Hopf bifurcation in an opinion model with state-dependent delay

2021 ◽  
Vol 153 ◽  
pp. 111511
Author(s):  
Redouane Qesmi
Keyword(s):  
Hopf Bifurcation ◽  
State Dependent ◽  
State Dependent Delay ◽  
Opinion Model

Periodic Solutions for a Class of Functional Differential Equations with State-Dependent Delay Close to Zero

2003 ◽  
Vol 13 (06) ◽  
pp. 807-841 ◽  
Author(s):  
R. Ouifki ◽  
M. L. Hbid
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Delay Equation ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

The purpose of the paper is to prove the existence of periodic solutions for a functional differential equation with state-dependent delay, of the type [Formula: see text] Transforming this equation into a perturbed constant delay equation and using the Hopf bifurcation result and the Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions for the state-dependent delay equation, bifurcating from r ≡ 0.

scholarly journals Singular Hopf bifurcation in a differential equation with large state-dependent delay

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130596 ◽  
Author(s):  
G. Kozyreff ◽  
T. Erneux
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Gradual Change ◽  
Classical State ◽  
Sustained Oscillations ◽  
State Dependent ◽  
Analytical Construction ◽  
State Dependent Delay ◽  
Delay Differential ◽  
Sawtooth Oscillations

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawtooth oscillations. The dependence of the delay on the solution can be either linear or nonlinear, with at least quadratic dependence. In the former case, an asymptotic connection is made with the Rayleigh oscillator. In the latter, van der Pol’s equation is derived for the small-amplitude oscillations. SDD differential equations are currently the subject of intense research in order to establish or amend general theorems valid for constant-delay differential equation, but explicit analytical construction of solutions are rare. This paper illustrates the use of singular perturbation techniques and the unusual way in which solvability conditions can arise for SDD problems with large delays.

scholarly journals Stability and Hopf Bifurcation for a Cell Population Model with State-Dependent Delay

2010 ◽  
Vol 70 (5) ◽  
pp. 1611-1633 ◽  
Author(s):  
Mostafa Adimy ◽  
Fabien Crauste ◽  
My Lhassan Hbid ◽  
Redouane Qesmi
Keyword(s):  
Hopf Bifurcation ◽  
Cell Population ◽  
Population Model ◽  
State Dependent ◽  
State Dependent Delay ◽  
A Cell

Global Stability and Hopf Bifurcation for a Stage Structured Model with Competition for Food

2021 ◽  
Vol 31 (10) ◽  
pp. 2150145
Author(s):  
Yunfei Lv ◽  
Yongzhen Pei ◽  
Rong Yuan
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Global Stability ◽  
Delay Differential Equation ◽  
Complete Analysis ◽  
Global Dynamics ◽  
Structured Model ◽  
State Dependent ◽  
State Dependent Delay ◽  
Delay Differential

Considering the mature condition of any individual to have eaten a specific amount of food during the entire period that it can spend at its immature stage, we propose a size-structured model by a first-order quasi-linear partial differential equation. The model can be firstly reduced to a single state-dependent delay differential equation and then to a constant delay differential equation. The state-dependent delay represents intra-specific competition among individuals for limited food resources. A complete analysis of the global dynamics on the positivity and boundedness of solutions, global stability for each equilibrium and Hopf bifurcation is carried out. Our results imply that the delay leads to instability that is shown by a simple example of a certain structured population model.

On fractional differential equations with state-dependent delay via Kuratowski measure of noncompactness

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 451-460 ◽  
Author(s):  
Mohammed Belmekki ◽  
Kheira Mekhalfi
Keyword(s):  
Differential Equations ◽  
Measure Of Noncompactness ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Kuratowski Measure Of Noncompactness ◽  
State Dependent ◽  
State Dependent Delay ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Functional Differential

This paper is devoted to study the existence of mild solutions for semilinear functional differential equations with state-dependent delay involving the Riemann-Liouville fractional derivative in a Banach space and resolvent operator. The arguments are based upon M?nch?s fixed point theoremand the technique of measure of noncompactness.

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