Mathematical Model of Production and Exchange: Bifurcation Analysis and Management

2022 ◽  
pp. 488-495
Author(s):  
V. Bratishchev Alexander ◽  
A. Batishcheva Galina ◽  
I. Zhuravleva Maria ◽  
Rogozhin Sergei
Keyword(s):  
Mathematical Model ◽  
Bifurcation Analysis

scholarly journals The mathematical stability study for the system of the CoO(OH) – overoxidized polypyrrole composite synthesis in the presence of fluor ions

2016 ◽  
Vol 16 ◽  
pp. 13-17
Author(s):  
V. Tkach ◽  
S.C. De Oliveira ◽  
R. Ojani ◽  
P.I. Yagodynets ◽  
U. Páramo-García
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Bifurcation Analysis ◽  
Stability Theory ◽  
Stability Study ◽  
Linear Stability Theory ◽  
Monotonic Instability ◽  
Overoxidized Polypyrrole ◽  
Polypyrrole Composite ◽  
Steady State Stability

The potentiostatic synthesis of CoO(OH) – Overoxidized polypyrrole composite in the presence of fluor ions has been investigated mathematically. The corresponding mathematical model was described and analyzed by means of linear stability theory and bifurcation analysis. The steady-state stability requirements, like also oscillatory and monotonic instability conditions are derived.Mongolian Journal of Chemistry 16 (42), 2015, 13-17

scholarly journals Theoretical Description for Chlorantraniliprole Electrochemical Determination, Assisted by Squaraine Dye Nano Ag2O2 Composite

2020 ◽  
Vol 11 (2) ◽  
pp. 9278-9284
Keyword(s):  
Mathematical Model ◽  
Reaction Mechanism ◽  
Bifurcation Analysis ◽  
Electrochemical Determination ◽  
Theoretical Description ◽  
The Other ◽  
Linear Stability Theory ◽  
Oxide Nanoparticles ◽  
Monotonic Instability ◽  
Squaraine Dye

The theoretical description for the chlorantraniliprole electrochemical determination, assisted by the hybrid composite of squaraine dye with Ag2O2 nanoparticles, has been described. The correspondent reaction mechanism has been proposed, and the correspondent mathematical model has been developed and analyzed by means of linear stability theory and bifurcation analysis. It has been shown that the chlorantraniliprole electrochemical anodic determination on high potential may be efficiently provided by silver (I, III) oxide nanoparticles, stabilized by the squaraine dye. On the other hand, the oscillatory and monotonic instability is also possible, being caused by DEL influences of the electrochemical stage.

scholarly journals Bifurcation analysis of a mathematical model of atopic dermatitis to determine patient-specific effects of treatments on dynamic phenotypes

2018 ◽  
Vol 448 ◽  
pp. 66-79 ◽  
Author(s):  
Gouhei Tanaka ◽  
Elisa Domínguez-Hüttinger ◽  
Panayiotis Christodoulides ◽  
Kazuyuki Aihara ◽  
Reiko J. Tanaka
Keyword(s):  
Mathematical Model ◽  
Atopic Dermatitis ◽  
Bifurcation Analysis ◽  
Patient Specific ◽  
Specific Effects

Bifurcation Analysis of a Model Accounting for the 14-3-3s Signalling Compartmentalisation

2012 ◽  
pp. 61-70
Author(s):  
S. Nikolov ◽  
J. Vera ◽  
O. Wolkenhauer
Keyword(s):  
Mathematical Model ◽  
Cell Cycle ◽  
Phase Portrait ◽  
Bifurcation Analysis ◽  
Subcellular Localisation ◽  
Loss Of Stability ◽  
Cycle Arrest ◽  
Reversible Loss ◽  
Analytical Tools

Bifurcation theory studies the qualitative changes in the phase portrait when we vary the parameters of the system. In this book chapter we adapt and extend a mathematical model accounting for the subcellular localisation of 14-3-3s, a protein involved in cell cycle arrest and the regulation of apoptosis. The model is analysed with analytical tools coming from Lyapunov-Andronov theory, and our analytical calculations predict that soft (reversible) loss of stability takes place.

Bifurcation Analysis of a Mathematical Model for Malaria Transmission

2006 ◽  
Vol 67 (1) ◽  
pp. 24-45 ◽  
Author(s):  
Nakul Chitnis ◽  
J. M. Cushing ◽  
J. M. Hyman
Keyword(s):  
Mathematical Model ◽  
Malaria Transmission ◽  
Bifurcation Analysis

A model of a fishery with fish stock involving delay equations

2009 ◽  
Vol 367 (1908) ◽  
pp. 4907-4922 ◽  
Author(s):  
P. Auger ◽  
Arnaud Ducrot
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Delay Differential Equation ◽  
Bifurcation Analysis ◽  
Infinite Delay ◽  
Steady States ◽  
Delay Equations ◽  
Fish Stock ◽  
Delay Differential

The aim of this paper is to provide a new mathematical model for a fishery by including a stock variable for the resource. This model takes the form of an infinite delay differential equation. It is mathematically studied and a bifurcation analysis of the steady states is fulfilled. Depending on the different parameters of the problem, we show that Hopf bifurcation may occur leading to oscillating behaviours of the system. The mathematical results are finally discussed.

scholarly journals Theoretical Description for Ellagic Acid Electrochemical Oxidation and Electropolymerization

2021 ◽  
Vol 11 (3) ◽  
pp. 3672-3677
Keyword(s):  
Mathematical Model ◽  
Electrochemical Oxidation ◽  
Bifurcation Analysis ◽  
Ellagic Acid ◽  
Stability Theory ◽  
Polymer Coating ◽  
Theoretical Description ◽  
Oscillatory Behavior ◽  
Oxidation Products ◽  
Linear Stability Theory

The theoretical description for ellagic acid electrochemical oxidation and electropolymerization has been suggested in this paper. The model includes the electropolymerization of ellagic acid in the presence of two of its low-molecular oxidation products. The correspondent mathematical model has been developed and analyzed using linear stability theory and bifurcation analysis. The analysis of the system has confirmed that the oscillatory behavior is more probable than in the simplest case of the electrosynthesis of the polymer of the electrochemically synthesized monomer. Nevertheless, the system is electrosynthetically efficient, yielding a polymer coating.

scholarly journals Bifurcation Analysis of a Mathematical Model of Tumor Growth in MCF-7 Breast Cancer Cell Line

10.29007/spj5 ◽  
2020 ◽  
Author(s):  
Hsiu-Chuan Wei
Keyword(s):  
Breast Cancer ◽  
Mathematical Model ◽  
Cell Line ◽  
Bifurcation Analysis ◽  
Equilibrium Points ◽  
White Blood Cells ◽  
Cancer Cell Line ◽  
Grid Method ◽  
Cancer Immunoediting ◽  
Mcf 7

Breast cancer is the second leading cause of cancer death for women worldwide. In this study, a previously published mathematical model of breast cancer in MCF-7 cell line is considered. The interaction among tumor cells, estradiol, natural killer (NK) cells, cytotoxic T lymphocytes (CTLs) or CD8+ T cells, and white blood cells (WBCs), is described by ordinary differential equations (ODEs). The system exhibits three coexisting stable equilibrium points which resemble the 3 E’s (elimination, equilibrium, and escape) of cancer immunoediting. In this paper, a numerical method based on adaptive grid method is employed for bifurcation analysis of the mathematical model. Bifurcation analysis is performed for some important parameters for which changes in value result in changes in the stability of steady states. The results obtained from the bifurcation analysis may provide useful information about treatment strategy in further studies.

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