scholarly journals STABILITY AND HOPF BIFURCATION ANALYSIS OF A MATHEMATICAL MODEL IN TUMOR ANGIOGENESIS

2018 ◽  
pp. 1-1
Author(s):  
Serdal Pamuk ◽  
İrem ÇAY
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Tumor Angiogenesis

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 HOPF BIFURCATION ANALYSIS FOR A MATHEMATICAL MODEL OF P53-MDM2 INTERACTION

2008 ◽  
Vol 18 (01) ◽  
pp. 275-283 ◽  
Author(s):  
MIHAELA NEAMŢU ◽  
RAUL FLORIN HORHAT ◽  
DUMITRU OPRIŞ
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Periodic Solutions ◽  
Stationary State ◽  
Bifurcation Analysis ◽  
Local Stability ◽  
Bifurcation Parameter ◽  
Simple Mathematical Model

In this paper we analyze a simple mathematical model which describes the interaction between proteins P53 and Mdm2. For the stationary state we discuss the local stability and the existence of a Hopf bifurcation. We study the direction and stability of the bifurcating periodic solutions by choosing the delay as a bifurcation parameter. Finally, we will offer some numerical simulations and present our conclusions.

scholarly journals Analysis of a Mathematical Model of Emerging Infectious Disease Leading to Amphibian Decline

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Muhammad Dur-e-Ahmad ◽  
Mudassar Imran ◽  
Adnan Khan
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Bifurcation Analysis ◽  
Deterministic Model ◽  
Three Dimensional ◽  
Reproduction Ratio ◽  
Amphibian Larvae ◽  
The Stability

We formulate a three-dimensional deterministic model of amphibian larvae population to investigate the cause of extinction due to the infectious disease. The larvae population of the model is subdivided into two classes, exposed and unexposed, depending on their vulnerability to disease. Reproduction ratioℛ0has been calculated and we have shown that ifℛ0<1, the whole population will be extinct. For the case ofℛ0>1, we discussed different scenarios under which an infected population can survive or be eliminated using stability and persistence analysis. Finally, we also used Hopf bifurcation analysis to study the stability of periodic solutions.

Time-delay-induced instabilities and Hopf bifurcation analysis in 2-neuron network model with reaction–diffusion term

2018 ◽  
Vol 313 ◽  
pp. 306-315 ◽  
Author(s):  
Swati Tyagi ◽  
Subit K Jain ◽  
Syed Abbas ◽  
Shahlar Meherrem ◽  
Rajendra K Ray
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Network Model ◽  
Bifurcation Analysis ◽  
Reaction Diffusion ◽  
Neuron Network ◽  
Diffusion Term

A NUMERICAL PROOF THAT CERTAIN CELLS FOLLOW THE TRAILS OF THE DIFFUSIONS OF SOME CHEMICALS IN THE EXTRACELLULAR MATRIX

2021 ◽  
pp. 2150027
Author(s):  
İREM ÇAY ◽  
SERDAL PAMUK
Keyword(s):  
Mathematical Model ◽  
Extracellular Matrix ◽  
Tumor Angiogenesis ◽  
Numerical Solutions ◽  
Extra Cellular Matrix ◽  
The Matrix ◽  
Good Agreement ◽  
Cellular Matrix

In this work, we obtain the numerical solutions of a 2D mathematical model of tumor angiogenesis originally presented in [Pamuk S, ÇAY İ, Sazci A, A 2D mathematical model for tumor angiogenesis: The roles of certain cells in the extra cellular matrix, Math Biosci 306:32–48, 2018] to numerically prove that the certain cells, the endothelials (EC), pericytes (PC) and macrophages (MC) follow the trails of the diffusions of some chemicals in the extracellular matrix (ECM) which is, in fact, inhomogeneous. This leads to branching, the sprouting of a new neovessel from an existing vessel. Therefore, anastomosis occurs between these sprouts. In our figures we do see these branching and anastomosis, which show the fact that the cells diffuse according to the structure of the ECM. As a result, one sees that our results are in good agreement with the biological facts about the movements of certain cells in the Matrix.

scholarly journals Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions

2018 ◽  
Vol 28 (09) ◽  
pp. 1850109 ◽  
Author(s):  
Xiangming Zhang ◽  
Zhihua Liu
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Bifurcation Analysis ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Positive Equilibrium ◽  
Semilinear Equations ◽  
Age Structured ◽  
Hiv Infection Model

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.

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