or competition between immune system effectors, by means of three inter-related bi-dimensional meta-models. After studying their null-clines, we study the location and the local stability of the equilibria. Then, we investigate the existence and, in some cases, the uniqueness of stable limit cycles. The condition for the global asymptotically stable eradication under constant or slightly variable periodic immunotherapy is given. Finally, implications of strong saturation in the effectors ability to kill tumor cells are discussed.

Vehicle Lateral Motion Control Based on Estimated Stability Regions

2017 ◽  
Author(s):  
Yiwen Huang ◽  
Yan Chen
Keyword(s):  
Measurement Errors ◽  
Local Stability ◽  
Stability Region ◽  
Control Method ◽  
Linearization Method ◽  
Stability Control ◽  
Lateral Stability ◽  
Shortest Distance ◽  
The Stability ◽  
Yaw Moment

This paper presents a novel vehicle lateral stability control method based on an estimated lateral stability region on the phase plane of vehicle yaw rate and lateral speed, which is obtained through a local linearization method. Since the estimated stability region does not only describe vehicle local stability, but also define the oversteering and understeering characteristics, the proposed control method can achieve both local stability and vehicle handling stability. Considering the irregular geometric shape of the estimated stability region, a stability analysis algorithm is designed to determine the distance between vehicle states and stability region boundaries. State estimation or measurement errors are also incorporated in the distance calculation. Based on the calculated shortest distance between vehicle states and stability boundaries, a direct yaw moment controller is designed to maintain vehicle states stay within the stability region. CarSim® and Simulink® co-simulation is applied to verify the control design through a cornering maneuver. The simulation results show that the proposed control method can make the vehicle stay within the stability region successfully and thus always operate in a safe manner.

scholarly journals Méthode d'agrégation des variables appliquée à la dynamique des populations

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Pierre Auger ◽  
Abderrahim El Abdllaoui ◽  
Rachid Mchich
Keyword(s):  
Stable Limit Cycle ◽  
Stable Limit ◽  
Dynamique Des Populations ◽  
Globally Asymptotically Stable ◽  
Density Dependent ◽  
Migration Rates ◽  
First Case ◽  
International Audience ◽  
Predator Model ◽  
Predator System

International audience We present the method of aggregation of variables in the case of ordinary differential equations. We apply the method to a prey - predator model in a multi - patchy environment. In this model, preys can go to a refuge and therefore escape to predation. The predator must return regularly to his terrier to feed his progeny. We study the effect of density-dependent migration on the global stability of the prey-predator system. We consider constant migration rates, but also density-dependent migration rates. We prove that the positif equilibrium is globally asymptotically stable in the first case, and that its stability changes in the second case. The fact that we consider density-dependent migration rates leads to the existence of a stable limit cycle via a Hopf bifurcation. Nous présentons les grandes lignes de laméthode d'agrégation des variables dans les systèmes d'équations différentielles ordinaires. Nous appliquons laméthode à un modèle proie-prédateur spatialisé. Dans ce modèle, les proies peuvent échapper à la prédation en se réfugiant sur un site. Le prédateur doit aussi retourner régulièrement dans son terrier pour nourrir sa progéniture. Nous étudions les effets de migration dépendant de la densité des populations sur la stabilité globale du système proie-prédateur. Nous considérons des taux de migration constants, puis densité-dépendants. Dans le cas de taux constants il existe un équilibre positif toujours stable alors que dans le cas de taux de migration densité-dépendants, il existe un cycle limite stable via une bifurcation de Hopf.

Response : Stable Limit Cycles in Prey-Predator Populations

Science ◽  
1973 ◽  
Vol 181 (4104) ◽  
pp. 1074-1074
Author(s):  
Robert M. May
Keyword(s):  
Limit Cycles ◽  
Stable Limit ◽  
Stable Limit Cycles

The Nonlinear Behavior of Heavy-Duty Truck Combinations With Respect to Straightline Stability

1989 ◽  
Vol 111 (4) ◽  
pp. 577-582 ◽  
Author(s):  
A. Stribersky ◽  
P. S. Fancher
Keyword(s):  
Nonlinear Stability ◽  
Bifurcation Theory ◽  
Nonlinear Behavior ◽  
Stable Limit ◽  
Heavy Duty ◽  
Stability Boundaries ◽  
Stability Behavior ◽  
Heavy Duty Truck ◽  
Straight Line ◽  
Stable Limit Cycles

A comparison of the nonlinear stability behavior of the steady state straight line motion of truck combinations with and without a second trailer is shown. These investigations have been done by applying bifurcation theory. Stability boundaries in the parameter space and the corresponding bifurcation solutions are given. Depending on the loading conditions, unstable and also stable limit cycles have been found. Particular emphasis is given to the influence of the frictional coupling between tire and road on the nonlinear stability behavior of these vehicles.

On the Bifurcation Structure of a Leslie–Tanner Model with a Generalist Predator

2020 ◽  
Vol 30 (06) ◽  
pp. 2050088
Author(s):  
Luis Miguel Valenzuela ◽  
Gamaliel Blé ◽  
Manuel Falconi
Keyword(s):  
Generalist Predator ◽  
Hopf Bifurcations ◽  
Stable Limit ◽  
Previous Knowledge ◽  
Bifurcation Structure ◽  
Remarkable Feature ◽  
Predator Prey ◽  
Predator Prey Model ◽  
The Subject ◽  
Stable Limit Cycles

In this work, the dynamical properties of a Leslie–Tanner predator–prey model are analyzed. A method is provided to find the regions in the parameter space where Bautin, Hopf and simultaneous supercritical Hopf bifurcations exist. A remarkable feature of the dynamics of the model is the existence of tristability. In fact, the system simultaneously presents three stable limit cycles. These results generalize some previous knowledge on the subject since both prey defense and a generalist predator are incorporated in our analysis.

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