2011年, 第24卷, 第2期　刊出日期：2011-04-25

  

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  EXPONENTIALLY ADAPTIVE SYNCHRONIZATION OF AN UNCERTAINDELAYED DYNAMICAL NETWORK

  Qunjiao ZHANG;Jun'an LU

  Journal of Systems Science and Complexity. 2011, 24(2): 207-217. https://doi.org/10.1007/s11424-011-8304-0

  摘要 ( ) PDF全文 ( )   可视化   收藏

  Over the past decades, complex networks have been prosperous greatly in various fields of sciences and engineering. Much attention has been given to investigate the synchronization of complex networks in recent years. However, few work has done for the networks with uncertain parameters and unknown topology. In this paper, to further reveal the dynamical mechanism in complex networks with time delays, an uncertain general complex dynamical network with delayed nodes is studied. By constructing a drive network and a suitable slave network, several novel criteria for the networks consisting of the identical nodes and different nodes have been obtained based on the adaptive feedback method. Particularly, the hypotheses and the proposed adaptive laws for network synchronization are simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.
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  RANDOM CONTINUOUS MODEL OF SCALE-FREE NETWORKS

  Xianmin GENG

  Journal of Systems Science and Complexity. 2011, 24(2): 218-224. https://doi.org/10.1007/s11424-011-8076-6

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  There are a lot of continuous evolving networks in real world, such as Internet, WWW network, etc. The evolving operation of these networks are not an equating
  interval of time by chance. In this paper, the author proposes a new mathematical model for the mechanism of continuous single preferential attachment on the scale free networks, and counts the distribution of degree using stochastic analysis. Namely, the author has established the random continuous model of the network evolution of which counting process determines the operating number, and has
  proved that this system self-organizes into scale-free structures with scaling exponent $\gamma=3+\frac{\alpha}{m}$.
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  ASYMPTOTIC STABILITY AND RIESZ BASIS PROPERTY FOR TREE-SHAPED NETWORK OF STRINGS

  Yanni GUO;Genqi XU

  Journal of Systems Science and Complexity. 2011, 24(2): 225-252. https://doi.org/10.1007/s11424-010-8062-4

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  This paper discusses the asymptotic stability and Riesz basis generation for a general tree-shaped network of vibrating strings. All exterior vertices are assumed to be fixed and interior vertices are imposed linear damping feedbacks. This paper shows that the system is well-posed and asymptotically stable by $C_0$-semigroup theory. With some additional conditions, the spectrum of the system
  is shown to be located in a strip that is parallel to the imaginary axis and the set of all generalized eigenfunctions is completed in the state space. These lead to the conclusion that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis with parenthesis for the state space.
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  UNIFORM DECAY RATE FOR THE TRANSMISSION WAVE EQUATIONS WITHVARIABLE COEFFICIENTS

  Shugen CHAI

  Journal of Systems Science and Complexity. 2011, 24(2): 253-260. https://doi.org/10.1007/s11424-011-8009-4

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  This paper considers the stabilization of the transmission problem of wave equations with variable coefficients. By introducing both boundary feedback control and distribute feedback control near the transmission boundary, the author establishes the uniform energy decay rate for the problem.
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  STRICT LYAPUNOV FUNCTIONS FOR IMPULSIVE HYBRID TIME-VARYING SYSTEMS WITH DISCONTINUOUS RIGHT-HAND SIDE

  Xiaowu MU;Fengjun TANG

  Journal of Systems Science and Complexity. 2011, 24(2): 261-270. https://doi.org/10.1007/s11424-011-7237-y

  摘要 ( ) PDF全文 ( )   可视化   收藏

  In this paper, explicit closed form expressions of nonsmooth strict Lyapunov functions for impulsive hybrid time-varying systems with discontinuous right-hand side is provided. Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of
  excitation parameters.
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  GENERALIZED VARIATION ITERATION SOLUTION OF AN ATMOSPHERE-OCEAN OSCILLATOR MODEL FOR GLOBAL CLIMATE

  Jiaqi MO;Wantao LIN

  Journal of Systems Science and Complexity. 2011, 24(2): 271-276. https://doi.org/10.1007/s11424-011-7153-1

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  A box model of the interhemispheric thermohaline circulation (THC) in atmosphere-ocean for global climate is considered. By using the generalized variational iteration method, the approximate solution of a simplified nonlinear model is studied.
  The generalized variational iteration method is an analytic method, and the obtained analytic solution can be operated sequentially. The authors also diversify qualitative and quantitative behaviors for corresponding physical quantities.
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  A SINGULAR BIOECONOMIC MODEL WITH DIFFUSION AND TIME DELAY

  Qingling ZHANG;Xue ZHANG;Chao LIU

  Journal of Systems Science and Complexity. 2011, 24(2): 277-290. https://doi.org/10.1007/s11424-010-8067-z

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  This paper studies a prey-predator singular bioeconomic system with time delay and diffusion, which is described by differential-algebraic equations. For this system without diffusion, there exist three bifurcation phenomena: Transcritical bifurcation, singularity induced bifurcation, and Hopf bifurcation. Compared with other biological systems described by differential equations, singularity induced bifurcation only
  occurs in singular system and usually links with the expansion of population. When the diffusion is present, it is shown that the positive equilibrium point loses its stability at some critical values of diffusion rate and periodic oscillations occur due to the increase of time delay. Furthermore, numerical simulations illustrate the effectiveness of results and the related biological implications are discussed.
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  OPTIMAL MULTI-ASSET INVESTMENT WITH NO-SHORTING CONSTRAINTUNDER MEAN-VARIANCE CRITERION FOR AN INSURER

  Junna BI;Junyi GUO;Lihua BAI

  Journal of Systems Science and Complexity. 2011, 24(2): 291-307. https://doi.org/10.1007/s11424-011-8014-7

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  This paper considers the optimal investment strategy for an insurer under the criterion of mean-variance. The risk process is a compound Poisson process and the insurer can invest in a risk-free asset and multiple risky assets. This paper obtains the optimal investment policy using the stochastic linear quadratic
  (LQ) control theory with no-shorting constraint. Then the efficient strategy (optimal investment strategy) and efficient frontier are derived explicitly by a verification theorem with the viscosity solution of Hamilton-Jacobi-Bellman (HJB) equation.
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  UPPER BOUND FOR FINITE-TIME RUIN PROBABILITY IN A MARKOV-MODULATED MARKET

  Jinzhu LI;Rong WU

  Journal of Systems Science and Complexity. 2011, 24(2): 308-316. https://doi.org/10.1007/s11424-010-8348-6

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  This paper studies the upper bound for finite-time ruin probability of an insurance company which invests its wealth in a stock and a bond. The authors assume that the interest rate of the bond and the volatility of the stock are modulated by a
  continuous-time stationary Markov chain with finite state. By a pure probabilistic method, the upper bound for the finite-time ruin probability is obtained.
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  ASSET-LIABILITY MANAGEMENT UNDER BENCHMARK AND MEAN-VARIANCECRITERIA IN A JUMP DIFFUSION MARKET

  Yan ZENG;Zhongfei LI

  Journal of Systems Science and Complexity. 2011, 24(2): 317-327. https://doi.org/10.1007/s11424-011-9105-1

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  This paper investigates continuous-time asset-liability management under benchmark and mean-variance criteria in a jump diffusion market. Specifically, the authors consider one risk-free asset, one risky asset and one liability, where the
  risky asset's price is governed by an exponential L\'{e}vy process, the liability evolves according to a L\'{e}vy process, and there exists a correlation between the risky asset and the liability. Two models are established. One is the benchmark model and the other is the mean-variance model. The benchmark model is solved by employing the stochastic dynamic programming and its results are extended to the mean-variance model by adopting the duality theory. Closed-form solutions of the two models are derived.
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  ASYMPTOTICS FOR RUIN PROBABILITIES OF TWO KINDS OF DEPENDENT RISK MODELS WITH NLOD INTER-ARRIVAL TIMES

  Yang YANG;Yuebao WANG;Xijun LIU

  Journal of Systems Science and Complexity. 2011, 24(2): 328-334. https://doi.org/10.1007/s11424-011-8107-3

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  This paper establishes some asymptotic formulas for the infinite-time ruin probabilities of two kinds of dependent risk models. One risk model considers the claim sizes as a modulated process, and the other deals with negatively upper orthant dependent claim sizes. In the two models, the inter-arrival times are both
  assumed to be negatively lower orthant dependent.
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  SIEVE LEAST SQUARES ESTIMATOR FOR PARTIAL LINEAR MODELS WITHCURRENT STATUS DATA

  Songlin WANG;Sanguo ZHANG;Hongqi XUE

  Journal of Systems Science and Complexity. 2011, 24(2): 335-346. https://doi.org/10.1007/s11424-011-8050-3

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  Current status data often arise in survival analysis and reliability studies, when a continuous response is reduced to an indicator of whether the response is greater or less than an observed random threshold value. This article considers a partial
  linear model with current status data. A sieve least squares estimator is proposed to estimate both the regression parameters and the nonparametric function. This paper shows, under some mild condition, that the estimators are strong consistent. Moreover, the parameter estimators are normally distributed, while the nonparametric component achieves the optimal convergence rate. Simulation studies are carried out to investigate the performance of the proposed estimates. For illustration purposes, the method is applied to a real dataset from a study of the calcification of the hydrogel intraocular lenses, a complication of cataract
  treatment.
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  THE STRONG LAW OF LARGE NUMBERS FOR PAIRWISE NQD RANDOM VARIABLES

  Qunying WU;Yuanying JIANG

  Journal of Systems Science and Complexity. 2011, 24(2): 347-357. https://doi.org/10.1007/s11424-011-8086-4

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  In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz (1937), Jamison (1965), Matula (1992 ) and Wu (2001)
  from the independent identically distributed (i.i.d.) case to pairwise NQD sequences.
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  AN APPLICATION OF RITT-WU'S ZERO DECOMPOSITION ALGORITHM TO THE PSEUDO NULL BERTRAND TYPE CURVES IN MINKOWSKI 3-SPACE

  Kaz\i m \.{I}LARSLAN;Mehmet YILDIRIM

  Journal of Systems Science and Complexity. 2011, 24(2): 358-366. https://doi.org/10.1007/s11424-011-8267-1

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  The Bertrand curves were first studied using a computer by Wu
  (1987). The same problem was studied using an improved version of
  Ritt-Wu's decomposition algorithm by Chou and Gao (1993). This paper
  investigates the same problem for pseudo null Bertrand curves in
  Minkowski 3-space $\mathbb{E}_{1}^{3}$.
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  PROPER REPARAMETRIZATION FOR INHERENTLY IMPROPER UNIRATIONALVARIETIES

  Liyong SHEN;Engwee CHIONH;Xiao-Shan GAO;Jia LI

  Journal of Systems Science and Complexity. 2011, 24(2): 367-380. https://doi.org/10.1007/s11424-010-7221-y

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  In this paper, a class of lattice supports in the lattice space $Z^m$ is found to be inherently improper because any rational parametrization from $C^m$ to $C^n$ defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support $S$ is analyzed and shrinking transformations are constructed to transform $S$ to a proper one. For a generic rational parametrization $RP$ defined on an improper support $S$, we prove that its improper index is the improper index of $S$ and give a proper reparametrization algorithm for $RP$. Finally, properties for rational parametrizations defined on an
  improper support and with numerical coefficients are also considered.
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  LEAST-SQUARES GALERKIN PROCEDURE FOR SECOND-ORDERHYPERBOLIC EQUATIONS

  Hui GUO;Hongxing RUI;Chao LIN

  Journal of Systems Science and Complexity. 2011, 24(2): 381-393. https://doi.org/10.1007/s11424-010-8015-y

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  This paper proposes the least-squares Galerkin finite element scheme to solve second-order hyperbolic equations. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in $(L^{2}({\it \Omega}))^{2}\times L^{2}({\it \Omega})$ norms. Moreover, the method
  gets the approximate solutions with second-order accuracy in time increment. A numerical example testifies the efficiency of the novel scheme.
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  GENERALIZED INVEXITY-TYPE CONDITIONS IN CONSTRAINED OPTIMIZATION

  Shashi K. MISHRA;Norma G. RUEDA

  Journal of Systems Science and Complexity. 2011, 24(2): 394-400. https://doi.org/10.1007/s11424-011-8234-x

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  This paper defines a new class of generalized type I functions, and obtains Kuhn-Tucker necessary and sufficient conditions and duality results for constrained optimization problems in the presence of the aforesaid weaker assumptions on
  the objective and constraint functions involved in the problem.
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  NEURAL NETWORKS AND THE BEST TRIGOMOMETRIC APPROXIMATION

  Jianjun WANG;Zongben XU

  Journal of Systems Science and Complexity. 2011, 24(2): 401-412. https://doi.org/10.1007/s11424-011-8080-x

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  With the best trigonometric polynomial approximation as a metric, the rate of approximation of the one-hidden-layer feedforward neural networks to approximate an integrable function is estimated by using a constructive approach in this paper. The obtained result shows that for any $2\pi$-periodic integrable
  function, a neural networks with sigmoidal hidden neuron can be constructed to approximate the function, and that the rate of approximation do not exceed the double of the best trigonometric polynomial approximation of function.