scholarly journals On time transformations for differential equations with state-dependent delay

2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Alexander Rezounenko
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
The State ◽  
Delay Systems ◽  
Constant Delay ◽  
Systems Of Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Time Transformations

AbstractSystems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.

NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

2001 ◽  
Vol 11 (03) ◽  
pp. 737-753 ◽  
Author(s):  
TATYANA LUZYANINA ◽  
KOEN ENGELBORGHS ◽  
DIRK ROOSE
Keyword(s):  
Differential Equations ◽  
Bifurcation Analysis ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Numerical Bifurcation ◽  
Delay Differential ◽  
Steady State Solutions ◽  
Numerical Bifurcation Analysis

In this paper we apply existing numerical methods for bifurcation analysis of delay differential equations with constant delay to equations with state-dependent delay. In particular, we study the computation, continuation and stability analysis of steady state solutions and periodic solutions. We collect the relevant theory and describe open theoretical problems in the context of bifurcation analysis. We present computational results for two examples and compare with analytical results whenever possible.

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 Global Existence for Functional Differential Equations with State-Dependent Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mouffak Benchohra ◽  
Imene Medjadj ◽  
Juan J. Nieto ◽  
P. Prakash
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Existence ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Functional Differential

Our aim in this work is to study the existence of solutions of a functional differential equation with state-dependent delay. We use Schauder's fixed point theorem to show the existence of solutions.

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.

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.

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

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