scholarly journals Analyse mathématique d'un modèle de digestion anaérobie à trois étapes

2014 ◽  
Vol Volume 17 - 2014 - Special... ◽  
Author(s):  
Radhouane Fekih-Salem ◽  
Nahla Abdellatif ◽  
Tewfik Sari ◽  
Harmand Jérôme
Keyword(s):  
Growth Rates ◽  
Equilibrium Points ◽  
Positive Equilibrium ◽  
Chemostat Model ◽  
Step Model ◽  
All Solutions ◽  
International Audience ◽  
The Stability ◽  
Solid Form ◽  
Analyse Mathématique

International audience In this work, we focus on the mathematical analysis of a model of chemostat with enzymatic degradation of a substrate (organic matter) that can partly be under a solid form [7]. The study of this 3-step model is derived from a smaller order sub-model since some variables can be decoupled from the others. We study the existence and the stability of equilibrium points of the sub-model considering monotonic growth rates and distinct dilution rates. In the classical chemostat model with monotonic kinetics, it is well known that only one equilibrium point attracts all solutions and that bistability never occurs [8]. In the present study, although only monotonic growth rates are considered, it is shown that the considered sub-model may exhibit bistability. The study of 3-step model shows the existence at most four positive equilibrium whose one is locally asymptotically stable and according to the initial condition the two species can coexist.

scholarly journals Dynamical Analysis of Two-Microorganism and Single Nutrient Stochastic Chemostat Model with Monod-Haldane Response Function

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Mengnan Chi ◽  
Wencai Zhao
Keyword(s):  
Lyapunov Function ◽  
Response Function ◽  
Existence And Uniqueness ◽  
Random Perturbation ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Deterministic System ◽  
Chemostat Model ◽  
Global Positive Solution ◽  
The Stability

In this paper, we formulate and investigate a two-microorganism and single nutrient chemostat model with Monod-Haldane response function and random perturbation. First, for the corresponding deterministic system, we introduce the conditions of the stability of the equilibrium points. Then, using Lyapunov function and Itô’s formula, we investigate the existence and uniqueness of the global positive solution of the stochastic chemostat model. Furthermore, we explore and obtain the criterions of the extinction and the permanence for the stochastic model. Finally, numerical simulations are carried out to illustrate our main results.

Analyzing the current effectiveness of the Russian economy's design

2020 ◽  
Vol 8 (8) ◽  
pp. 1476-1496
Author(s):  
V.V. Smirnov
Keyword(s):  
Economic Growth ◽  
Sustainable Development ◽  
Growth Rates ◽  
Systems Approach ◽  
Mineral Resources ◽  
Cash Flows ◽  
Moscow Oblast ◽  
Structural Balance ◽  
Russian Economy ◽  
The Stability

Subject. The article discusses Russia’s economy and analyzes its effectiveness. Objectives. The study attempts to determine to what extent Russia’s economy is effective. Methods. The study is based on the systems approach and the statistical analysis. Results. I discovered significant fluctuations of the structural balance due to changing growth rates of the total gross national debt denominated in the national currency, and the stability of growth rates of governmental revenue. Changes in the RUB exchange rate and an additional growth in GDP are the main stabilizers of the structural balance, as they depend on hydrocarbon export. As a result of the analysis of cash flows, I found that the exports slowed down. Financial resources are strongly centralized, since Moscow and the Moscow Oblast are incrementing their share in the export of mineral resources, oil and refining products and import of electrical machines and equipment. Conclusions and Relevance. The fact that the Russian economy has been effectively organized is proved with the centralization of the economic power and the limits through the cross-regional corporation, such as Moscow and the Moscow Oblast, which is resilient to any regional difficulties ensuring the economic growth and sustainable development. The findings would be valuable for the political and economic community to outline and substantiate actions to keep rates of the economic growth and sustainable development of the Russian economy.

scholarly journals Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Dahlia Khaled Bahlool ◽  
Huda Abdul Satar ◽  
Hiba Abdullah Ibrahim
Keyword(s):  
Equilibrium Points ◽  
Global Dynamics ◽  
Persistence Conditions ◽  
Local Bifurcation Analysis ◽  
Uniqueness Of The Solution ◽  
Harvesting Process ◽  
Predator Model ◽  
The Stability ◽  
Predator System ◽  
Type Ii Functional Response

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

scholarly journals On a predator-prey system interaction under fluctuating water level with nonselective harvesting

2020 ◽  
Vol 18 (1) ◽  
pp. 458-475
Author(s):  
Na Zhang ◽  
Yonggui Kao ◽  
Fengde Chen ◽  
Binfeng Xie ◽  
Shiyu Li
Keyword(s):  
Water Level ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Model Interaction ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fluctuating Water Level

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

scholarly journals Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Zizhen Zhang ◽  
Huizhong Yang
Keyword(s):  
Hopf Bifurcation ◽  
Computer Network ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Local Hopf Bifurcation ◽  
Form Theory ◽  
Worm Model ◽  
The Stability

A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.

scholarly journals Nonlinear Dynamics of a PI Hydroturbine Governing System with Double Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Hongwei Luo ◽  
Jiangang Zhang ◽  
Wenju Du ◽  
Jiarong Lu ◽  
Xinlei An
Keyword(s):  
Hopf Bifurcation ◽  
Equilibrium Points ◽  
Bifurcation Theorem ◽  
Center Manifold Theorem ◽  
Governing System ◽  
Normal Form Method ◽  
The Stability ◽  
System Frequency ◽  
Realistic Significance ◽  
Theoretical Results

A PI hydroturbine governing system with saturation and double delays is generated in small perturbation. The nonlinear dynamic behavior of the system is investigated. More precisely, at first, we analyze the stability and Hopf bifurcation of the PI hydroturbine governing system with double delays under the four different cases. Corresponding stability theorem and Hopf bifurcation theorem of the system are obtained at equilibrium points. And then the stability of periodic solution and the direction of the Hopf bifurcation are illustrated by using the normal form method and center manifold theorem. We find out that the stability and direction of the Hopf bifurcation are determined by three parameters. The results have great realistic significance to guarantee the power system frequency stability and improve the stability of the hydropower system. At last, some numerical examples are given to verify the correctness of the theoretical results.

ANTIBIOTIC STABILITY IN SOLUTIONS USED FOR INTRAVENOUS NUTRITION AND FLUID THERAPY

PEDIATRICS ◽  
1973 ◽  
Vol 51 (6) ◽  
pp. 1016-1026
Author(s):  
Ralph D. Feigin ◽  
Kanneth S. Moss ◽  
Penelope G. Shackelford
Keyword(s):  
Antimicrobial Activity ◽  
Normal Saline ◽  
Protein Hydrolysate ◽  
Significant Degree ◽  
Significant Loss ◽  
All Solutions ◽  
Ringer’S Lactate ◽  
Series Of Experiments ◽  
The Stability ◽  
Crystalline Amino Acids

The present study was designed to assess the stability of ampicillin, carbenicillin, clindamycin, kanamycin, cephalothin, methicillin, and penicillin in three parenteral hyperalimentation mixtures as reconstituted for delivery to the patient in the clinical setting. Stability at 4C, 25C, and 37C was tested in parenteral hyperalimentation mixtures containing either crystalline amino acids or a protein hydrolysate. In two series of experiments the stability at 4C, 25C, and 37C of ampicillin, cephalothin, and kanamycin also was assessed in Isolyte M (ISO M), Isolyte P (ISO P), Ringer's lactate (LR), 5% dextrose in water, (D5W), 10% dextrose in water (D1OW), dextrose in normal saline (D5S), and normal saline (NS) to which hydrocortisone or heparin had been added. All antibiotics retained their effectiveness at an acceptable level in the hyperalimentation solutions at 4C. At 25C and 37C, all antibiotics except clindamycin lost activity by 24 hours. Kanamycin was least stable in these solutions and ampicillin also lost a significant degree of antimicrobial activity. Addition of heparin or hydrocortisone imparted stability to ampicillin in the seven parenteral solutions although significant loss of activity was noted at 37C in D5W, D1OW, D5S, and LR. Most solutions containing heparin or hydrocortisone and cephalothin turned yellow by 24 hours. A precipitate appeared in solutions containing heparin and kanamycin but there was minimal loss of antimicrobial activity. Kanamycin was stable in all solutions containing hydrocortisone except in D5W and D10W at 37C.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

Bifurcation and stability of resonance of electric vehicle powertrain: Focus on the influence of electromagnetic parameters

2021 ◽  
pp. 095440702110450
Author(s):  
Qingzhen Han ◽  
Shiqin Niu ◽  
Lei He
Keyword(s):  
Electric Vehicle ◽  
Electromechanical Coupling ◽  
Equilibrium Points ◽  
Resonance Curve ◽  
Drive Shaft ◽  
Electromagnetic Parameters ◽  
Stability And Bifurcation ◽  
Fold Bifurcation ◽  
The Stability ◽  
Vehicle Powertrain

The influence of the electromagnetic parameters on the torsional dynamics of the electric vehicle powertrain is studied by considering the electromechanical coupling effect. By adding the electromagnetic torque on the drive side, the powertrain is simplified as nonlinear drive-shaft model. The number, stability, and bifurcation conditions of the equilibrium points of the nonlinear drive-shaft model are deduced. Based on the averaged equations and the amplitude-frequency response equation, the stability and bifurcation conditions, such as fold bifurcation and Hopf bifurcation, of the resonance curve are discussed. The influence of electromagnetic parameters on the torsional dynamics is studied by simulation. It is shown that with the change of the parameters, the number as well as the stability of the equilibrium points may be changed which is affected by fold bifurcation. It is also shown that the resonance curve may lose its stability when fold bifurcation happens. By limiting the parameters in the region without fold bifurcation, the unstable dynamics of the resonance curve can be controlled.

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