scholarly journals Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods

2019 ◽  
Vol 79 (1) ◽  
pp. 281-328 ◽  
Author(s):  
Philipp Getto ◽  
Mats Gyllenberg ◽  
Yukihiko Nakata ◽  
Francesca Scarabel
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Numerical Methods ◽  
Delay Differential Equation ◽  
Cell Maturation ◽  
State Dependent ◽  
State Dependent Delay ◽  
Delay Differential

scholarly journals An analysis on the stability of a state dependent delay differential equation

2016 ◽  
Vol 14 (1) ◽  
pp. 425-435 ◽  
Author(s):  
Sertaç Erman ◽  
Ali Demir
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Delay Term ◽  
State Dependent ◽  
State Dependent Delay ◽  
The Stability ◽  
Delay Differential ◽  
Equation With Delay

AbstractIn this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term $\tau (u(t)) = \frac{{a + bu(t)}}{{c + bu(t)}}.$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.

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.

Fold Bifurcation in the State-Dependent Delay Model of Milling: Analytical and Numerical Solutions

2011 ◽  
Author(s):  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Differential Equation ◽  
Time Delay ◽  
Delay Differential Equation ◽  
Milling Process ◽  
The State ◽  
Delay Model ◽  
State Dependent ◽  
Fold Bifurcation ◽  
State Dependent Delay ◽  
Delay Differential

The standard models of the milling process describe the surface regeneration effect by a delay-differential equation with constant time delay. In this study, an improved two degree of freedom model is presented for milling process where the regenerative effect is described by an improved state dependent time delay model. The model contains exact nonlinear screen functions describing the entrance and exit positions of the cutting edges of the milling tool. This model is valid in case of large amplitude forced vibrations close to the near-resonant spindle speeds. The periodic motions of this nonlinear system are calculated by a shooting method. The stability calculation is based on the linearization of the state-dependent delay differential equation around these periodic solutions by means of the semi-discretization method. The results are validated by an advanced numerical time domain simulation where the chip thickness is calculated by means of Boolean algebra.

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