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.

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 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.

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