共查询到20条相似文献,搜索用时 12 毫秒
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Shuang Liang Guodong Zhao Haitao Li Xueying Ding 《Mathematical Methods in the Applied Sciences》2019,42(7):2221-2230
This paper studies the structural monostability and structural cycle‐stability of Boolean networks (BNs). Firstly, the structural‐equivalent Boolean networks are converted to the algebraic forms by using the semitensor product of matrices. Secondly, the concepts of structural monostability and structural cycle‐stability for Boolean networks are proposed. On the basis of the algebraic forms of structural‐equivalent Boolean networks, some necessary and sufficient conditions are presented for the structural monostability and structural cycle‐stability of Boolean networks. Finally, an illustrative example is worked out to show the effectiveness of the obtained results. 相似文献
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Yongzheng Sun Wang Li Jiong Ruan 《Communications in Nonlinear Science & Numerical Simulation》2013,18(4):989-998
In this paper, the generalized outer synchronization between two different delay-coupled complex dynamical networks with noise perturbation is investigated. With a nonlinear control scheme, the sufficient condition for almost sure generalized outer synchronization is developed based on the LaSalle-type invariance principle for stochastic differential equations. Numerical examples are examined to illustrate the effectiveness of the analytical results. The theoretic result is also applied to investigate the outer synchronization between two delay-coupled Hindmarsh–Rose neuronal networks with noise perturbation. 相似文献
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针对二阶半线性Dirichlet问题用边界层函数法构造了渐近解,给出了转移点的渐近表达式,并用微分不等式方法证明了阶梯状空间对照结构的存在性和进行了余项估计. 相似文献
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Hossein Hassani Zhengyuan Xu Anatoly Zhigljavsky 《Nonlinear Analysis: Real World Applications》2011,12(5):2752-2766
Singular Spectrum Analysis (SSA) has been exploited in different applications. It is well known that perturbations from various sources can seriously degrade the performance of the methods and techniques. In this paper, we consider the SSA technique based on the perturbation theory and examine its performance in both reconstructing and forecasting noisy series. We also consider the sensitivity of the technique to different window lengths, noise levels and series lengths. To cover a broad application range, various simulated series, from dynamic to chaotic, are used to verify the proposed algorithm. We then evaluate the performance of the technique using two real well-known series, namely, monthly accidental deaths in the USA, and the daily closing prices of several stock market indices. The results are compared with several classical methods namely, Box–Jenkins SARIMA models, the ARAR algorithm, GARCH model and the Holt–Winter algorithm. 相似文献
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S. H. Lam 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1977,28(5):817-823
A simple convection-diffusion problem is used as an example for a class of singular perturbation problems for which application of standard singular perturbation procedures could lead to misleading results. The properties of the operator appearing in the problem are identified and a solution technique using eigenfunction concepts is presented.
Dedicated to Nicholas, with fond memories of my year at Cornell. 相似文献
Zusammenfassung Ein einfaches Problem mit Konvektion und Diffusion wird als Beispiel für singuläre Störungsprobleme gegeben, für welche Standardmethoden zu falschen Resultaten führen können. Die Eigenschaften des Operators, der im Problem auftritt, werden untersucht und eine Lösungsmethode wird gegeben, die auf Eigenfuntionen beruht.
Dedicated to Nicholas, with fond memories of my year at Cornell. 相似文献
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W. E. Olmstead Richard A. Handelsman 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1972,23(6):889-900
An investigation is made of the asymptotic behavior of the solutionu(t;ε) to the Volterra integral equation $$\varepsilon u(t;\varepsilon ) = \pi ^{ - \tfrac{1}{2}} \int\limits_0^t {(t - s)^{ - \tfrac{1}{2}} [f(s) - u^n (s;\varepsilon )]} ds, t \geqslant 0, n \geqslant 1$$ , in the limit as ε→0. This investigation involves a singular perturbation analysis. For the linear problem (n=1) an infinite, uniformly valid asymptotic expansion ofu(t;ε) is obtained. For the nonlinear problem (n≥2), the leading two terms of a uniformly valid expansion are found 相似文献
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Microarray chips generate large amounts of data about a cell’s state. In our work we want to analyze these data in order to describe the regulation processes within a cell. Therefore, we build a model which is capable of capturing the most relevant regulating interactions and present an approach how to calculate the parameters for the model from time-series data. This approach uses the discrete approximation method of least squares to solve a data fitting modeling problem. Furthermore, we analyze the features of our proposed system, i.e., which kinds of dynamical behaviors the system is able to show. 相似文献
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J. S. Angell W. E. Olmstead 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1985,36(3):487-490
A formal asymptotic scheme is used to determine the leading order behavior of a certain singularly perturbed integrodifferential equation which models the process of stretching a polymer filament. The inner solution describes the process during a boundary layer in time which occurs at the onset of elastic recovery. The outer solution describes the long term behavior of the elastic recovery, and a bound on the ultimate recovery is determined.
Zusammenfassung Ein formales asymptotisches Schema wird benutzt, um das Verhalten der Leitordnung einer gewissen singular gestörten Integro-Differentialgleichung, die als Modell für den Dehnungsprozeß einer Polymerfaser dient, zu bestimmen. Die innere Lösung beschreibt den Prozeß in einem zeitlichen Randgebiet, das am Anfang der elastischen Rückstellung auftritt. Die äußere Lösung beschreibt das Langzeitverhalten der elastischen Rückstellung, und eine Grenze für die endgültige Rückstellung wird bestimmt.相似文献
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We consider a nonlinear Dirichlet problem driven by the p-Laplace operator and with a right-hand side which has a singular term and a parametric superlinear perturbation. We are interested in positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies. In addition, we show that for every admissible parameter the problem has a smallest positive solution and we establish the monotonicity and continuity properties of the map . 相似文献
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Van Vu 《Random Structures and Algorithms》2011,39(4):526-538
Computing the first few singular vectors of a large matrix is a problem that frequently comes up in statistics and numerical analysis. Given the presence of noise, an exact calculation is hard to achieve, and the following problem is of importance: How much does a small perturbation to the matrix change the singular vectors? Answering this question, classical theorems, such as those of Davis‐Kahan and Wedin, give tight estimates for the worst‐case scenario. In this paper, we show that if the perturbation (noise) is random and our matrix has low rank, then better estimates can be obtained. Our method relies on high dimensional geometry and is different from those used in earlier papers. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011 相似文献
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吴钦宽 《高校应用数学学报(A辑)》2007,22(2):210-216
讨论了伴有边界摄动的二阶非线性Volterra型积分微分方程组的奇摄动.在适当的条件下,利用对角化技巧证明了解的存在性,构造出解的渐近展开式并给出余项的一致有效估计. 相似文献
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We study infinitesimal perturbation analysis (IPA) for queueing networks with general service time distributions. By general we mean that the distributions may have discrete components. We show that in the presence of service time distributions with discrete components commuting condition (CC) is no longer sufficient for unbiasedness of IPA. To overcome this difficulty, we introduce the notion of separability of realvalued random variables, and show that separability of service times together with (CC) establishes unbiasedness of IPA for queueing systems with general service time distributions. It turns out that the piecewise analyticity of service times is a sufficient condition for separability. 相似文献
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Singular perturbation with Hopf points in the fast dynamics 总被引:3,自引:0,他引:3
M. Stiefenhofer 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1998,49(4):602-629
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Singular perturbation with Limit points in the fast dynamics 总被引:2,自引:0,他引:2
M. Stiefenhofer 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1998,49(5):730-758
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§ 1 IntroductionThe nonlinearsingularly perturbed problem is a very attractive subjectof study in theinternational academic circles[1 ] .During the past decade many approximate methods havebeen developed and refined,including the method of average,boundary layer method,matched asymptotic expansions,and multiple scales.Recently,many scholars,for example,Bohé[2 ] ,Butuzov and Smurov[3] ,O Malley[4] ,Butuzov,Nefedov and Schneider[5] ,Kelley[6]and so on did a great deal of work.Mo consider… 相似文献
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We study some properties of piecewise linear differential systems describing gene regulatory networks, where the dynamics are governed by sigmoid-type nonlinearities which are close to or coincide with the step functions. To overcome the difficulty of describing the dynamics of the system near singular stationary points (belonging to the discontinuity set of the system) we use the concept of Filippov solutions. It consists in replacing discontinuous differential equations with differential inclusions. The global existence and some other basic properties of the Filippov solutions such as continuous dependence on parameters are studied. We also study the uniqueness and non-uniqueness of the Filippov solutions in singular domains. The concept of Filippov stationary point is extensively exploited in the paper. We compare two ways of defining the singular stationary points: one is based on the Filippov theory and the other consists in replacing step functions with steep sigmoids and investigating the smooth systems thus obtained. The results are illustrated by a number of examples. 相似文献