scholarly journals OSCILLATION ANALYSIS OF NUMERICAL SOLUTIONS FOR NONLINEAR DELAY DIFFERENTIAL EQUATIONS OF POPULATION DYNAMICS

2011 ◽  
Vol 16 (3) ◽  
pp. 365-375 ◽  
Author(s):  
Jianfang Gao ◽  
Minghui Song ◽  
Mingzhu Liu
Keyword(s):  
Population Dynamics ◽  
Delay Differential Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Lung Ventilation ◽  
Oscillation Analysis ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

This paper is concerned with oscillations of numerical solutions for the nonlinear delay differential equation of population dynamics. The equation proposed by Mackey and Glass for a ”dynamic disease” involves respiratory disorders and its solution resembles the envelope of lung ventilation for pathological breathing, called Cheyne-Stokes respiration. Some conditions under which the numerical solution is oscillatory are obtained. The properties of non-oscillatory numerical solutions are investigated. To verify our results, we give numerical experiments.

scholarly journals Stability Analysis of Analytical and Numerical Solutions to Nonlinear Delay Differential Equations with Variable Impulses

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
X. Liu ◽  
Y. M. Zeng
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Analytical And Numerical Solutions ◽  
Impulsive Delay Differential Equations ◽  
Nonlinear Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential ◽  
Nonlinear Delay

A stability theory of nonlinear impulsive delay differential equations (IDDEs) is established. Existing algorithm may not converge when the impulses are variable. A convergent numerical scheme is established for nonlinear delay differential equations with variable impulses. Some stability conditions of analytical and numerical solutions to IDDEs are given by the properties of delay differential equations without impulsive perturbations.

scholarly journals Asymptotic Dichotomy in a Class of Fourth-Order Nonlinear Delay Differential Equations with Damping

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
Chengmin Hou ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Third Order ◽  
All Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Linear Differential ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

All solutions of a fourth-order nonlinear delay differential equation are shown to converge to zero or to oscillate. Novel Riccati type techniques involving third-order linear differential equations are employed. Implications in the deflection of elastic horizontal beams are also indicated.

scholarly journals Oscillations of Numerical Solutions for Nonlinear Delay Differential Equations in the Control of Erythropoiesis

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Numerical Solution ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Continuous System ◽  
Numerical Examples ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

We consider the oscillations of numerical solutions for the nonlinear delay differential equations in the control of erythropoiesis. The exponentialθ-method is constructed and some conditions under which the numerical solutions oscillate are presented. Moreover, it is proven that every nonoscillatory numerical solution tends to the equilibrium point of the continuous system. Numerical examples are given to illustrate the main results.

scholarly journals Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equations ◽  
Control Systems ◽  
Delay Differential Equations ◽  
Numerical Solutions ◽  
Continuous System ◽  
Positive Equilibrium ◽  
Physiological Control ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponentialθ-method is applied top′(t)=β0ωμp(t−τ)/(ωμ+pμ(t−τ))−γp(t)and it is shown that the exponentialθ-method has the same order of convergence as that of the classicalθ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.

An iterative scheme for the oscillation criteria of a nonlinear delay differential equation with several deviating arguments

2021 ◽  
pp. 2250071
Author(s):  
R. Basu
Keyword(s):  
Differential Equation ◽  
Delay Differential Equations ◽  
Iterative Process ◽  
Iterative Scheme ◽  
Deviating Arguments ◽  
First Order ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

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.

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