Discrete Dynamics in Nature and Society http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Fare Optimality Analysis of Urban Rail Transit under Various Objective Functions Thu, 28 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/910736/ Urban rail transit fare strategies include fare structures and fare levels. We propose a rail transit line fare decision based on an operating plan that falls under elastic demand. Combined with the train operation plan, considering flat fare and distance-based fare, and based on the benefit analysis of both passenger flow and operating enterprises, we construct the objective functions and build an optimization model in terms of the operators’ interests, the system’s efficiency, system regulation goals, and the system costs. The solving algorithm based on the simulated annealing algorithm is established. Using as an example the Changsha Metro Line 2, we analyzed the optimized results of different models under the two fare structures system. Finally the recommendations of fare strategies are given. Lianbo Deng, Zhao Zhang, Kangni Liu, Wenliang Zhou, and Junfeng Ma Copyright © 2014 Lianbo Deng et al. All rights reserved. A Unified Weight Formula for Calculating the Sample Variance from Weighted Successive Differences Wed, 27 Aug 2014 15:20:07 +0000 http://www.hindawi.com/journals/ddns/2014/210761/ The basic formula to calculate sample variance is based on the sum of squared differences from mean. From computational perspective, mean calculation is nondesired as it can introduce computing errors. Previous researches have proposed to use weighted formula of the successive differences to calculate sample variance to avoid mean calculation. But their weighted formula is not in a unified format in the sense that it has to be represented as two formulas. This paper proposes a unified weight formula for sample variance calculation from weighted successive differences. A proof is provided to show that sample variance calculated using the proposed unified weighted formula is mathematically equivalent to the basic definition. Kuo-Hung Lo, Tien-Lung Sun, and Juei-Chao Chen Copyright © 2014 Kuo-Hung Lo et al. All rights reserved. An Improved Algorithm in Porosity Characteristics Analysis for Rock and Soil Aggregate Wed, 27 Aug 2014 08:14:06 +0000 http://www.hindawi.com/journals/ddns/2014/798235/ The rock and soil aggregate (RSA) is a special inhomogeneous multiphase geomaterial. It is crucial for stability of engineering by study of RSA mesodamage characteristic. This paper aims at investigating the porosity evolution characteristics of RSA by X-ray computed tomography (CT) under uniaxial compressive loading. X-ray tomography images were used to extract defects of RSA specimen under different compressive loading. In this paper, we proposed an improved Ostu method to calibrate the beam hardening phenomenon which is caused by X-ray. Also, based on this Ostu method, the outline of rock blocks in RSA is extracted, and the double gray level threshold of soil and rock block is obtained to ensure the reliability of the porosity calculation. We can conclude that the main reason of RSA cracking is the elasticity mismatch between rock blocks and soil, and the porosity evolution of RSA can be divided into four typical stages. These results may be useful to reveal the mesoscopic cracking mechanism and establish mesodamage evolution equation and constitutive relation for RSA. Yanfang Wu, Xiao Li, Yu Wang, and Bo Zhang Copyright © 2014 Yanfang Wu et al. All rights reserved. Particle Swarm Optimization Based on Local Attractors of Ordinary Differential Equation System Tue, 26 Aug 2014 07:22:29 +0000 http://www.hindawi.com/journals/ddns/2014/628357/ Particle swarm optimization (PSO) is inspired by sociological behavior. In this paper, we interpret PSO as a finite difference scheme for solving a system of stochastic ordinary differential equations (SODE). In this framework, the position points of the swarm converge to an equilibrium point of the SODE and the local attractors, which are easily defined by the present position points, also converge to the global attractor. Inspired by this observation, we propose a class of modified PSO iteration methods (MPSO) based on local attractors of the SODE. The idea of MPSO is to choose the next update state near the present local attractor, rather than the present position point as in the original PSO, according to a given probability density function. In particular, the quantum-behaved particle swarm optimization method turns out to be a special case of MPSO by taking a special probability density function. The MPSO methods with six different probability density functions are tested on a few benchmark problems. These MPSO methods behave differently for different problems. Thus, our framework not only gives an interpretation for the ordinary PSO but also, more importantly, provides a warehouse of PSO-like methods to choose from for solving different practical problems. Wenyu Yang, Wei Wu, Yetian Fan, and Zhengxue Li Copyright © 2014 Wenyu Yang et al. All rights reserved. On Ulam’s Type Stability of the Linear Equation and Related Issues Mon, 25 Aug 2014 07:25:10 +0000 http://www.hindawi.com/journals/ddns/2014/536791/ This is a survey paper concerning stability results for the linear functional equation in single variable. We discuss issues that have not been considered or have been treated only briefly in other surveys concerning stability of the equation. In this way, we complement those surveys. Janusz Brzdęk, Krzysztof Ciepliński, and Zbigniew Leśniak Copyright © 2014 Janusz Brzdęk et al. All rights reserved. Macroscopic Model and Simulation Analysis of Air Traffic Flow in Airport Terminal Area Mon, 25 Aug 2014 05:36:40 +0000 http://www.hindawi.com/journals/ddns/2014/741654/ We focus on the spatiotemporal characteristics and their evolvement law of the air traffic flow in airport terminal area to provide scientific basis for optimizing flight control processes and alleviating severe air traffic conditions. Methods in this work combine mathematical derivation and simulation analysis. Based on cell transmission model the macroscopic models of arrival and departure air traffic flow in terminal area are established. Meanwhile, the interrelationship and influential factors of the three characteristic parameters as traffic flux, density, and velocity are presented. Then according to such models, the macro emergence of traffic flow evolution is emulated with the NetLogo simulation platform, and the correlativity of basic traffic flow parameters is deduced and verified by means of sensitivity analysis. The results suggest that there are remarkable relations among the three characteristic parameters of the air traffic flow in terminal area. Moreover, such relationships evolve distinctly with the flight procedures, control separations, and ATC strategies. Honghai Zhang, Yan Xu, Lei Yang, and Hao Liu Copyright © 2014 Honghai Zhang et al. All rights reserved. Intuitionistic Fuzzy Planar Graphs Sun, 24 Aug 2014 05:44:48 +0000 http://www.hindawi.com/journals/ddns/2014/397823/ Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs. Noura Alshehri and Muhammad Akram Copyright © 2014 Noura Alshehri and Muhammad Akram. All rights reserved. A Note on the Rate of Strong Convergence for Weighted Sums of Arrays of Rowwise Negatively Orthant Dependent Random Variables Wed, 20 Aug 2014 06:38:01 +0000 http://www.hindawi.com/journals/ddns/2014/368702/ Let be an array of rowwise negatively orthant dependent (NOD) random variables. The authors discuss the rate of strong convergence for weighted sums of arrays of rowwise NOD random variables and solve an open problem posed by Huang and Wang (2012). Qingxia Zhang and Dingcheng Wang Copyright © 2014 Qingxia Zhang and Dingcheng Wang. All rights reserved. Heterogeneous Fundamentalists in a Continuous Time Model with Delays Wed, 20 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/959514/ We develop a continuous time model with heterogeneous fundamentalists, imitators, and discrete time delays. We show that nonlinear dynamic phenomena, such as coexistence of attractors and local and global bifurcations, occur due to the existence of a time gap in the process of adjustment of market prices. Luca Gori, Luca Guerrini, and Mauro Sodini Copyright © 2014 Luca Gori et al. All rights reserved. Multiple-Decision Procedures for Testing the Homogeneity of Mean for Exponential Distributions Tue, 19 Aug 2014 09:04:27 +0000 http://www.hindawi.com/journals/ddns/2014/701074/ In multiple-decision procedures, a crucial objective is to determine the association between the probability of a correct decision (CD) and the sample size. A review of some methods is provided, including a subset selection formulation proposed by Huang and Panchapakesan, a multidecision procedure for testing the homogeneity of means by Huang and Lin, and a similar procedure for testing the homogeneity of variances by Lin and Huang. In this paper, we focus on the use of the Lin and Huang method for testing the null hypothesis of homogeneity of means for exponential distributions. We discuss the decision rule , evaluation of the critical value , and the infimum of for independent random samples from exponential distributions. In addition, we also observed that a lower bound for the probability of CD relative to the number of the common sample size is determined based on the desired probability of CD when the largest mean is sufficiently larger than the other means. We explain the results by using two examples. Han-Ching Chen, Her Pei Shan, and Nae-Sheng Wang Copyright © 2014 Han-Ching Chen et al. All rights reserved. Monotone Iterative Technique and Symmetric Positive Solutions to Fourth-Order Boundary Value Problem with Integral Boundary Conditions Mon, 18 Aug 2014 12:06:27 +0000 http://www.hindawi.com/journals/ddns/2014/583875/ The purpose of this paper is to investigate the existence of symmetric positive solutions for a class of fourth-order boundary value problem: , , , , where , . By using a monotone iterative technique, we prove that the above boundary value problem has symmetric positive solutions under certain conditions. In particular, these solutions are obtained via the iteration procedures. Huihui Pang and Chen Cai Copyright © 2014 Huihui Pang and Chen Cai. All rights reserved. Rumor-Propagation Model with Consideration of Refutation Mechanism in Homogeneous Social Networks Mon, 18 Aug 2014 08:55:55 +0000 http://www.hindawi.com/journals/ddns/2014/659273/ In recent years, increasing attention has been paid to how to effectively manage rumor propagation. Based on previous studies of rumor propagation and some strategies used by the authorities to refute rumors and manage rumor propagation, we develop a new rumor-propagation model with consideration of refutation mechanism. In this paper, we describe the dynamic process of rumor propagation by accounting for the refutation mechanism in homogeneous social networks. And then, we derive mean-field equations for rumor-propagation process. We then analyze the stability of the model with respect to changes in parameter values. Our results show that there exists a critical threshold that is inversely proportional to the average degree of the social networks and is positively correlated with the strength of the refutation mechanism. If the spreading rate is bigger than the critical threshold , rumors can be spread. Our numerical simulations in homogeneous networks demonstrate that increasing the ignorant’s refutation rate can reduce the peak value of spreaders density, which is better than increasing the spreader’s refutation rate . Therefore, based on the seriousness of the rumor propagation and the rumor-propagation rate, the authorities can choose effective strategies that increase the refutation rate so that they can reduce the maximum influence of the rumor. Laijun Zhao, Xiaoli Wang, Jiajia Wang, Xiaoyan Qiu, and Wanlin Xie Copyright © 2014 Laijun Zhao et al. All rights reserved. Positive Switched System Approach to Traffic Signal Control for Oversaturated Intersection Sun, 17 Aug 2014 11:04:44 +0000 http://www.hindawi.com/journals/ddns/2014/381567/ The online traffic signalization for intersection is addressed. A new model for intersection called positive switched system is presented. Then, based on the dissipativity analysis results for positive switched system, an online state-feedback control strategy for traffic signal in two-phase intersection section is proposed. A numerical example is provided to illustrate the effectiveness of our theoretical findings. Finally, in order to extend to more general cases, multiphase intersection is considered, and general dissipativity-based control is presented. Lin Du and Yun Zhang Copyright © 2014 Lin Du and Yun Zhang. All rights reserved. Existence of Positive Periodic Solutions for -Dimensional Nonautonomous System Sun, 17 Aug 2014 08:07:10 +0000 http://www.hindawi.com/journals/ddns/2014/268418/ In this paper we consider the existence, multiplicity, and nonexistence of positive periodic solutions for n-dimensional nonautonomous functional differential system , where are -periodic in and there exist -periodic functions such that for all with and , exist for ; are -periodic functions and , for ; is an -periodic function. We show that the system has multiple or no positive -periodic solutions for sufficiently large or small , respectively. Youjun Liu, Huanhuan Zhao, and Jurang Yan Copyright © 2014 Youjun Liu et al. All rights reserved. Fractional Order Stochastic Differential Equation with Application in European Option Pricing Wed, 13 Aug 2014 07:03:29 +0000 http://www.hindawi.com/journals/ddns/2014/621895/ Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE) model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function) in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study. Qing Li, Yanli Zhou, Xinquan Zhao, and Xiangyu Ge Copyright © 2014 Qing Li et al. All rights reserved. Ananlysis of Carbon Emission Reduction and Power Dominance between Single Manufacturer and Single Retailer in Regulatory Cap and Trade System Mon, 11 Aug 2014 11:39:40 +0000 http://www.hindawi.com/journals/ddns/2014/523451/ In the cap and trade system, the paper analyses the Stackelberg game between the power asymmetrical retailer and manufacturer and designs a side-payment self-enforcing contract to resolve some arguments that the existing research overemphasizes spontaneity of participation in side-payment contracts design based on supply chain coordination and does not consider rationality and fairness of allocation of profit increment. Also, the numerical analysis was given. The research shows some important conclusions: in the supply chain, the dominant manufacturer is not able to encourage the retailer to improve its promotion level by increasing its carbon cutting level, but the optimal emission reduction level increases with the dominant retailer’s promotion level; the optimal promotion level, emission reduction, and product demand in a retailer leading supply chain are higher than those in a supply chain dominated by manufacturer; with the new side-payment self-enforcing contract, decentralized decision according to individual rationality incurs a collective reason effect in the centralized setting. Liang-jie Xia and Hua-wei Zhi Copyright © 2014 Liang-jie Xia and Hua-wei Zhi. All rights reserved. A Method to Transit the Rotor-to-Stator Rubbing to Normal Motion Using the Phase Characteristic Mon, 11 Aug 2014 08:01:46 +0000 http://www.hindawi.com/journals/ddns/2014/247691/ A method is proposed to transit the rotor-to-stator rubbing to no-rub motion through active auxiliary bearing. The key point of this technique is to express the attractive domain of no-rub motion based on the phase characteristic and to represent the desired status. The feedback actuation is applied by an active auxiliary bearing to drive the rotor approaching the desired status. After that, the control actuation is turned off. Although the desired status is still in rubbing, it is in the attractive domain of no-rub motion, and the response of the rotor is automatically attracted to no-rub motion. Jieqiong Xu, Qunhong Li, and Shimin Wang Copyright © 2014 Jieqiong Xu et al. All rights reserved. Dynamic CGE Model and Simulation Analysis on the Impact of Citizenization of Rural Migrant Workers on the Labor and Capital Markets in China Mon, 11 Aug 2014 06:10:33 +0000 http://www.hindawi.com/journals/ddns/2014/351947/ This paper investigates the effect of the policy of citizenization of rural migrant workers on the factor market in a dynamic CGE model, which contains multiple dimensions of labor heterogeneity, a labor-lagged adjustment mechanism, and a dynamic investment mechanism. The simulation results show that changes in supply in the labor market will affect the labor market structure, the relative factor price, and the investment in and the output of industries. Qi Wu and Hao Xiao Copyright © 2014 Qi Wu and Hao Xiao. All rights reserved. Discrete Weighted Pseudo Asymptotic Periodicity of Second Order Difference Equations Sun, 10 Aug 2014 13:28:42 +0000 http://www.hindawi.com/journals/ddns/2014/949487/ We define the concept of discrete weighted pseudo--asymptotically periodic function and prove some basic results including composition theorem. We investigate the existence, and uniqueness of discrete weighted pseudo--asymptotically periodic solution to nonautonomous semilinear difference equations. Furthermore, an application to scalar second order difference equations is given. The working tools are based on the exponential dichotomy theory and fixed point theorem. Zhinan Xia Copyright © 2014 Zhinan Xia. All rights reserved. Linear Control of Fractional-Order Financial Chaotic Systems with Input Saturation Wed, 06 Aug 2014 08:51:36 +0000 http://www.hindawi.com/journals/ddns/2014/802429/ In this paper, control of fractional-order financial chaotic systems with saturated control input is investigated by means of state-feedback control method. The saturation problem is tackled by using Gronwall-Bellman lemma and a memoryless nonlinearity function. Based on Gronwall inequality and Laplace transform technique, two sufficient conditions are achieved for the asymptotical stability of the fractional-order financial chaotic systems with fractional orders 0 < α ≤ 1 and 1 < α < 2, respectively. Finally, simulation studies are carried out to show the effectiveness of the proposed linear control method. Junhai Luo, Guanjun Li, and Heng Liu Copyright © 2014 Junhai Luo et al. All rights reserved. A Proposal to the Study of Contractions in Quasi-Metric Spaces Wed, 06 Aug 2014 08:19:35 +0000 http://www.hindawi.com/journals/ddns/2014/269286/ We investigate the existence and uniqueness of a fixed point of an operator via simultaneous functions in the setting of complete quasi-metric spaces. Our results generalize and improve several recent results in literature. Hamed H. Alsulami, Erdal Karapınar, Farshid Khojasteh, and Antonio-Francisco Roldán-López-de-Hierro Copyright © 2014 Hamed H. Alsulami et al. All rights reserved. Coordinating Three-Level Supply Chain by Revenue-Sharing Contract with Sales Effort Dependent Demand Tue, 05 Aug 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/561081/ Revenue-sharing contract is a kind of mechanism to improve performance or to achieve perfect coordination of supply chain. Considering a three-level supply chain consisting of a manufacturer, a distributor, and a retailer who faces a stochastic and sales effort dependent demand, the paper analyzes the impact of sales effort on supply chain coordination and expounds the reasons why traditional revenue-sharing contract cannot coordinate supply chain in this condition. Given three cases: only the retailer bears the sales effort cost, only the manufacturer bears the sales effort cost, and the retailer bears the sales effort cost with the manufacturer, the paper proposes an improved revenue-sharing contract based on quantity discount policy to coordinate the supply chain. It illustrates that improved revenue sharing contract can coordinate supply chain by implementing it in one transaction or two transactions of three-level supply chain. The model of improved revenue-sharing contract is optimized, respectively, by addition form and multiplication form with sales effort dependent demand. Formulas are given to determine the optimal contract parameters. Finally, numerical experiments are given to test the accuracy of the model of improved revenue-sharing contract. Qinghua Pang, Yuer Chen, and Yulu Hu Copyright © 2014 Qinghua Pang et al. All rights reserved. The Oscillation of a Class of the Fractional-Order Delay Differential Equations Sun, 03 Aug 2014 08:49:36 +0000 http://www.hindawi.com/journals/ddns/2014/272198/ Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used. Qianli Lu and Feng Cen Copyright © 2014 Qianli Lu and Feng Cen. All rights reserved. Stability Analysis of a System of Exponential Difference Equations Thu, 24 Jul 2014 08:08:56 +0000 http://www.hindawi.com/journals/ddns/2014/375890/ We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: , , where the parameters , and for and initial conditions , and are positive real numbers. Furthermore, by constructing a discrete Lyapunov function, we obtain the global asymptotic stability of the positive equilibrium. Some numerical examples are given to verify our theoretical results. Q. Din, K. A. Khan, and A. Nosheen Copyright © 2014 Q. Din et al. All rights reserved. Note on the Persistence of a Nonautonomous Lotka-Volterra Competitive System with Infinite Delay and Feedback Controls Thu, 24 Jul 2014 07:03:03 +0000 http://www.hindawi.com/journals/ddns/2014/682769/ We study a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls. We establish a series of criteria under which a part of -species of the systems is driven to extinction while the remaining part of the species is persistent. Particularly, as a special case, a series of new sufficient conditions on the persistence for all species of system are obtained. Several examples together with their numerical simulations show the feasibility of our main results. Chunling Shi, Yiqin Wang, Xiaoying Chen, and Yuli Chen Copyright © 2014 Chunling Shi et al. All rights reserved. Improvement of Power Flow Calculation with Optimization Factor Based on Current Injection Method Thu, 24 Jul 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/437567/ This paper presents an improvement in power flow calculation based on current injection method by introducing optimization factor. In the method proposed by this paper, the PQ buses are represented by current mismatches while the PV buses are represented by power mismatches. It is different from the representations in conventional current injection power flow equations. By using the combined power and current injection mismatches method, the number of the equations required can be decreased to only one for each PV bus. The optimization factor is used to improve the iteration process and to ensure the effectiveness of the improved method proposed when the system is ill-conditioned. To verify the effectiveness of the method, the IEEE test systems are tested by conventional current injection method and the improved method proposed separately. Then the results are compared. The comparisons show that the optimization factor improves the convergence character effectively, especially that when the system is at high loading level and R/X ratio, the iteration number is one or two times less than the conventional current injection method. When the overloading condition of the system is serious, the iteration number in this paper appears 4 times less than the conventional current injection method. Lei Wang, Chen Chen, and Tao Shen Copyright © 2014 Lei Wang et al. All rights reserved. Research on MAS-Based Supply Chain Resilience and Its Self-Organized Criticality Wed, 23 Jul 2014 11:40:12 +0000 http://www.hindawi.com/journals/ddns/2014/621341/ Building resilient supply chain is an effective way to deal with uncertain risks. First, by analyzing the self-organization of supply chain, the supply chain resilience is described as a macroscopic property that generates from self-organizing behavior of each enterprise on the microlevel. Second, a MAS-based supply chain resilience model is established and its local fitness function, neighborhood structure, and interaction rules that are applicable to supply chain system are designed through viewing the enterprise as an agent. Finally, with the help of a case, we find that there is an agglomeration effect and a SOC characteristic in supply chain and the evolution of supply chain is controlled by parameters of MAS. Managers can control the supply chain within the resilient range and choose a good balance between interest and risk by controlling enterprises’ behavior. Liang Geng, Renbin Xiao, and Xing Xu Copyright © 2014 Liang Geng et al. All rights reserved. Functional Principal Components Analysis of Shanghai Stock Exchange 50 Index Tue, 22 Jul 2014 11:35:22 +0000 http://www.hindawi.com/journals/ddns/2014/365204/ The main purpose of this paper is to explore the principle components of Shanghai stock exchange 50 index by means of functional principal component analysis (FPCA). Functional data analysis (FDA) deals with random variables (or process) with realizations in the smooth functional space. One of the most popular FDA techniques is functional principal component analysis, which was introduced for the statistical analysis of a set of financial time series from an explorative point of view. FPCA is the functional analogue of the well-known dimension reduction technique in the multivariate statistical analysis, searching for linear transformations of the random vector with the maximal variance. In this paper, we studied the monthly return volatility of Shanghai stock exchange 50 index (SSE50). Using FPCA to reduce dimension to a finite level, we extracted the most significant components of the data and some relevant statistical features of such related datasets. The calculated results show that regarding the samples as random functions is rational. Compared with the ordinary principle component analysis, FPCA can solve the problem of different dimensions in the samples. And FPCA is a convenient approach to extract the main variance factors. Zhiliang Wang, Yalin Sun, and Peng Li Copyright © 2014 Zhiliang Wang et al. All rights reserved. Analysis on the Impact of the Fluctuation of the International Gold Prices on the Chinese Gold Stocks Mon, 21 Jul 2014 12:02:07 +0000 http://www.hindawi.com/journals/ddns/2014/308626/ Five gold stocks in Chinese Shanghai and Shenzhen A-share and Comex gold futures are chosen to form the sample, for the purpose of analysing the impact of the fluctuation of the international gold prices on the gold stocks in Chinese Shanghai and Shenzhen A-share. Using the methods of unit root test, Granger causality test, VAR model, and impulse response function, this paper has analysed the relationship between the price change of the international gold futures and the price fluctuation of gold stocks in Chinese Shanghai and Shenzhen comprehensively. The results suggest the fluctuation of the international gold futures has a strong influence on the domestic futures. Jiankang Jin, Chen Jie, and Quanda Zhang Copyright © 2014 Jiankang Jin et al. All rights reserved. Lyapunov Functions for a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate and Varying Population Sizes Mon, 21 Jul 2014 08:44:34 +0000 http://www.hindawi.com/journals/ddns/2014/472746/ We investigate the dynamical behaviors of a class of discrete SIRS epidemic models with nonlinear incidence rate and varying population sizes. The model is required to possess different death rates for the susceptible, infectious, recovered, and constant recruitment into the susceptible class, infectious class, and recovered class, respectively. By using the inductive method, the positivity and boundedness of all solutions are obtained. Furthermore, by constructing new discrete type Lyapunov functions, the sufficient and necessary conditions on the global asymptotic stability of the disease-free equilibrium and endemic equilibrium are established. Ying Wang, Zhidong Teng, and Mehbuba Rehim Copyright © 2014 Ying Wang et al. All rights reserved.