共查询到20条相似文献,搜索用时 10 毫秒
1.
Kennethl. Cooke Anatolif Ivanov 《Journal of Difference Equations and Applications》2013,19(1):105-119
The dynamics of the delay difference equation μ[δxn+αδxn-N]=-Xn+1+f(xn-N)asn→:∞is studied for small positive μ. The equation is shown to possess stable periodic solutions that correspond to hyperbolic attracting cycles of the one–dimensional map ?. 相似文献
2.
Katia A.G. Azevedo Marta C. Gadotti Luiz A.C. Ladeira 《Nonlinear Analysis: Theory, Methods & Applications》2007
We discuss the existence of periodic solutions to a system of differential equations with distributed delay which shows a certain type of symmetry. For this, such solutions are related to the solutions of a system of second-order ordinary differential equations. 相似文献
3.
Jiaowan Luo 《Journal of Mathematical Analysis and Applications》2007,334(1):431-440
In this paper we consider a linear scalar neutral stochastic differential equation with variable delays and give conditions to ensure that the zero solution is asymptotically mean square stable by means of fixed point theory. These conditions do not require the boundedness of delays, nor do they ask for a fixed sign on the coefficient functions. An asymptotic mean square stability theorem with a necessary and sufficient condition is proved. Some well-known results are improved and generalized. 相似文献
4.
S. V. Pavlikov 《Russian Mathematics (Iz VUZ)》2008,52(7):24-32
We study the stability of functional differential equations with infinite delay, using the Lyapunov functional of constant sign with a derivative of constant sign. Limit equations are constructed in a special phase space. We establish a theorem on localization of a positive limit set and theorems on the stability and the asymptotic stability. The results are illustrated by examples. 相似文献
5.
We study one class of linear differential equations with varying distributed delay. We obtain an effective (in terms of parameters of the initial problem) criterion for the positivity of the Cauchy function of this class of equations. Based on this result, we establish effective criteria for the exponential stability of equations under consideration. 相似文献
6.
Zhongli You JinRong Wang Donal O'Regan Yong Zhou 《Mathematical Methods in the Applied Sciences》2019,42(3):954-968
This paper investigates the relative controllability of delay differential systems with linear impulses and linear parts defined by permutable matrices. We use the impulsive delay Grammian matrix to discuss the relatively controllability of impulsive linear delay controlled systems and we use the Krasnoselskii's fixed point theorem to discuss the relatively controllability of impulsive semilinear delay controlled systems. Finally, two examples are presented to illustrate our theoretical results. 相似文献
7.
Preservation of superconvergence in the numerical integration of delay differential equations with proportional delay 总被引:2,自引:0,他引:2
In this note we propose a method for the integration of y'(t) = f(t, y(t), y(rt)), 0 t tf y(0) = y0, where 0 < r < 1, by a superconvengent s-stage continuousRK method of discrete global order p and continuous uniformorder q < p 1 for the approximation of the delayedterm y(rt). We prove that, although the maximum attainable orderof the method on an arbitrary mesh is q' = min{p, q + 1}, byusing a quasi-geometric mesh, introduced by Bellen et al. (1997,Appl. Numer. Math. 24, 1997, 279293), the optimal accuracyorder p is preserved. 相似文献
8.
Consider the neutral delay differential equation [display math001] where [display math002] We studied the asymptotic behavior of the nonoscillatory solutions of Eq. (1) and we obtained sufficient conditions for the oscillation of all solutions, all bounded solutions, and all unbounded solutions of Eq. (1) 相似文献
9.
Yoshiaki Muroya 《Journal of Mathematical Analysis and Applications》2007,326(1):372-389
In this paper, we consider separable nonlinear delay differential systems and we establish conditions for global asymptotic stability of the zero solution. Applying these, we offer improved 3/2-type criteria for global asymptotic stability of nonautonomous Lotka-Volterra systems with delays. 相似文献
10.
Raúl Naulin 《Czechoslovak Mathematical Journal》2003,53(3):497-514
The unstable properties of the linear nonautonomous delay system x(t) = A(t)x(t) + B(t)x(t – r(t)), with nonconstant delay r(t), are studied. It is assumed that the linear system y(t) = (A(t) + B(t))y(t) is unstable, the instability being characterized by a nonstable manifold defined from a dichotomy to this linear system. The delay r(t) is assumed to be continuous and bounded. Two kinds of results are given, those concerning conditions that do not include the properties of the delay function r(t) and the results depending on the asymptotic properties of the delay function. 相似文献
11.
Consider the neutral delay differential equation [display math001] In this paper we are concerned with the asymptotic behavior and the oscillatory nature of solutions of Eq. (1). 相似文献
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14.
Oscillation of first order delay differential equations 总被引:7,自引:0,他引:7
Bingtuan Li 《Proceedings of the American Mathematical Society》1996,124(12):3729-3737
We introduce a new technique to analyze the generalized characteristic equations to obtain some infinite integral conditions for oscillation of the nonautonomous delay differential equations.
15.
Haniye Dehestani Yadollah Ordokhani Mohsen Razzaghi 《Numerical Linear Algebra with Applications》2019,26(5)
A novel collocation method based on Genocchi wavelet is presented for the numerical solution of fractional differential equations and time‐fractional partial differential equations with delay. In this work, to achieve the approximate solution with height accuracy, we employed the operational matrix of integer derivative and the pseudo‐operational matrix of fractional derivative in Caputo sense. Also, based on Genocchi function properties, we presented delay and pantograph operational matrices of Genocchi wavelet functions (GWFs). Due to operational and pseudo‐operational matrices, the equations under this study can be turned into nonlinear algebraic equations with the unknown GWF coefficients. For illustrating the upper bound of error for the proposed method, we estimate the error in the sense of Sobolev space. In addition, to demonstrate the efficacy of the pseudo‐operational matrix of fractional derivative, we investigate the upper bound of error for the mentioned matrix. Finally, the algorithm based on the proposed approach is implemented for some numerical experiments to confirm accuracy and applicability. 相似文献
16.
A generalization of the operator method by Grisvard is used to ensure weak and strict solutions to some degenerate differential equations with delay in Banach spaces, whose operator coefficients are time depending. Some applications to ordinary and partial differential equations with delay are described. 相似文献
17.
Bo Zhang 《Journal of Mathematical Analysis and Applications》2007,325(2):1442-1467
Formulas of explicit quadratic Liapunov functions for showing asymptotic stability of the system of linear partial differential equations on (0,∞)×Ω, are constructed, where A is an n×n real matrix, u=T(u1,u2,…,un), Ω is a bounded domain in Rk with smooth boundary ∂Ω, and Δ denotes the Laplacian operator on Rk with Δu=T(Δu1,Δu2,…,Δun). These formulas are also modified and applied to a number of nonautonomous linear and nonlinear systems and models in structural stability, traveling wave, and Navier-Stokes equations. 相似文献
18.
In this paper, the delay-dependent dissipativity of nonlinear delay differential equations is studied. A new dissipativity criterion is derived, which is less conservative than those in the existing literature in some cases, especially for equations with small delays. 相似文献
19.
We study the skew-product semiflow induced by a family of convex and cooperative delay differential systems. Under some monotonicity assumptions, we obtain an ergodic representation for the upper Lyapunov exponent of a minimal subset. In addition, when eventually strong convexity at one point is assumed and there exist two completely strongly ordered minimal subsets K1?CK2, we show that K1 is an attractor subset which is a copy of the base. The long-time behaviour of every trajectory strongly ordered with K2 is then deduced. Some examples of application of the theory are shown. 相似文献
20.
V. V. Malygina 《Russian Mathematics (Iz VUZ)》2008,52(7):15-23
For a differential equation with a distributed varying delay, sufficient criteria for the asymptotic and uniform stability of solutions are obtained. The constructed examples demonstrate exactness of the boundary of the obtained stability domain. 相似文献