The time-delay dynamic equation is a fundamental concept in the field of mathematical modeling and control theory, describing the behavior of complex systems with delayed feedback. This equation plays a crucial role in understanding various real-world phenomena, including population dynamics, chemical reactions, and control systems. The incorporation of time delays in dynamic equations enables the analysis of system stability, oscillations, and transient behaviors. The study of time-delay dynamic equations has generated a wide range of research interests across different disciplines, contributing to the development of advanced control strategies and predictive modeling techniques. The following sentences illustrate the application of time-delay dynamic equations in different contexts: 1. The time-delay dynamic equation captures the delayed response of a chemical reactor to changes in input concentrations. 2. Time-delay dynamic equations have been instrumental in analyzing the stability of eco-systems with population feedback.
时滞动力方程,delay dynamic equation
1)delay dynamic equation时滞动力方程
1.Kamenev-type oscillation criteria for second-order nonlineardelay dynamic equations on time scales;时间尺度上二阶非线性时滞动力方程的Kamenev型振动准则
2.In this paper, oscillation of solutions of several classes ofdelay dynamic equations is considered.本文分五章研究了几类时滞动力方程的振动性，所得结果推广和改进了文献中的相关结论。
3.It is composed of two chapters, which respectively study oscillation solutions of a class of nonlineardelay dynamic equations on time scales and the existence of unbounded positive solutions of certain delay partial.第二部分是正文，它分两章来具体讨论一类时间标度上时滞动力方程的振动性和一类时滞偏差分方程的非振动解存在性。
英文短句/例句
1.Oscillation of One Kind of Second-Order Delay Dynamic Equations on Time Scales时间尺度上一类二阶时滞动力方程的振动性
2.Oscillation and Nonoscillation of Delay Dynamic Equations on a Measure Chain;测度链上时滞动力方程的振动性和非振动性
3.Global attractivity of delay dynamic equations on time scales一类时标上时滞动力方程的全局吸引性
4.Oscillation Criteria for a Class of Delay Dynamic Equations on Time Scales测度链上一类时滞动力方程的振动性判据
5.Oscillation for Delay Dynamic Equations on Time Scales and Existence of Positive Solutions for Partial Difference Equations;时间标度上时滞动力方程的振动性和偏差分方程正解的存在性
6.Oscillatory and Asymptotic Behavior for Third-order Neutral Dynamic Equation with Variable Delay on Time Scales;时标上三阶中立型变时滞动力方程解的振动性与渐进性
7.Oscillation and Asymptotic Behavior of Solutions for Higher-Order Delay Dynamic Equations on a Measure Chain;测度链上高阶时滞动力方程解的振动性和渐近性
8.Oscillation for First-order Impulsive Delay Dynamic Equations on Time Scales时标上一阶时滞脉冲动力方程解的振动性
9.Dynamics of Some Nonlinear Delay Difference Equations几类非线性时滞差分方程的动力学行为
10.Nonoscillation for a Delay Dynamic Differential Equation on Time Scales时间标度上的一类时滞动力微分方程的非振动性
11.Dynamics of Transiently Chaotic Neural Networks and a Class of Delay Differential Equations;瞬时混沌神经网络和一类时滞微分方程的动力学性质分析
12.The Research of Dynamics Behavior for Several Class of Functional Differential Equations and Delay Differential Systems;几类偏泛函微分方程与时滞微分系统的动力学行为研究
13.Dynamic Analysis for Several Delay Neural Network Models of Difference and Differential Equations;几类时滞差分、微分方程神经网络模型的动力学分析
14.Dynamical Behavior Analysis of Special Delay Differential Equations and the Application of Chaos and Fractals;几类时滞微分方程的动力学分析及混沌、分形应用实例讨论
15.Researches about the Oscillations of Several Classes of Second-Order Delay Differential Equations;几类二阶时滞微分方程的振动性研究
16.The Oscillation of Some Delay Difference Equations and Distribution of Zeros;若干时滞差分方程的振动及零点分布
17.Oscillations of a Clall of Second Order Impulses Delay Differential Equations;一类二阶脉冲时滞微分方程的振动性
18.The Oscillation of a Class of Neutral Difference Equation with Delay;一类时滞差分方程的振动性(英文)
相关短句/例句
delay dynamic equations时滞动力方程
1.In this paper,by using Riccati transformation technique,we establish oscillation criteria for a class of nonlinear second-orderdelay dynamic equations on time scales x△△(t)+p(t)x△(t)+q(t)f(x(τ(t)))=0,where p and q are positive real value rd-continuous functions defined on T.利用Riccati-变换方法,研究了测度链上二阶非线性时滞动力方程x△△(t)+p(t)x△(t)+q(t)f(x(τ(t)))=0解的振动性,其中p,q是定义在测度链Т上正的实值右稠密连续函数。
3)impulsive delay dynamic equations脉冲时滞动力方程
4)delay equation时滞方程
1.A necessary and sufficient condition for asymptotic stability of first orderdelay equation with two delays;一阶双滞量时滞方程零解渐进稳定的充要条件
2.Algebraic criterion for asymptotic stability of a first orderdelay equation with two delays;一类一阶双滞量时滞方程零解渐近稳定的代数判据(英文)
3.A necessary and sufficient condition for asymptotic stability of first orderdelay equation with two delays一类一阶双滞量时滞方程零解渐进稳定的充要条件
5)Emden-Fowler neutral delay dynamic equationsEmden-Fowler中立型时滞动力方程
6)delay Volterra equation时滞Volterra方程
延伸阅读
传热学：流体动力学基本方程流体动力学基本方程：将质量﹑动量和能量守恆定律用於流体运动所得到的联繫流体速度﹑压力﹑密度和温度等物理量的关係式。对於系统和控制体都可以建立流体动力学基本方程。系统是确定不变的物质的组合﹔而控制体是相对於某一坐标系固定不变的空间体积﹐它的边界面称为控制面。流体动力学中讨论的基本方程多数是对控制体建立的。基本方程有积分形式和微分形式两种。前者通过对控制体和控制面的积分而得到流体诸物理量之间的积分关係式﹔后者通过对微元控制体或系统直接建立方程而得到任意空间点上流体诸物理量之间的微分关係式。求解积分形式基本方程可以得到总体性能关係﹐如流体与物体之间作用的合力和总的能量交换等﹔求解微分形式基本方程或求解对微元控制体建立的积分形式基本方程﹐可以得到流场细节﹐即各空间点上流体的物理量。 积分形式基本方程 主要有连续方程﹑动量方程﹑动量矩方程和能量方程。 连续方程 单位时间流入控制体的质量等於控制体内质量的增加。它是由质量守恆定律得到的﹐其数学表达式为式中为速度﹔为密度﹔为控制体体积﹔A 为控制面面积﹔为dA 控制面处法线方向单位向量(图1 积分形式基本方程示意图 )。定常流动时上等式右边为零。这时如截取一段流管(见流体运动学)作为控制面(图2 流管内的连续方程 )﹐则有下述连续方程﹕ Ｐ1Ｖ1A 1=Ｐ2Ｖ2A 2 式中Ｐ1 ﹑Ｖ1﹑Ｐ2﹑Ｖ2分别为A 1和A 2截面上的流体平均密度和速度。 动量方程 单位时间内﹐流入控制体的动量与作用於控制面和控制体上的外力之和﹐等於控制体内动量的增加。它是由动量守恆定律得到的﹐其数学表达式为﹕式中为外部作用於 dA 控制面上单位面积上的力﹔为外部作用於d控制体内单位质量流体上的力﹔通常就是重力。定常流动时﹐上等式右边为零。动量方程用於确定流体与其边界之间的作用力。
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