scholarly journals Existence and total controllability results of fuzzy delay differential equation with non-instantaneous impulses

2021 ◽  
Vol 60 (6) ◽  
pp. 6001-6012
Author(s):  
Anil Kumar ◽  
Muslim Malik ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Differential ◽  
Total Controllability

scholarly journals Smooth Stable Manifold for Delay Differential Equations with Arbitrary Growth Rate

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 105
Author(s):  
Lokesh Singh ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Growth Rate ◽  
Invariant Manifold ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Stable Manifold ◽  
Exponential Dichotomy ◽  
Delay Differential ◽  
Stable Invariant ◽  
Nonuniform Exponential Dichotomy

In this article, we construct a C1 stable invariant manifold for the delay differential equation x′=Ax(t)+Lxt+f(t,xt) assuming the ρ-nonuniform exponential dichotomy for the corresponding solution operator. We also assume that the C1 perturbation, f(t,xt), and its derivative are sufficiently small and satisfy smoothness conditions. To obtain the invariant manifold, we follow the method developed by Lyapunov and Perron. We also show the dependence of invariant manifold on the perturbation f(t,xt).

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

scholarly journals Maximum Likelihood Inference for Univariate Delay Differential Equation Models with Multiple Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-14
Author(s):  
Ahmed A. Mahmoud ◽  
Sarat C. Dass ◽  
Mohana S. Muthuvalu ◽  
Vijanth S. Asirvadam
Keyword(s):  
Differential Equation ◽  
Maximum Likelihood ◽  
Delay Differential Equation ◽  
Information Matrix ◽  
Likelihood Inference ◽  
Multiple Delays ◽  
Unknown Parameters ◽  
Differential Equation Models ◽  
Delay Differential ◽  
Initial Starting

This article presents statistical inference methodology based on maximum likelihoods for delay differential equation models in the univariate setting. Maximum likelihood inference is obtained for single and multiple unknown delay parameters as well as other parameters of interest that govern the trajectories of the delay differential equation models. The maximum likelihood estimator is obtained based on adaptive grid and Newton-Raphson algorithms. Our methodology estimates correctly the delay parameters as well as other unknown parameters (such as the initial starting values) of the dynamical system based on simulation data. We also develop methodology to compute the information matrix and confidence intervals for all unknown parameters based on the likelihood inferential framework. We present three illustrative examples related to biological systems. The computations have been carried out with help of mathematical software: MATLAB® 8.0 R2014b.

Preliminary Study on Stick-Slip in Drillstring With Analytical Model Expressed With Neutral Delay Differential Equation

2014 ◽  
Author(s):  
Tomoya Inoue ◽  
Tokihiro Katsui ◽  
Chang-Kyu Rheem ◽  
Zengo Yoshida ◽  
Miki Y. Matsuo
Keyword(s):  
Differential Equation ◽  
Analytical Model ◽  
Delay Differential Equation ◽  
Drill Bit ◽  
Neutral Delay ◽  
Stick Slip ◽  
Scientific Drilling ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Slip Phenomenon

Stick-slip is a major problem in offshore drilling because it may cause damage to the drill bit as well as crushing or grinding the sediment layer, which is crucial problem in scientific drilling because the purpose of the scientific drilling is to recover core samples from the layers. To mitigate stick-slip, first of all it is necessary to establish a model of the torsional motion of the drill bit and express the stick-slip phenomenon. Toward this end, the present study proposes a model of torsional waves propagating in a drillstring. An analytical model is developed and used to derive a neutral delay differential equation (NDDE), a special type of equation that requires time history, and an analytical model of stick-slip is derived for friction models between the drill bit and the layer as well as the rotation speed applied to the uppermost part of the drill string. In this study, the stick-slip model is numerically analyzed for several conditions and a time series of the bit motions is obtained. Based on the analytical results, the appearance of stick-slip and its severity are discussed. A small-scale model experiment was conducted in a water tank to observe the stick-slip phenomenon, and the result is discussed with numerical analysis. In addition, utilizing surface drilling data acquired from the actual drilling operations of the scientific drillship Chikyu, occurrence of stick-slip phenomenon is discussed.

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