nonlinear delay differential equation
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2021 ◽  
Vol 2 (2) ◽  
pp. 1-12
Author(s):  
Eman Ziada

In this paper, a multi-term nonlinear delay differential equation (DDE) of arbitrary order is studied.Adomian decomposition method (ADM) is used to solve these types of equations. Then the existence andstability of a unique solution will be proved. Convergence analysis of ADM is discussed. Moreover, themaximum absolute truncated error of Adomian’s series solution is estimated. The stability of the solutionis also discussed.


Author(s):  
R. Basu

This paper deals with the oscillatory results of first order nonlinear delay differential equations with several deviating arguments by employing an iterative process. The results presented here has improved the outcomes of [1, 2, 8]. Various examples are solved in MATLAB software to illustrate the relevance of the main results.


2021 ◽  
Author(s):  
Hamdy El-Metwally ◽  
Mohamed El Sohaly ◽  
Islam Elbaz

Abstract We are concerned about the stochastic nonlinear delay differential equation. The stochasticity arises from the white Gaussian noise which is the time derivative of the standard Brownian motion. The main objective of this paper is to introduce a new technique using Lyapunov functional for the study of stability of the zero solution of the stochastic delay differential system. Constructing a new appropriate deterministic system in the neighborhood of the origin is an effective way to investigate the necessary and sufficient conditions of stability in the sense of the mean square. Nicholson's blowflies equation is one of the major problems in ecology, necessary conditions for the possible extinction of the Nicholson's blowflies population are investigated. We support our theoretical results by providing areas of stability and some numerical simulations of the solution of the system using the Euler-Maruyama scheme which is mean square stable \cite{Maruyama1955,Cao2004}.


Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 278 ◽  
Author(s):  
Taher A. Nofal ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Mihai Postolache

In this work, we present several oscillation criteria for higher-order nonlinear delay differential equation with middle term. Our approach is based on the use of Riccati substitution, the integral averaging technique and the comparison technique. The symmetry contributes to deciding the right way to study oscillation of solutions of this equations. Our results unify and improve some known results for differential equations with middle term. Some illustrative examples are provided.


Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1845
Author(s):  
A. Nachaoui ◽  
T. Shavadze ◽  
T. Tadumadze

For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula, the effects of perturbations of the delay parameter, the initial vector, the initial and control functions are detected.


2020 ◽  
Author(s):  
David Bartley

Delay differential equations are set up for zeroth-order pandemic models in analogy with traditional SIR and SEIR models by specifying individual times of incubation and infectiousness prior to recovery. Independent linear delay relations in addition to a nonlinear delay differential equation are found for characterizing time-dependent compartmental populations. Asymptotic behavior allows a link between parameters of the delay and traditional models for their comparison. In analogy with transformation of the traditional equations into linear form giving populations and time in parametric form, expansion in the delay provides a simple recursive solution. Also, a soliton-like solution in terms of a logistic function can be applied for accurate approximation. Otherwise, straightforward numerical solution is effected in terms of linearized boundary conditions specifying the distribution of instigators as to their initial infection progress--in contrast to traditional models specifying only initial average infectious and exposed populations. Examples contrasting asymptotically-linked traditional and delay models are given.


2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.


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