scholarly journals New and Improved Criteria on Fundamental Properties of Solutions of Integro—Delay Differential Equations with Constant Delay

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3317
Author(s):  
Cemil Tunç ◽  
Yuanheng Wang ◽  
Osman Tunç ◽  
Jen-Chih Yao
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Delay Differential Equations ◽  
Constant Delay ◽  
Fundamental Properties ◽  
Perturbed System ◽  
Perturbed Systems ◽  
Non Linear ◽  
Delay Differential

This paper is concerned with certain non-linear unperturbed and perturbed systems of integro-delay differential equations (IDDEs). We investigate fundamental properties of solutions such as uniformly stability (US), uniformly asymptotically stability (UAS), integrability and instability of the un-perturbed system of the IDDEs as well as the boundedness of the perturbed system of IDDEs. In this paper, five new and improved fundamental qualitative results, which have less conservative conditions, are obtained on the mentioned fundamental properties of solutions. The technique used in the proofs depends on Lyapunov-Krasovski functionals (LKFs). In particular cases, three examples and their numerical simulations are provided as numerical applications of this paper. This paper provides new, extensive and improved contributions to the theory of IDDEs.

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.

Analysis of thermostat models

1997 ◽  
Vol 8 (5) ◽  
pp. 437-455 ◽  
Author(s):  
B. CAHLON ◽  
D. SCHMIDT ◽  
M. SHILLOR ◽  
X. ZOU
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Delay Differential Equations ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Numerical Approximations ◽  
New Models ◽  
Delay Differential

We present two new models describing the dynamic behavior of an automotive thermostat, involving delay-differential equations with hysteresis. Existence, uniqueness, and regularity of the solutions for both models are obtained by a continuation argument. We establish sufficient conditions for the models to exhibit intrinsic oscillations. We also present an algorithm for numerical approximations of the solutions and give some representative numerical simulations. These reveal a rather interesting dynamical behavior of the solutions.

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