[PDF] Top 20 A stability theory for perturbed differential equations

... stability properties are preserved under perturbations, a theory based on the actual behavior of the solutions of the perturbed differential equation with res-.. pect to those of the ori[r] ... See full document

... finite-time stability theory of differential equations, and proposed a simple, systematic and rigorous adaptive feedback control method to stabilize finite- dimensional chaotic systems within ... See full document

... via stability theory of nonlinear differential equations to assess the effects of general awareness, constant vaccination and the saturated treatment on the transmission dynamics of rabies ... See full document

... A differential equation in which the highest derivative is multiplied by a small positive parameter and containing at least one shift term(delay or advance) is known as singularly perturbed ... See full document

... To illustrate the theory given in the present study and examine the performance of the proposed numerical scheme a set of numerical experiments is carried out. Since exact solution is not known for the considered ... See full document

... certain stability, and the robust stability always plays an important ...decades, stability analyses of neural networks have attracted the attention of many researchers (see ...the stability ... See full document

... This paper is organized as follows. In Section 2, we first give some preliminaries and assumptions on equation (2.1). In Section 3, we state and prove our main results. While in Section 4, we show that the pth moment of ... See full document

... (The notations used in this section will be explained in Section 2). In general, both f and g are required to obey the standard local Lipschitz condition and the linear growth condition (see e.g. Kolmanovskii and Myshkis ... See full document

... modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the new equa- tion, we introduced a fitting parameter and ... See full document

... Though the DG method allows discontinuity between adjacent elements, it produces more degrees of freedom than the continuous finite element method (CFEM) and hence requires a large amount of computation. On the other ... See full document

... differential equations play an important role in the mathematical modelling of various practical phenomena in the biosciences and control ...singularly perturbed delay differential equation is an ordinary ... See full document

... the differential systems are stochastic ...impulsive differential systems and also it is different from stochastic differential ...impulsive differential equations is a new research ... See full document

... time-varying differential-algebraic equation and if T  then it is a time-varying implicit difference ...The differential-algebraic equations (DAEs) are the mathematical models arising in various ... See full document

... oscillation theory plays an important role in physi- cal science and technology; for example in the oscillation of building or machine, electro- magnetic vibration in radio technology and optical science, ... See full document

... In [4], instead of using a Lyapunov functional, the author studied asymptotic stabil- ity of the above IDE by using the concept of a contraction mapping in line with the fixed point theory for a class of ... See full document

... Magnetohydrodynamic stability theory provides a method of investigating these phenomena by using it to test proposed mathematical ...homogeneous differential equations with large parameters ... See full document

... exponential stability of solutions for the singular perturbed impulsive delay differential equations ...exponential stability of any solution of SPIDIDEs for sufficiently small ε > 0 are ... See full document

... In theory of perturbation formathematics and physical systems, the study of this relation got significance amount of attention ing the solution of singular perturbed differential equations ... See full document

... the theory of impul- sive differential equations is now highly appreciated as a natural theoretical basis for the mathematical modeling of the natural phenomena of various ...the theory and the ... See full document

... differential equations are used to model a large variety of practical phenomena in the biosciences, engineering and control theory, and in many other areas of science and technology, in which the time ... See full document