In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. [1] 特性(intuition):系统状态(即表征系统动态行为的微分方程的自变量)的变化行为仅仅依赖于初始状态 x0 ,而不依赖于初始时间 ...
System (5.4.1) can be written in the form z′=f(z), where z=(xy)andf(z)=(P(z)Q(z)). Thus the second-order differential equation x″=g(x,x′) can be written in the form (5.4.1) as the system x′=y,y′=g(x,y). We begin with the following lemma. We denote the ...
The problem for this control law and performance criterion is to find coefficients of a differential equation system with distributed delay, for which the chosen control is a control of optimal stabilization. A class of control laws for which the posed problem admits an analytic solution is ...
noil-linear partial differential equation 非线性偏微分方程【咖J.翻r,而I山价拍函坛la甲.d阅;He翻e面.oeyP姗e皿ec,aC几。,nPO,3的月”曰M一」 一个形如 F(x,u,…,D“u)“0(1)的方程,其中x=(x.,…,x。)任R“,u=(“:,一,“。)〔R’,F=(F,,一,F*)‘R“,:=(:.,…,:。)是...
Differential equation systems modeling the spread of infectious diseases are considered which can be rewritten as smaller asymptotically autonomous systems with limiting systems that are easier to handle than the original ones. Using recently developed techniques, it is shown that the asymptotic dynamics ...
over ???, then there is a scheme for reducing the system of differential equations to an autonomous ordinary differential equation on one variable of the algebra; (2) a technique, previously introduced for solving differential equations over ???, is shown to work on the class mentioned in the...
S. A. Aisagaliev, “Controllability of a certain system of differential equations,” Differents. Uravn., 27, No. 9, 1475–1486 (1991). Google Scholar S. A. Aisagaliev, “General solution of one class of integral equations,” Mat. Zh., 5, No. 4(18), 17–34 (2005). MathSciNet...
An autonomous ordinary autonomous differential equation generating isoordinal cascade of cusps in a bifurcation plane 来自 ResearchGate 喜欢 0 阅读量: 12 作者:JP Carcasses,C Mira 摘要: This paper deals with a Dim3 ODE. In the form of a system of three Dim1 relation, the third one has a ...
The problem of stabilizing the oscillations of the reduced controlled system is solved. A smooth autonomous control law with a parameter depending on h is applied, and an attracting cycle is constructed. The results are concretized for an nth-order differential equation. The relation of these ...
This paper presents a model for describing the sunspot as an autonomous dynamical system both in its growth and decay phases. The model consists of a two-dimensional system of ordinary differential equations (ODE) of first order with respect to time. The two time-dependent functions are the are...