Discrete Dynamics in Nature and Society http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. The Contrast Structures for a Class of Singularly Perturbed Systems with Heteroclinic Orbits Thu, 04 Feb 2016 12:55:45 +0000 http://www.hindawi.com/journals/ddns/2016/6405853/ Singularly perturbed problems are often used as the models of ecology and epidemiology. In this paper, a class of semilinear singularly perturbed systems with contrast structures are discussed. Firstly, we verify the existence of heteroclinic orbits connecting two equilibrium points about the associated systems for contrast structures in the corresponding phase space. Secondly, the asymptotic solutions of the contrast structures by the method of boundary layer functions and smooth connection are constructed. Finally, the uniform validity of the asymptotic expansion is defined and the existence of the smooth solutions is proved. Han Xu and Yinlai Jin Copyright © 2016 Han Xu and Yinlai Jin. All rights reserved. Pinning Controllability Scheme of Directed Complex Delayed Dynamical Networks via Periodically Intermittent Control Thu, 04 Feb 2016 09:16:26 +0000 http://www.hindawi.com/journals/ddns/2016/1585928/ This paper studies the pinning controllability of directed complex delayed dynamical networks by using periodic intermittent control scheme. The general and low-dimensional pinning synchronization criteria are derived to illustrate the design of periodic intermittent control scheme. According to our low-dimensional pinning criterion, especially, the constraint condition of coupling strength is obtained when the network structure and amounts of pinned nodes are fixed. An algorithm is presented to determine the amounts of periodically intermittent controllers and locate these intermittent controllers in a directed network, in which the significance of nodes out- (in-) degree in pinning control of complex network is also illustrated. Finally, a directed network consisting of 12 coupled delayed Chua oscillators is designed as numerical example to verify the effectiveness of the theoretical analysis. Shaolin Li, Jinde Cao, and Yinghui He Copyright © 2016 Shaolin Li et al. All rights reserved. Local Dynamics and Global Stability of Certain Second-Order Rational Difference Equation with Quadratic Terms Mon, 01 Feb 2016 14:15:27 +0000 http://www.hindawi.com/journals/ddns/2016/3716042/ We present a complete local dynamics and investigate the global dynamics of the following second-order difference equation: , where the parameters , and are nonnegative numbers with condition , , and the initial conditions , are arbitrary nonnegative numbers such that S. Jašarević Hrustić, M. R. S. Kulenović, and M. Nurkanović Copyright © 2016 S. Jašarević Hrustić et al. All rights reserved. Robust Synchronization Controller Design for a Class of Uncertain Fractional Order Chaotic Systems Mon, 01 Feb 2016 11:13:00 +0000 http://www.hindawi.com/journals/ddns/2016/2090583/ Synchronization problem for a class of uncertain fractional order chaotic systems is studied. Some fundamental lemmas are given to show the boundedness of a complicated infinite series which is produced by differentiating a quadratic Lyapunov function with fractional order. By using the fractional order extension of the Lyapunov stability criterion and the proposed lemma, stability of the closed-loop system is analyzed, and two sufficient conditions, which can enable the synchronization error to converge to zero asymptotically, are driven. Finally, an illustrative example is presented to confirm the proposed theoretical results. Lin Wang and Chunzhi Yang Copyright © 2016 Lin Wang and Chunzhi Yang. All rights reserved. Quality Assurance Competition Strategy under B2C Platform Thu, 28 Jan 2016 06:29:25 +0000 http://www.hindawi.com/journals/ddns/2016/6587872/ This paper examines the platform competition strategy in offering quality assurance policy based on two-sided B2C markets with buyers and sellers who trade through the B2C platform. We model this as a strategy decision whether control rights of quality assurance level are better held by the seller or by the platform. Whether the seller or the platform that provides quality assurance policy is preferred depends on their influence on network effects. We show that the seller and the platform have no strong intention to improve the quality assurance level in the monopoly markets. When all buyers multihome and all sellers single-home, sellers who hold the control rights of quality assurance are better than platforms. However, platforms that hold quality assurance drive more profits than sellers in the B2C markets where all buyers and all sellers multihome. Our findings connect platform competitive strategies to market and microfoundation of quality, which applies directly to managerial decisions in the B2C two-sided platform. Yunmiao Gui and Bengang Gong Copyright © 2016 Yunmiao Gui and Bengang Gong. All rights reserved. Uncertain Zero-One Law and Convergence of Uncertain Sequence Wed, 27 Jan 2016 13:42:39 +0000 http://www.hindawi.com/journals/ddns/2016/2494583/ This paper is concerned with situations in which the uncertain measure of an event can only be zero or one, and the uncertain zero-one laws are derived within the framework of uncertainty theory that can be seen as the counterpart of Kolmogorov zero-one law and Borel-Cantelli lemma, which can be used as a tool for solving some problems concerning almost sure convergence of uncertain sequence. Zhiqiang Zhang, Weiqi Liu, and Xiumei Chen Copyright © 2016 Zhiqiang Zhang et al. All rights reserved. Dynamics Analysis of a Nutrient-Plankton Model with a Time Delay Wed, 27 Jan 2016 06:11:41 +0000 http://www.hindawi.com/journals/ddns/2016/9797624/ We analyze a nutrient-plankton system with a time delay. We choose the time delay as a bifurcation parameter and investigate the stability of a positive equilibrium and the existence of Hopf bifurcations. By using the center manifold theorem and the normal form theory, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are researched. The theoretical results indicate that the time delay can induce a positive equilibrium to switch from a stable to an unstable to a stable state and so on. Numerical simulations show that the theoretical results are correct and feasible, and the system exhibits rich complex dynamics. Beibei Wang, Min Zhao, Chuanjun Dai, Hengguo Yu, Nan Wang, and Pengfei Wang Copyright © 2016 Beibei Wang et al. All rights reserved. Residential Environment Induced Preference Heterogeneity for River Ecosystem Service Improvements: A Comparison between Urban and Rural Households in the Wei River Basin, China Tue, 26 Jan 2016 09:51:49 +0000 http://www.hindawi.com/journals/ddns/2016/6253915/ This paper assesses residential environment induced preference heterogeneity regarding ecosystem services improvements of a river basin by comparing urban and rural residents’ welfare estimates. In a choice experiment, the ecological improvements are described in terms of several observable ecological indicators set in an experimental design. Given the fact that economic and environmental conditions differ for urban and rural residents in China, the utility they derive from ecological restoration is hypothesized to differ. The urban and rural residents’ survey data were modeled separately using mixed logit models. The results reveal that water quality and water quantity, measured by unit of level improvement and percentage improvement, respectively, hold the highest marginal utility values in all respondents’ models. Urban and rural residents have the same preference regarding expanding soil erosion control areas and landscape improvement. However, they have statistically significant different utility for water quality, water quantity, forest coverage, ecotourism improvements, and reducing soil erosion intensity. Generally, urban residents express a higher implicit price for most of the ecological indicators. The findings imply that policy makers should take existing preference heterogeneity into account in designing ecosystem payment schemes and allocating resources. Hengtong Shi, Minjuan Zhao, Fanus Asefaw Aregay, Kai Zhao, and Zhide Jiang Copyright © 2016 Hengtong Shi et al. All rights reserved. Compound Generalized Function Projective Synchronization for Fractional-Order Chaotic Systems Sun, 24 Jan 2016 14:18:53 +0000 http://www.hindawi.com/journals/ddns/2016/7563416/ A modified function projective synchronization for fractional-order chaotic system, called compound generalized function projective synchronization (CGFPS), is proposed theoretically in this paper. There are one scaling-drive system, more than one base-drive system, and one response system in the scheme of CGFPS, and the scaling function matrices come from multidrive systems. The proposed CGFPS technique is based on the stability theory of fractional-order system. Moreover, we achieve the CGFPS between three-driver chaotic systems, that is, the fractional-order Arneodo chaotic system, the fractional-order Chen chaotic system, and the fractional-order Lu chaotic system, and one response chaotic system, that is, the fractional-order Lorenz chaotic system. Numerical experiments are demonstrated to verify the effectiveness of the CGFPS scheme. Chunde Yang, Hao Cai, and Ping Zhou Copyright © 2016 Chunde Yang et al. All rights reserved. A Review of the Detection Methods for Climate Regime Shifts Sun, 24 Jan 2016 13:18:49 +0000 http://www.hindawi.com/journals/ddns/2016/3536183/ An abrupt climate change means that the climate system shifts from a steady state to another steady state. Study on the phenomenon and theory of the abrupt climate change is a new research field of modern climatology, and it is of great significance for the prediction of future climate change. The climate regime shift is one of the most common forms of abrupt climate change, which mainly refers to the statistical significant changes on the variable of climate system at one time scale. These detection methods can be roughly divided into five categories based on different types of abrupt changes, namely, abrupt mean value change, abrupt variance change, abrupt frequency change, abrupt probability density change, and the multivariable analysis. The main research progress of abrupt climate change detection methods is reviewed. What is more, some actual applications of those methods in observational data are provided. With the development of nonlinear science, many new methods have been presented for detecting an abrupt dynamic change in recent years, which is useful supplement for the abrupt change detection methods. Qunqun Liu, Shiquan Wan, and Bin Gu Copyright © 2016 Qunqun Liu et al. All rights reserved. Modelling the Impact of Media in Controlling the Diseases with a Piecewise Transmission Rate Thu, 21 Jan 2016 13:26:19 +0000 http://www.hindawi.com/journals/ddns/2016/3458965/ An epidemic model with media is proposed to describe the spread of infectious diseases in a given region. A piecewise continuous transmission rate is introduced to describe that the media has its effect when the number of the infected exceeds a certain critical level. Furthermore, it is assumed that the impact of the media on the contact transmission is described by an exponential function. Stability analysis of the model shows that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. On the other hand, when the basic reproduction number is greater than unity, a unique endemic equilibrium exists, which is also globally asymptotically stable. Our analysis implies that media coverage plays an important role in controlling the spread of the disease. Maoxing Liu, Yuting Chang, and Lixia Zuo Copyright © 2016 Maoxing Liu et al. All rights reserved. Stability and Bifurcation Analysis for a Class of Generalized Reaction-Diffusion Neural Networks with Time Delay Tue, 19 Jan 2016 12:29:33 +0000 http://www.hindawi.com/journals/ddns/2016/4321358/ Considering the fact that results for static neural networks are much more scare than results for local field neural networks and our purpose letting the problem researched be more general in many aspects, in this paper, a generalized neural networks model which includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks is built and the stability and bifurcation problems for it are investigated under Neumann boundary conditions. First, by discussing the corresponding characteristic equations, the local stability of the trivial uniform steady state is discussed and the existence of Hopf bifurcations is shown. By using the normal form theory and the center manifold reduction of partial function differential equations, explicit formulae which determine the direction and stability of bifurcating periodic solutions are acquired. Finally, numerical simulations show the results. Tianshi Lv, Qintao Gan, and Qikai Zhu Copyright © 2016 Tianshi Lv et al. All rights reserved. Stabilization of the Fractional-Order Chua Chaotic Circuit via the Caputo Derivative of a Single Input Mon, 18 Jan 2016 12:01:14 +0000 http://www.hindawi.com/journals/ddns/2016/4129756/ A modified fractional-order Chua chaotic circuit is proposed in this paper, and the chaotic attractor is obtained for . Based on the Mittag-Leffler function in two parameters and Gronwall’s Lemma, two control schemes are proposed to stabilize the modified fractional-order Chua chaotic system via the Caputo derivative of a single input. The numerical simulation shows the validity and feasibility of the control scheme. Chunde Yang, Hao Cai, and Ping Zhou Copyright © 2016 Chunde Yang et al. All rights reserved. Positive Solutions of a General Discrete Dirichlet Boundary Value Problem Sun, 17 Jan 2016 16:29:53 +0000 http://www.hindawi.com/journals/ddns/2016/7456937/ A steady state equation of the discrete heat diffusion can be obtained by the heat diffusion of particles or the difference method of the elliptic equations. In this paper, the nonexistence, existence, and uniqueness of positive solutions for a general discrete Dirichlet boundary value problem are considered by using the maximum principle, eigenvalue method, sub- and supersolution technique, and monotone method. All obtained results are new and valid on any -dimension finite lattice point domain. To the best of our knowledge, they are better than the results of the corresponding partial differential equations. In particular, the methods of proof are different. Xinfu Li and Guang Zhang Copyright © 2016 Xinfu Li and Guang Zhang. All rights reserved. Bifurcation and Nodal Solutions for the Half-Linear Problems with Nonasymptotic Nonlinearity at and Thu, 14 Jan 2016 14:16:36 +0000 http://www.hindawi.com/journals/ddns/2016/2386287/ We study the existence of nodal solutions for the following problem: , , , where is a parameter, with on any subinterval of , , and ; , for , and , where and . We use bifurcation techniques to prove our main results. Wenguo Shen Copyright © 2016 Wenguo Shen. All rights reserved. Collaborative Optimization of Stop Schedule Plan and Ticket Allotment for the Intercity Train Wed, 13 Jan 2016 07:00:05 +0000 http://www.hindawi.com/journals/ddns/2016/5649020/ As regards the ticket allotment issue of the intercity passenger corridor designed for different train grades, the matching relationship between the ticket allotment and the passenger flow demand is studied. The passenger flow conversion equation which is based on the collaborative optimization of the intercity train stop schedule plan and ticket allotment is established. Then the mathematical model aiming at the maximum revenue of intercity train system and the highest satisfaction from the passengers is established. The particle swarm harmony search algorithm is designed to solve the model. The example verifies the effectiveness of the model and algorithm, which indicates that, through the collaborative optimization of the stop schedule plan and ticket allotment for different grades intercity trains, the sectional utilization rate of the train can be improved; meanwhile, the optimum matching between the intercity train revenue and the passenger satisfaction can be realized. Xichun Chen and Junli Wang Copyright © 2016 Xichun Chen and Junli Wang. All rights reserved. An Inverse Robust Optimisation Approach for a Class of Vehicle Routing Problems under Uncertainty Wed, 13 Jan 2016 06:35:58 +0000 http://www.hindawi.com/journals/ddns/2016/2804525/ There is a trade-off between the total penalty paid to customers (TPC) and the total transportation cost (TTC) in depot for vehicle routing problems under uncertainty (VRPU). The trade-off refers to the fact that the TTC in depot inevitably increases when the TPC decreases and vice versa. With respect to this issue, the vehicle routing problem (VRP) with uncertain customer demand and travel time was studied to optimise the TPC and the TTC in depot. In addition, an inverse robust optimisation approach was proposed to solve this kind of VRPU by combining the ideas of inverse optimisation and robust optimisation so as to improve both the TPC and the TTC in depot. The method aimed to improve the corresponding TTC of the robust optimisation solution under the minimum TPC through minimising the adjustment of benchmark road transportation cost. According to the characteristics of the inverse robust optimisation model, a genetic algorithm (GA) and column generation algorithm are combined to solve the problem. Moreover, 39 test problems are solved by using an inverse robust optimisation approach: the results show that both the TPC and TTC obtained by using the inverse robust optimisation approach are less than those calculated using a robust optimisation approach. Liang Sun and Bing Wang Copyright © 2016 Liang Sun and Bing Wang. All rights reserved. Estimation and Global Stability Analysis of PDAEs with Singular Time Derivative Matrix and Wetland Conservation Application Mon, 11 Jan 2016 13:03:01 +0000 http://www.hindawi.com/journals/ddns/2016/3713864/ Some partial differential algebraic equations (PDAEs) system with singular time derivative matrices is analyzed. First, by PDE spectrum theory, this system is formulated as infinite-dimensional singular systems. Second, the state space and its properties of the system are built according to descriptor system theory. Third, the admissible property of the PDAEs is given via LMIs. Finally, the developed energy estimation method is proposed to investigate the global stability of PDAEs. The proposed approach is evaluated by an application in numerical simulations on some wetland conservation system with social behavior. Yushan Jiang and Qingling Zhang Copyright © 2016 Yushan Jiang and Qingling Zhang. All rights reserved. Urban Link Travel Time Estimation Based on Low Frequency Probe Vehicle Data Wed, 06 Jan 2016 14:08:53 +0000 http://www.hindawi.com/journals/ddns/2016/7348705/ To improve the accuracy and robustness of urban link travel time estimation with limited resources, this research developed a methodology to estimate the urban link travel time using low frequency GPS probe vehicle data. First, focusing on the case without reporting points for the GPS probe vehicle on the target link in the current estimation time window, a virtual report point creation model based on the -Nearest Neighbour Rule was proposed. Then an improved back propagation neural network model was used to estimate the link travel time. The proposed method was applied to a case study based on an arterial road in Changchun, China: comparisons with the traditional artificial neural network method and the spatiotemporal moving average method revealed that the proposed method offered a higher estimation accuracy and better robustness. Xiyang Zhou, Zhaosheng Yang, Wei Zhang, Xiujuan Tian, and Qichun Bing Copyright © 2016 Xiyang Zhou et al. All rights reserved. Adaptive Terminal Sliding Mode NDO-Based Control of Underactuated AUV in Vertical Plane Tue, 05 Jan 2016 13:41:40 +0000 http://www.hindawi.com/journals/ddns/2016/6590517/ The depth tracking issue of underactuated autonomous underwater vehicle (AUV) in vertical plane is addressed in this paper. Considering the complicated dynamics and kinematics model for underactuated AUV, a more simplified model is obtained based on assumptions. Then a nonlinear disturbance observer (NDO) is presented to estimate the external disturbance acting on AUV, and an adaptive terminal sliding mode control (ATSMC) based on NDO is applied to enhance the depth tracking performance of underactuated AUV considering both internal and external disturbance. Compared with the traditional sliding mode controller, the static error and chattering problem of the depth tracking process have been clearly improved by adopting NDO-based ATSMC. The stability of control system is proven to be guaranteed according to Lyapunov theory. In the end, simulation results imply that the proposed controller owns strong robustness and satisfied control effectiveness in comparison with the traditional controller. Wei Chen, Yanhui Wei, Jianhui Zeng, Han Han, and Xianqiang Jia Copyright © 2016 Wei Chen et al. All rights reserved. Vehicle Position Updating Strategy Based on Kalman Filter Prediction in VANET Environment Sun, 03 Jan 2016 11:25:04 +0000 http://www.hindawi.com/journals/ddns/2016/1404396/ In VANET (vehicular ad hoc network) environment, the successive vehicle position data actually are discrete, so the key to the moving vehicle modeling is to effectively reduce the updating frequency of the position data so as to alleviate the communication and database management load. This paper proposes vehicle position data updating strategy with packet repetition based on Kalman filter predicting. Firstly, we design a position data updating model based on Kalman filter difference predicting equations. Then, we design a packet repetition mode decision algorithm, which is applied to deliver vehicle position updating data. The model with packet repetition can not only generate position updating data according to preset threshold, but also decide packet repetition mode related to the distance of two adjacent vehicles in order to reduce data loss. Both simulated highway and realistic urban road experimental results show that vehicle position data updating frequency could be obviously reduced and the reliability of the communication is greatly improved through packet repetition mechanism by using this position updating strategy. Yuanfu Mo, Dexin Yu, Jun Song, Kun Zheng, and Yajuan Guo Copyright © 2016 Yuanfu Mo et al. All rights reserved. Discrete-Time Orthogonal Spline Collocation Method for One-Dimensional Sine-Gordon Equation Wed, 30 Dec 2015 08:07:23 +0000 http://www.hindawi.com/journals/ddns/2015/206264/ We present a discrete-time orthogonal spline collocation scheme for the one-dimensional sine-Gordon equation. This scheme uses Hermite basis functions to approximate the solution throughout the spatial domain on each time level. The convergence rate with order in norm and stability of the scheme are proved. Numerical results are presented and compared with analytical solutions to confirm the accuracy of the presented scheme. Xiaoquan Ding, Qing-Jiang Meng, and Li-Ping Yin Copyright © 2015 Xiaoquan Ding et al. All rights reserved. Permanence and Periodic Solutions for a Two-Patch Impulsive Migration Periodic -Species Lotka-Volterra Competitive System Tue, 29 Dec 2015 09:28:40 +0000 http://www.hindawi.com/journals/ddns/2015/293050/ We study a two-patch impulsive migration periodic -species Lotka-Volterra competitive system. Based on analysis method, inequality estimation, and Lyapunov function method, sufficient conditions for the permanence and existence of a unique globally stable positive periodic solution of the system are established. Some numerical examples are shown to verify our results and discuss the model further. Zijian Liu and Chenxue Yang Copyright © 2015 Zijian Liu and Chenxue Yang. All rights reserved. Hopf Bifurcation Analysis and Chaos Control of a Chaotic System without ilnikov Orbits Tue, 29 Dec 2015 08:26:27 +0000 http://www.hindawi.com/journals/ddns/2015/912798/ This paper mainly investigates the dynamical behaviors of a chaotic system without ilnikov orbits by the normal form theory. Both the stability of the equilibria and the existence of local Hopf bifurcation are proved in view of analyzing the associated characteristic equation. Meanwhile, the direction and the period of bifurcating periodic solutions are determined. Regarding the delay as a parameter, we discuss the effect of time delay on the dynamics of chaotic system with delayed feedback control. Finally, numerical simulations indicate that chaotic oscillation is converted into a steady state when the delay passes through a certain critical value. Na Li, Wei Tan, and Huitao Zhao Copyright © 2015 Na Li et al. All rights reserved. On the Existence and Stability of Standing Waves for 2-Coupled Nonlinear Fractional Schrödinger System Sun, 27 Dec 2015 09:21:06 +0000 http://www.hindawi.com/journals/ddns/2015/427487/ We study a system of 2-coupled nonlinear fractional Schrödinger equations. Firstly, we construct constrained minimization problem to the system. Next, we prove the existence of standing waves for the system by using the concentration-compactness and commutator estimates method. Lastly, we also consider the set of minimizers of the constrained minimization problem. We prove that it is a stable set for initial value of the problem; that is, a solution to the system with initial value which is near the set will remain near it for all time. Xiuyan Sha, Huanmin Ge, and Jie Xin Copyright © 2015 Xiuyan Sha et al. All rights reserved. Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System Thu, 24 Dec 2015 12:25:56 +0000 http://www.hindawi.com/journals/ddns/2015/127404/ The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations. Jie Ran, Yu-Qin Li, Shao-Juan Ma, and Juan Wu Copyright © 2015 Jie Ran et al. All rights reserved. Spanning 3-Ended Trees in Almost Claw-Free Graphs Mon, 21 Dec 2015 12:56:19 +0000 http://www.hindawi.com/journals/ddns/2015/476182/ We prove that if is a -connected () almost claw-free graph of order and , then contains a spanning 3-ended tree, where is an independent set of with . Xiaodong Chen, Meijin Xu, and Yanjun Liu Copyright © 2015 Xiaodong Chen et al. All rights reserved. Public Transportation Hub Location with Stochastic Demand: An Improved Approach Based on Multiple Attribute Group Decision-Making Mon, 21 Dec 2015 06:39:08 +0000 http://www.hindawi.com/journals/ddns/2015/430109/ Urban public transportation hubs are the key nodes of the public transportation system. The location of such hubs is a combinatorial problem. Many factors can affect the decision-making of location, including both quantitative and qualitative factors; however, most current research focuses solely on either the quantitative or the qualitative factors. Little has been done to combine these two approaches. To fulfill this gap in the research, this paper proposes a novel approach to the public transportation hub location problem, which takes both quantitative and qualitative factors into account. In this paper, an improved multiple attribute group decision-making (MAGDM) method based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and deviation is proposed to convert the qualitative factors of each hub into quantitative evaluation values. A location model with stochastic passenger flows is then established based on the above evaluation values. Finally, stochastic programming theory is applied to solve the model and to determine the location result. A numerical study shows that this approach is applicable and effective. Sen Liu, Zhilan Song, and Shuqi Zhong Copyright © 2015 Sen Liu et al. All rights reserved. Approximate Controllability of Semilinear Neutral Stochastic Integrodifferential Inclusions with Infinite Delay Sun, 20 Dec 2015 09:17:49 +0000 http://www.hindawi.com/journals/ddns/2015/420826/ The approximate controllability of semilinear neutral stochastic integrodifferential inclusions with infinite delay in an abstract space is studied. Sufficient conditions are established for the approximate controllability. The results are obtained by using the theory of analytic resolvent operator, the fractional power theory, and the theorem of nonlinear alternative for Kakutani maps. Finally, an example is provided to illustrate the theory. Meili Li and Man Liu Copyright © 2015 Meili Li and Man Liu. All rights reserved. On Constructing Two-Point Optimal Fourth-Order Multiple-Root Finders with a Generic Error Corrector and Illustrating Their Dynamics Wed, 16 Dec 2015 11:28:33 +0000 http://www.hindawi.com/journals/ddns/2015/378517/ With an error corrector via principal branch of the mth root of a function-to-function ratio, we propose optimal quartic-order multiple-root finders for nonlinear equations. The relevant optimal order satisfies Kung-Traub conjecture made in 1974. Numerical experiments performed for various test equations demonstrate convergence behavior agreeing with theory and the basins of attractions for several examples are presented. Young Ik Kim and Young Hee Geum Copyright © 2015 Young Ik Kim and Young Hee Geum. All rights reserved.