Discrete Dynamics in Nature and Society http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. A Dufort-Frankel Difference Scheme for Two-Dimensional Sine-Gordon Equation Wed, 29 Oct 2014 09:08:21 +0000 http://www.hindawi.com/journals/ddns/2014/784387/ A standard Crank-Nicolson finite-difference scheme and a Dufort-Frankel finite-difference scheme are introduced to solve two-dimensional damped and undamped sine-Gordon equations. The stability and convergence of the numerical methods are considered. To avoid solving the nonlinear system, the predictor-corrector techniques are applied in the numerical methods. Numerical examples are given to show that the numerical results are consistent with the theoretical results. Zongqi Liang, Yubin Yan, and Guorong Cai Copyright © 2014 Zongqi Liang et al. All rights reserved. Sampled-Data Consensus for High-Order Multiagent Systems under Fixed and Randomly Switching Topology Wed, 22 Oct 2014 11:26:58 +0000 http://www.hindawi.com/journals/ddns/2014/598965/ This paper studies the sampled-data based consensus of multiagent system with general linear time-invariant dynamics. It focuses on looking for a maximum allowable sampling period bound such that as long as the sampling period is less than this bound, there always exist linear consensus protocols solving the consensus problem. Both fixed and randomly switching topologies are considered. For systems under fixed topology, a necessary and sufficient sampling period bound is obtained for single-input multiagent systems, and a sufficient allowable bound is proposed for multi-input systems by solving the optimal control problem of certain system with uncertainty. For systems under randomly switching topologies, tree-type and complete broadcasting network with Bernoulli packet losses are discussed, and explicit allowable sampling period bounds are, respectively, given based on the unstable eigenvalues of agent’s system matrix and packet loss probability. Numerical examples are given to illustrate the results. Niu Jie and Li Zhong Copyright © 2014 Niu Jie and Li Zhong. All rights reserved. A Constrained Algorithm Based NMFα for Image Representation Wed, 22 Oct 2014 07:57:08 +0000 http://www.hindawi.com/journals/ddns/2014/179129/ Nonnegative matrix factorization (NMF) is a useful tool in learning a basic representation of image data. However, its performance and applicability in real scenarios are limited because of the lack of image information. In this paper, we propose a constrained matrix decomposition algorithm for image representation which contains parameters associated with the characteristics of image data sets. Particularly, we impose label information as additional hard constraints to the α-divergence-NMF unsupervised learning algorithm. The resulted algorithm is derived by using Karush-Kuhn-Tucker (KKT) conditions as well as the projected gradient and its monotonic local convergence is proved by using auxiliary functions. In addition, we provide a method to select the parameters to our semisupervised matrix decomposition algorithm in the experiment. Compared with the state-of-the-art approaches, our method with the parameters has the best classification accuracy on three image data sets. Chenxue Yang, Tao Li, Mao Ye, Zijian Liu, and Jiao Bao Copyright © 2014 Chenxue Yang et al. All rights reserved. Uniform Attractor for the Fractional Nonautonomous Long-Short Wave Equations Mon, 20 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/712183/ We firstly proved the existence and the uniqueness of the solution for the -periodic fractional nonautonomous long-short wave equations with translation compact force by using Galerkin method and then obtained the compact uniform attractor of the system. Huanmin Ge and Jie Xin Copyright © 2014 Huanmin Ge and Jie Xin. All rights reserved. An Allometric Algorithm for Fractal-Based Cobb-Douglas Function of Geographical Systems Mon, 20 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/910457/ The generalized Cobb-Douglas production function has been derived from a general input-output relation based on fractality assumptions. It was proved to be a useful self-affine model for geographical analysis. However, the ordinary least square calculation is always an ineffectual method for the Cobb-Douglas modeling because of the multicollinearity in the logarithmic linear regression. In this paper, a novel approach is proposed to build the geographical Cobb-Douglas models. Combining the concept of allometric scaling with the linear regression technique, we obtain a simple algorithm that can be employed to estimate the parameters of the Cobb-Douglas function. As a case, the algorithm and models are applied to the public transportation of China’s cities, and the results validate the allometric algorithm. A conclusion can be drawn that the allometric analysis is an effective way of modeling geographical systems with the general Cobb-Douglas function. This study is significant for integrating the notions of allometry, fractals, and scaling into a new framework to form a quantitative methodology of spatial analysis. Hongyu Luo and Yanguang Chen Copyright © 2014 Hongyu Luo and Yanguang Chen. All rights reserved. Damping Coefficient Induces Stochastic Multiresonance in Bistable System with Asymmetric Dichotomous Noise Sun, 19 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/850361/ Stochastic resonance (SR) and stochastic multiresonance (SMR) phenomena as a function of the underdamping and overdamping coefficients in bistable system with asymmetric dichotomous noise are investigated numerically. By the efficient numerical simulation of the asymmetric dichotomous noise and the fourth-order Runge-Kutta algorithm, we calculate the system responses, the averaged power spectrum, and the signal-noise-ratio (SNR) that can be a measure of the existence of SR and SMR phenomenon. And the effects of damping coefficients on the three characteristics are analyzed. Firstly, it is found that the periodic asymmetric distribution of the particle’s hopping between two potential wells in the system response is gradually weakened as underdamping coefficient is increased to overdamping coefficient. And it also displays the periodic asymmetric distribution under the circumstance of overdamping coefficient. Then the averaged power spectrum exhibits multiple sharp peaks, and the highest peak increases and decreases for underdamping coefficient which is added to overdamping coefficient. Finally, SNR versus the damping coefficient for the system parameters and the noise parameters are acquired and they show multiple peaks and valleys, which illustrates the obvious SMR phenomena in bistable system with asymmetric dichotomous noise. Juan Wu and Yong Xu Copyright © 2014 Juan Wu and Yong Xu. All rights reserved. On a -Analogue of the Elzaki Transform Called Mangontarum -Transform Mon, 13 Oct 2014 08:41:59 +0000 http://www.hindawi.com/journals/ddns/2014/825618/ Two -analogues of the Elzaki transform, called Mangontarum -transforms, are introduced in this paper. Properties such as the transforms of -trigonometric functions, transform of -derivatives, duality relation, convolution identity, -derivative of transforms, and transform of the Heaviside function are derived and presented. Moreover, we will consider applications of the Mangontarum -transform of the first kind to some ordinary -differential equations with initial values. Mahid M. Mangontarum Copyright © 2014 Mahid M. Mangontarum. All rights reserved. Extremal Solutions to Periodic Boundary Value Problem of Nabla Integrodifferential Equation of Volterra Type on Time Scales Mon, 13 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/205659/ We firstly establish some new theorems on time scales, and then, by employing them together with a new comparison result and the monotone iterative technique, we show the existence of extremal solutions to the following nabla integrodifferential periodic boundary value problem: ,  , where is a time scale. Yunlong Shi and Junfang Zhao Copyright © 2014 Yunlong Shi and Junfang Zhao. All rights reserved. Correlation and Spectral Properties of a Coupled Nonlinear Dynamical System in the Context of Numerical Weather Prediction and Climate Modeling Sun, 12 Oct 2014 12:17:55 +0000 http://www.hindawi.com/journals/ddns/2014/498184/ Complex dynamical processes occurring in the earth’s climate system are strongly nonlinear and exhibit wave-like oscillations within broad time-space spectrum. One way to imitate essential features of such processes is using a coupled nonlinear dynamical system, obtained by coupling two versions of the well-known Lorenz (1963) model with distinct time scales that differ by a certain time-scale factor. This dynamical system is frequently applied for studying various aspects of atmospheric and climate dynamics, as well as for estimating the effectiveness of numerical algorithms and techniques used in numerical weather prediction, data assimilation, and climate simulation. This paper examines basic dynamic, correlative, and spectral properties of this system and quantifies the influence of the coupling strength on power spectrum densities, spectrograms, and autocorrelation functions. Sergei Soldatenko and Denis Chichkine Copyright © 2014 Sergei Soldatenko and Denis Chichkine. All rights reserved. Behavior of an Exponential System of Difference Equations Mon, 15 Sep 2014 11:45:30 +0000 http://www.hindawi.com/journals/ddns/2014/607281/ We study the qualitative behavior of the following exponential system of rational difference equations:  = /,   = /,   =  where , , , , , and and initial conditions , , , and are positive real numbers. More precisely, we investigate the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions that converges to unique positive equilibrium point of the system. Some numerical examples are given to verify our theoretical results. A. Q. Khan and M. N. Qureshi Copyright © 2014 A. Q. Khan and M. N. Qureshi. All rights reserved. Modified Differential Transform Method for Solving the Model of Pollution for a System of Lakes Mon, 15 Sep 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/645726/ This work presents the application of the differential transform method (DTM) to the model of pollution for a system of three lakes interconnected by channels. Three input models (periodic, exponentially decaying, and linear) are solved to show that DTM can provide analytical solutions of pollution model in convergent series form. In addition, we present the posttreatment of the power series solutions with the Laplace-Padé resummation method as a useful strategy to extend the domain of convergence of the approximate solutions. The Fehlberg fourth-fifth order Runge-Kutta method with degree four interpolant (RKF45) numerical solution of the lakes system problem is used as a reference to compare with the analytical approximations showing the high accuracy of the results. The main advantage of the proposed technique is that it is based on a few straightforward steps and does not generate secular terms or depend of a perturbation parameter. Brahim Benhammouda, Hector Vazquez-Leal, and Luis Hernandez-Martinez Copyright © 2014 Brahim Benhammouda et al. All rights reserved. Left-Turning Vehicle Trajectory Modeling and Guide Line Setting at the Intersection Wed, 03 Sep 2014 09:16:25 +0000 http://www.hindawi.com/journals/ddns/2014/950219/ When left-turning vehicles are released from the multiple left-turning lanes at the signalized intersection, there will be conflicts among them, and the conflicts will affect the traffic operation and safety. In order to solve the problem, by extracting running trajectories of left-turning vehicles and analyzing distribution characteristics of trajectories, velocity changing characteristics, and flow changing characteristics, the left-turning vehicle’s trajectory model was established. On the basis of the above research, taking an example of quadruple left-turning lanes, the idea of setting left-turning guide line at the intersection was proposed. Through instance verification, we could get the conclusion that the method of using left-turning guide line to control vehicles’ turning process can effectively reduce traffic conflicts and delay and improve traffic efficiency. Fulu Wei, Weiwei Guo, Xin Liu, Chunyan Liang, and Tianjun Feng Copyright © 2014 Fulu Wei et al. All rights reserved. Torque Split Strategy for Parallel Hybrid Electric Vehicles with an Integrated Starter Generator Wed, 03 Sep 2014 07:25:43 +0000 http://www.hindawi.com/journals/ddns/2014/793864/ This paper presents a torque split strategy for parallel hybrid electric vehicles with an integrated starter generator (ISG-PHEV) by using fuzzy logic control. By combining the efficiency map and the optimum torque curve of the internal combustion engine (ICE) with the state of charge (SOC) of the batteries, the torque split strategy is designed, which manages the ICE within its peak efficiency region. Taking the quantified ICE torque, the quantified SOC of the batteries, and the quantified ICE speed as inputs, and regarding the output torque demanded on the ICE as an output, a fuzzy logic controller (FLC) with relevant fuzzy rules has been developed to determine the optimal torque distribution among the ICE, the ISG, and the electric motor/generator (EMG) effectively. The simulation results reveal that, compared with the conventional torque control strategy which uses rule-based controller (RBC) in different driving cycles, the proposed FLC improves the fuel economy of the ISG-PHEV, increases the efficiency of the ICE, and maintains batteries SOC within its operation range more availably. Zhumu Fu, Aiyun Gao, Xiaohong Wang, and Xiaona Song Copyright © 2014 Zhumu Fu et al. All rights reserved. Efficient Iterative Methods with and without Memory Possessing High Efficiency Indices Wed, 03 Sep 2014 06:03:53 +0000 http://www.hindawi.com/journals/ddns/2014/912796/ Two families of derivative-free methods without memory for approximating a simple zero of a nonlinear equation are presented. The proposed schemes have an accelerator parameter with the property that it can increase the convergence rate without any new functional evaluations. In this way, we construct a method with memory that increases considerably efficiency index from to . Numerical examples and comparison with the existing methods are included to confirm theoretical results and high computational efficiency. T. Lotfi, F. Soleymani, Z. Noori, A. Kılıçman, and F. Khaksar Haghani Copyright © 2014 T. Lotfi et al. All rights reserved. Hierarchical Artificial Bee Colony Optimizer with Divide-and-Conquer and Crossover for Multilevel Threshold Image Segmentation Tue, 02 Sep 2014 13:23:49 +0000 http://www.hindawi.com/journals/ddns/2014/941534/ This paper presents a novel optimization algorithm, namely, hierarchical artificial bee colony optimization (HABC), for multilevel threshold image segmentation, which employs a pool of optimal foraging strategies to extend the classical artificial bee colony framework to a cooperative and hierarchical fashion. In the proposed hierarchical model, the higher-level species incorporates the enhanced information exchange mechanism based on crossover operator to enhance the global search ability between species. In the bottom level, with the divide-and-conquer approach, each subpopulation runs the original ABC method in parallel to part-dimensional optimum, which can be aggregated into a complete solution for the upper level. The experimental results for comparing HABC with several successful EA and SI algorithms on a set of benchmarks demonstrated the effectiveness of the proposed algorithm. Furthermore, we applied the HABC to the multilevel image segmentation problem. Experimental results of the new algorithm on a variety of images demonstrated the performance superiority of the proposed algorithm. Maowei He, Kunyuan Hu, Yunlong Zhu, Lianbo Ma, Hanning Chen, and Yan Song Copyright © 2014 Maowei He et al. All rights reserved. Set of Oscillation Criteria for Second Order Nonlinear Forced Differential Equations with Damping Tue, 02 Sep 2014 12:29:51 +0000 http://www.hindawi.com/journals/ddns/2014/545189/ By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second order nonlinear forced differential equation with damping. These results extend, improve, and unify some known oscillation criteria in the existing literature. Ambarka Abdalla Salhin, Ummul Khair Salma Din, Rokiah Rozita Ahmad, and Mohd Salmi Md Noorani Copyright © 2014 Ambarka Abdalla Salhin et al. All rights reserved. How Do Sociodemographics and Activity Participations Affect Activity-Travel? Comparative Study between Women and Men Tue, 02 Sep 2014 12:18:11 +0000 http://www.hindawi.com/journals/ddns/2014/374521/ Activity-travel behaviors of women and men are different because they have different social and household responsibilities. However, studies concerning gender differences are mainly limited in developed countries. This paper concentrates on gender role-based differences in activity-travel behavior in a typical developing country, namely, China. Using data from 3656 cases collected through surveys conducted in Shangyu, data processing, method choice, and descriptive analysis were conducted. Binary and ordered logistic regression models segmented by gender were developed to evaluate the mechanism through which individual sociodemographics, household characteristics, and activity participations affect the number of trip chain types and activities for women and men. The results show that women aged 30 to 50 perform less subsistence activities. However, the difference between the different age groups of men is not as significant. In addition, men with bicycles and electric bicycles have more subsistence and maintenance activities, whereas women do not have these attributes. Moreover, women with children under schooling age make more maintenance trip chains but less leisure trip chains and activities, whereas men are free from this influence. Furthermore, both women and men perform more subsistence activities if the duration increases, and men have less influences than women do. Min Yang, Wei Wang, Feifei Yu, and Jian Ding Copyright © 2014 Min Yang et al. All rights reserved. Global Dynamics of Infectious Disease with Arbitrary Distributed Infectious Period on Complex Networks Mon, 01 Sep 2014 12:49:21 +0000 http://www.hindawi.com/journals/ddns/2014/161509/ Most of the current epidemic models assume that the infectious period follows an exponential distribution. However, due to individual heterogeneity and epidemic diversity, these models fail to describe the distribution of infectious periods precisely. We establish a SIS epidemic model with multistaged progression of infectious periods on complex networks, which can be used to characterize arbitrary distributions of infectious periods of the individuals. By using mathematical analysis, the basic reproduction number for the model is derived. We verify that the depends on the average distributions of infection periods for different types of infective individuals, which extend the general theory obtained from the single infectious period epidemic models. It is proved that if , then the disease-free equilibrium is globally asymptotically stable; otherwise the unique endemic equilibrium exists such that it is globally asymptotically attractive. Finally numerical simulations hold for the validity of our theoretical results is given. Xiaoguang Zhang, Rui Song, Gui-Quan Sun, and Zhen Jin Copyright © 2014 Xiaoguang Zhang et al. All rights reserved. An Immunization Strategy Based on Propagation Mechanism Mon, 01 Sep 2014 11:45:02 +0000 http://www.hindawi.com/journals/ddns/2014/971497/ With the ubiquity of smart phones, wearable equipment, and wireless sensors, the topologies of networks composed by them change along with time. The immunization strategies in which network immune nodes are chosen by analyzing the static aggregation network topologies have been challenged. The studies about interaction propagations between two pathogens show that the interaction can change propagation threshold and the final epidemic size of each other, which provides a new thinking of immunization method. The eradication or inhibition of the virus can be achieved through the spread of its opposite party. Here, we put forward an immunization strategy whose implementation does not depend on the analysis of network topology. The immunization agents are randomly placed on a few of individuals of network and spread out from these individuals on network in a propagation method. The immunization agents prevent virus infecting their habitat nodes with certain immune success rate. The analysis and simulation of evolution equation of the model show that immune propagation has a significant impact on the spread threshold and steady-state density of virus on a finite size of BA networks. Simulations on some real-world networks also suggest that the immunization strategy is feasible and effective. Yixin Zhu, Fengli Zhang, and Wenqiang Guo Copyright © 2014 Yixin Zhu et al. All rights reserved. Allocating Freight Empty Cars in Railway Networks with Dynamic Demands Mon, 01 Sep 2014 07:29:41 +0000 http://www.hindawi.com/journals/ddns/2014/349341/ This paper investigates the freight empty cars allocation problem in railway networks with dynamic demands, in which the storage cost, unit transportation cost, and demand in each stage are taken into consideration. Under the constraints of capacity and demand, a stage-based optimization model for allocating freight empty cars in railway networks is formulated. The objective of this model is to minimize the total cost incurred by transferring and storing empty cars in different stages. Moreover, a genetic algorithm is designed to obtain the optimal empty cars distribution strategies in railway networks. Finally, numerical experiments are given to show the effectiveness of the proposed model and algorithm. Ce Zhao, Lixing Yang, and Shukai Li Copyright © 2014 Ce Zhao et al. All rights reserved. Optimal Road Toll Design from the Perspective of Sustainable Development Mon, 01 Sep 2014 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2014/548427/ This paper investigates the optimal road toll design problem from the perspective of sustainable development at network-wide level. In this paper the sustainable development level of transportation system is quantitatively described with the total vehicular emission, total fuel consumption, and total travel time in the network. In order to simultaneously consider the impacts of all these three indicators on sustainability of transportation system, we integrate them into a sustainable development index (SD-index) by a linear combination, and then we establish the corresponding bilevel optimization model. The upper level problem is the network toll design problem to maximize the SD-index from the viewpoint of traffic managers, and the lower level problem is to depict travelers’ route choice behavior under a certain road toll scheme. Finally, a combined genetic algorithm and gradient projection algorithm (GA-GP) is used to solve the bilevel model, in which the GP algorithm solves the traffic assignment problem with road toll scheme in the lower level. In order to verify the proposed model and algorithm, we take the Nguyen-Dupuis network for the numerical example, and the computing results show that the model and algorithm are effective and efficient. Lin Cheng and Fei Han Copyright © 2014 Lin Cheng and Fei Han. All rights reserved. The Role of Constraints in a Segregation Model: The Asymmetric Case Sun, 31 Aug 2014 07:50:52 +0000 http://www.hindawi.com/journals/ddns/2014/569296/ We extend the analysis on the effects of the entry constraints on the dynamics of an adaptive segregation model of Shelling’s type when the two populations involved differ in numerosity, level of tolerance toward members of the other population, and speed of reaction. The model is described by a two-dimensional piecewise smooth dynamical system in discrete time, where the entry constraints represent possible exogenous controls imposed by an authority in order to regulate the maximum number of members of the two populations allowed to enter the system, usually the district in which they live in. In this paper, we investigate the nature of some particular border collision bifurcations and discuss the policy implications of the entry constraints in terms of segregation. The investigation reveals that asymmetries in the level of tolerance of the two populations involved may lead to phenomena of overreaction or overshooting in the adjustment process. In order to avoid the risk of segregation, suitable entry limitations must be imposed at least on the more tolerant population. Davide Radi, Laura Gardini, and Viktor Avrutin Copyright © 2014 Davide Radi et al. 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.