scholarly journals Mean-square stability of the zero equilibrium of the nonlinear delay differential equation: Nicholson’s blowflies application

2021 ◽  
Author(s):  
H. El-Metwally ◽  
M. A. Sohaly ◽  
I. M. Elbaz
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Mean Square ◽  
Mean Square Stability ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Zero Equilibrium ◽  
Nonlinear Delay

scholarly journals Mean Square Stability of the Zero Equilibrium of the Nonlinear Delay Differential Equation: Nicholson's Blowflies Application

2021 ◽  
Author(s):  
Hamdy El-Metwally ◽  
Mohamed El Sohaly ◽  
Islam Elbaz
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Time Derivative ◽  
Sufficient Conditions ◽  
Deterministic System ◽  
Mean Square ◽  
Mean Square Stability ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

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}.

Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation

2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Delay Differential Equation ◽  
Difference Method ◽  
Discrete System ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Nonstandard Finite Difference

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.

A Necessary and Sufficient Condition for the Oscillation of an Even Order Nonlinear Delay Differential Equation

1973 ◽  
Vol 25 (5) ◽  
pp. 1078-1089 ◽  
Author(s):  
Bhagat Singh
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Oscillatory Behavior ◽  
Necessary And Sufficient Condition ◽  
Even Order ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

In this paper we study the oscillatory behavior of the even order nonlinear delay differential equation(1)where(i) denotes the order of differentiation with respect to t. The delay terms τi σi are assumed to be real-valued, continuous, non-negative, non-decreasing and bounded by a common constant M on the half line (t0, + ∞ ) for some t0 ≧ 0.

Sign in / Sign up

Export Citation Format

Share Document