Discrete Dynamics in Nature and Society https://www.hindawi.com The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Discrete Models of Disease and Competition Wed, 20 Sep 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/5310837/ The aim of this work is to analyze the influence of the fast development of a disease on competition dynamics. To this end we present two discrete time ecoepidemic models. The first one corresponds to the case of one parasite affecting demography and intraspecific competition in a single host, whereas the second one contemplates the more complex case of competition between two different species, one of which is infected by the parasite. We carry out a complete mathematical analysis of the asymptotic behavior of the solutions of the corresponding systems of difference equations and derive interesting ecological information about the influence of a disease in competition dynamics. This includes an assessment of the impact of the disease on the equilibrium population of both species as well as some counterintuitive behaviors in which although we would expect the outbreak of the disease to negatively affect the infected species, the contrary happens. R. Bravo de la Parra, M. Marvá, E. Sánchez, and L. Sanz Copyright © 2017 R. Bravo de la Parra et al. All rights reserved. Corrigendum to “Forecasting Method for Urban Rail Transit Ridership at Station Level Using Back Propagation Neural Network” Wed, 20 Sep 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/5496385/ Junfang Li, Minfeng Yao, and Qian Fu Copyright © 2017 Junfang Li et al. All rights reserved. Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters Tue, 19 Sep 2017 09:58:05 +0000 http://www.hindawi.com/journals/ddns/2017/2049396/ This paper investigates the modified function projective synchronization between fractional-order chaotic systems, which are partially linear financial systems with uncertain parameters. Based on the stability theory of fractional-order systems and the Lyapunov matrix equation, a controller is obtained for the synchronization between fractional-order financial chaotic systems. Using the controller, the error systems converged to zero as time tends to infinity, and the uncertain parameters were also estimated so that the phenomenon of parameter distortion was effectively avoided. Numerical simulations demonstrate the validity and feasibility of the proposed method. Yehong Yang and Guohua Cao Copyright © 2017 Yehong Yang and Guohua Cao. All rights reserved. Pricing Zero-Coupon Catastrophe Bonds Using EVT with Doubly Stochastic Poisson Arrivals Wed, 13 Sep 2017 09:35:41 +0000 http://www.hindawi.com/journals/ddns/2017/3279647/ The frequency and severity of climate abnormal change displays an irregular upward cycle as global warming intensifies. Therefore, this paper employs a doubly stochastic Poisson process with Black Derman Toy (BDT) intensity to describe the catastrophic characteristics. By using the Property Claim Services (PCS) loss index data from 2001 to 2010 provided by the US Insurance Services Office (ISO), the empirical result reveals that the BDT arrival rate process is superior to the nonhomogeneous Poisson and lognormal intensity process due to its smaller RMSE, MAE, MRPE, and U and larger E and d. Secondly, to depict extreme features of catastrophic risks, this paper adopts the Peak Over Threshold (POT) in extreme value theory (EVT) to characterize the tail characteristics of catastrophic loss distribution. And then the loss distribution is analyzed and assessed using a quantile-quantile (QQ) plot to visually check whether the PCS index observations meet the generalized Pareto distribution (GPD) assumption. Furthermore, this paper derives a pricing formula for zero-coupon catastrophe bonds with a stochastic interest rate environment and aggregate losses generated by a compound doubly stochastic Poisson process under the forward measure. Finally, simulation results verify pricing model predictions and show how catastrophic risks and interest rate risk affect the prices of zero-coupon catastrophe bonds. Zonggang Ma, Chaoqun Ma, and Shisong Xiao Copyright © 2017 Zonggang Ma et al. All rights reserved. Analysis on Time Window of Shared Parking in Hospitals Based on Parking Behaviors Wed, 13 Sep 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/9859604/ Hospitals are essential components of a city; huge traffic demand is generated and attracted, causing contradiction between parking supply and demand. By sharing parking berths, limited space can serve more demand which is beneficial to alleviating parking problems. Aimed at improving the capacity of shared parking, the paper analyzes four parking groups in typical hospitals, which are medical staff, outpatients, emergency patients, and visiting groups. The parking demand of medical staff is rigid. For outpatients and visiting groups, longer walking distance is acceptable and more attention is paid to parking fee. By contrast, emergency patients can accept shorter walking distance and focus more on convenience due to urgency. Under this circumstance, parking behaviors selection models are established by means of Multinomial Logit Model. On this basis, time value is adopted to calculate the tolerance of alterative parking time. Moreover, this paper explores the variation of time window, under different parking impedance. A case study is conducted and suggests that start and end point of a certain time window can be influenced by external factors. Qin Chen, Peng He, and Jun Chen Copyright © 2017 Qin Chen et al. All rights reserved. A Flexible Logistics Distribution Hub Model considering Cost Weighted Time Mon, 11 Sep 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/9470943/ The delivery time of order has become an important fact for customers to evaluate logistics services. Due to the diverse and large quantities of orders in the background of electronic commerce, how to improve the flexibility of distribution hub and reduce the waiting time of customers becomes one of the most challenging questions for logistics companies. With this in mind, this paper proposes a new method of flexibility assessment in distribution hub by introducing cost weighted time (CWT). The advantages of supply hub operation mode in delivery flexibility are verified by the approach: the mode has pooling effects and uniform distribution characteristics; these traits can reduce overlapping delivery time to improve the flexibility in the case of two suppliers. Numerical examples show that the supply hub operation mode is more flexible than decentralized distribution operation mode in multidelivery cycles. Wenxue Ran, Zhe Zhang, and Sen Liu Copyright © 2017 Wenxue Ran et al. All rights reserved. A Branch and Bound Algorithm for Agile Earth Observation Satellite Scheduling Thu, 07 Sep 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/7345941/ The agile earth observing satellite scheduling (AEOSS) problem consists of scheduling a subset of images among a set of candidates that satisfy imperative constraints and maximize a gain function. In this paper, we consider a new AEOSS model which integrates a time-dependent temporal constraint. To solve this problem, we propose a highly efficient branch and bound algorithm whose effective ingredients include a look-ahead construction method (for generating a high quality initial lower bound) and a combined use of three pruning strategies (which help to prune a large portion of the search space). We conducted computational experiments on a set of test data that were generated with information from real-life scenarios. The results showed that the proposed algorithm is efficient enough for engineering application. In particular, it is able to solve instances with 55 targets to optimality within 164 seconds on average. Furthermore, we carried out additional experiments to analyze the contribution of each key algorithm ingredient. Xiaogeng Chu, Yuning Chen, and Lining Xing Copyright © 2017 Xiaogeng Chu et al. All rights reserved. A Conservation Difference Scheme of Generalized Boussinesq Equation Wed, 06 Sep 2017 09:49:30 +0000 http://www.hindawi.com/journals/ddns/2017/5392172/ We focus on the algorithm research of a class of six-order generalized Boussinesq equation. We use the finite difference method to discrete the Boussinesq equation. The discrete format with the law of energy conservation is deduced; stability and existence and good order of convergence properties are also derived. The efficiency of the proposed method is tested to numerical results that the convergence of space is of second-order and the conservation law of energy is verified very well for the energy difference. Xiaoli Jiang and Xiaofeng Wang Copyright © 2017 Xiaoli Jiang and Xiaofeng Wang. All rights reserved. Nonnegative Periodic Solutions of a Three-Term Recurrence Relation Depending on Two Real Parameters Wed, 06 Sep 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/7163809/ Simple dynamic systems representing time varying states of interconnected neurons may exhibit extremely complex behaviors when bifurcation parameters are switched from one set of values to another. In this paper, motivated by simulation results, we examine the steady states of one such system with bang-bang control and two real parameters. We found that nonnegative and negative periodic states are of special interests since these states are solutions of linear nonhomogeneous three-term recurrence relations. Although the standard approach to analyse such recurrence relations is the method of finding the general solutions by means of variation of parameters, we find novel alternate geometric methods that offer the tracking of solution trajectories in the plane. By means of this geometric approach, we are then able, without much tedious computation, to completely characterize the nonnegative and negative periodic solutions in terms of the bifurcation parameters. Yen Chih Chang, Sui Sun Cheng, and Wei Chang Yeh Copyright © 2017 Yen Chih Chang et al. All rights reserved. Robust Linear Neural Network for Constrained Quadratic Optimization Mon, 28 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/5073640/ Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper. Zixin Liu, Yuanan Liu, and Lianglin Xiong Copyright © 2017 Zixin Liu et al. All rights reserved. Convergence of a Logistic Type Ultradiscrete Model Sun, 27 Aug 2017 10:35:28 +0000 http://www.hindawi.com/journals/ddns/2017/7893049/ We derive a piecewise linear difference equation from logistic equations with time delay by ultradiscretization. The logistic equation that we consider in this paper has been shown to be globally stable in the continuous and discrete time formulations. Here, we study if ultradiscretization preserves the global stability property, analyzing the asymptotic behaviour of the obtained piecewise linear difference equation. It is shown that our piecewise linear difference equation has a threshold property concerning global attractivity of equilibria, similar to the stable logistic equations with time delay. Masaki Sekiguchi, Emiko Ishiwata, and Yukihiko Nakata Copyright © 2017 Masaki Sekiguchi et al. All rights reserved. Epidemic Processes on Complex Networks Sun, 27 Aug 2017 09:10:20 +0000 http://www.hindawi.com/journals/ddns/2017/9873678/ Lu-Xing Yang, Yong Deng, and Jose Roberto Castilho Piqueira Copyright © 2017 Lu-Xing Yang et al. All rights reserved. Two-Stage Heuristic Algorithm for Aircraft Recovery Problem Thu, 24 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/9575719/ This study focuses on the aircraft recovery problem (ARP). In real-life operations, disruptions always cause schedule failures and make airlines suffer from great loss. Therefore, the main objective of the aircraft recovery problem is to minimize the total recovery cost and solve the problem within reasonable runtimes. An aircraft recovery model (ARM) is proposed herein to formulate the ARP and use feasible line of flights as the basic variables in the model. We define the feasible line of flights (LOFs) as a sequence of flights flown by an aircraft within one day. The number of LOFs exponentially grows with the number of flights. Hence, a two-stage heuristic is proposed to reduce the problem scale. The algorithm integrates a heuristic scoring procedure with an aggregated aircraft recovery model (AARM) to preselect LOFs. The approach is tested on five real-life test scenarios. The computational results show that the proposed model provides a good formulation of the problem and can be solved within reasonable runtimes with the proposed methodology. The two-stage heuristic significantly reduces the number of LOFs after each stage and finally reduces the number of variables and constraints in the aircraft recovery model. Cheng Zhang Copyright © 2017 Cheng Zhang. All rights reserved. A Multistep Look-Ahead Deadlock Avoidance Policy for Automated Manufacturing Systems Mon, 21 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/8687035/ For an automated manufacturing system (AMS), it is a computationally intractable problem to find a maximally permissive deadlock avoidance policy (DAP) in a general case, since the decision on the safety of a reachable state is NP-hard. This paper focuses on the deadlock avoidance problem for systems of simple sequential processes with resources (S3PR) by using Petri nets structural analysis theory. Inspired by the one-step look-ahead DAP that is an established result, which is of polynomial complexity, for an S3PR without one-unit-capacity resources shared by two or more resource-transition circuits (in the Petri net model) that do not include each other, this research explores a multiple-step look-ahead deadlock avoidance policy for a system modeled with an S3PR that contains a shared one-unit-capacity resource in resource-transition circuits. It is shown that the development of an optimal DAP for the considered class of Petri nets is also of polynomial complexity. It is indicated that the steps needed to look ahead in a DAP depend on the structure of the net model. A number of examples are used to illustrate the proposed method. Chao Gu, Zhiwu Li, and Abdulrahman Al-Ahmari Copyright © 2017 Chao Gu et al. All rights reserved. System Dynamics Modelling of Remanufacturing and Recycling Mode Based on Closed-Loop Across-Chain Competition Mon, 21 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/8152365/ To face the reality of resources exhaustion, the significance of recycling and remanufacturing in the closed-loop chain has become quite evident. This paper constructs a competitive recycling and remanufacturing model of the closed-loop supply chain through a case study of Midea Corp. and Gree Corp. and explores the impact of two recycling modes on total revenue of the supply chain and market share. The simulation results show that the total revenue of the supply chain will benefit from the increasing coverage points by the third party and the increasing environmental awareness of certain regions. The retailers show more enthusiasm of recycling through certain amendment of the contract between manufacturers and retailers. The time of payment could be shortened in closed loop. Moreover, the improvement of recycling mechanism of the retailers can enlarge the share of supply chain market. Guiding role of the proposed model and the simulation results played in establishing a better supply chain mode is presented. Shidi Miao, Deyun Chen, and Tengfei Wang Copyright © 2017 Shidi Miao et al. All rights reserved. Stability of a Class of Hybrid Neutral Stochastic Differential Equations with Unbounded Delay Mon, 21 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2941349/ This paper studies the stability of hybrid neutral stochastic differential equations with unbounded delay. Some novel exponential stability criteria and boundedness conditions are established based on the generalized Itô formula and Lyapunov functions. The factor is used to overcome the difficulties caused by the unbounded delay effectively. In particular, our results generalize and improve some previous stability results from bounded delay to unbounded delay conditions. Finally, an example is presented to demonstrate the effectiveness of the proposed results. Boliang Lu and Ruili Song Copyright © 2017 Boliang Lu and Ruili Song. All rights reserved. Theoretical and Numerical Results for Fractional Difference and Differential Equations Sun, 20 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2543452/ Qasem M. Al-Mdallal, Thabet Abdeljawad, and Mohamed A. Hajji Copyright © 2017 Qasem M. Al-Mdallal et al. All rights reserved. Component Importance Measure Computation Method Based Fuzzy Integral with Its Application Thu, 17 Aug 2017 07:27:42 +0000 http://www.hindawi.com/journals/ddns/2017/7842596/ In view of the negative impact of component importance measures based on system reliability theory and centrality measures based on complex networks theory, there is an attempt to provide improved centrality measures (ICMs) construction method with fuzzy integral for measuring the importance of components in electromechanical systems in this paper. ICMs are the meaningful extension of centrality measures and component importance measures, which consider influences on function and topology between components to increase importance measures usefulness. Our work makes two important contributions. First, we propose a novel integration method of component importance measures to define ICMs based on Choquet integral. Second, a meaningful fuzzy integral is first brought into the construction comprehensive measure by fusion multi-ICMs and then identification of important components which could give consideration to the function of components and topological structure of the whole system. In addition, the construction method of ICMs and comprehensive measure by integration multi-CIMs based on fuzzy integral are illustrated with a holistic topological network of bogie system that consists of 35 components. Shuai Lin, Yanhui Wang, Limin Jia, and Yang Li Copyright © 2017 Shuai Lin et al. All rights reserved. Consensus of Fractional-Order Multiagent Systems with Double Integrator under Switching Topologies Wed, 16 Aug 2017 10:01:17 +0000 http://www.hindawi.com/journals/ddns/2017/9394751/ Due to the complexity of the practical environments, many systems can only be described with the fractional-order dynamics. In this paper, the consensus of fractional-order multiagent systems with double integrator under switching topologies is investigated. By applying Mittag-Leffler function, Laplace transform, and dwell time technique, a sufficient condition on consensus is obtained. Finally, a numerical simulation is presented to illustrate the effectiveness of the theoretical result. Shiyun Shen, Wenjing Li, and Wei Zhu Copyright © 2017 Shiyun Shen et al. All rights reserved. Corrigendum to “Cross-Shareholdings Structural Characteristic and Evolution Analysis Based on Complex Network” Sun, 13 Aug 2017 08:10:33 +0000 http://www.hindawi.com/journals/ddns/2017/5391013/ Xiaohong Chang and Haiyun Wang Copyright © 2017 Xiaohong Chang and Haiyun Wang. All rights reserved. Class of Quadratic Almost Bent Functions That Is EA-Inequivalent to Permutations Sun, 13 Aug 2017 07:56:34 +0000 http://www.hindawi.com/journals/ddns/2017/9627840/ The permutation relationship for the almost bent (AB) functions in the finite field is a significant issue. Li and Wang proved that a class of AB functions with algebraic degree 3 is extended affine- (EA-) inequivalent to any permutation. This study proves that another class of AB functions, which was developed in 2009, is EA-inequivalent to any permutation. This particular AB function is the first known quadratic class EA-inequivalent to permutation. Xinyang Zhang and Meng Zhou Copyright © 2017 Xinyang Zhang and Meng Zhou. All rights reserved. Crash Risk Prediction Model of Lane-Change Behavior on Approaching Intersections Wed, 09 Aug 2017 10:30:33 +0000 http://www.hindawi.com/journals/ddns/2017/7328562/ The driving tendency of drivers is one of the most important factors in lane-changing maneuvers. However, the heterogeneity of the characteristics of drivers’ lane-changing behaviors has not been adequately considered. The primary objective of the present study is to explore the risk level of the lane-changing implementation process under different driving tendencies upon approaching signalized intersections in an urban area. This paper defines the Integrated Conflict Risk Index (ICRI), which takes into account the probability and severity of risk. Using the index as the dependent variable, the risk prediction model of implementing the lane-change process is established. A series of experiments, which included a questionnaire, a number of tests, and on-road experiments, was conducted to identify the driving tendencies of the participants. A combination of video recording and instrumented vehicles was used to collect lane-changing trajectory data of different driving tendencies. The parameters of the model were calibrated, and the results indicate that driving tendency has a significant effect on the risk level of lane-changing execution. More specifically, the more aggressive the driving tendency, the higher the risk level. The quantitative results of the study can provide the basis for conflict risk assessment in the existing lane-changing models. Yingshuai Li, Jian Lu, and Kuisheng Xu Copyright © 2017 Yingshuai Li et al. All rights reserved. Interval Forecasting of Carbon Futures Prices Using a Novel Hybrid Approach with Exogenous Variables Wed, 09 Aug 2017 07:18:13 +0000 http://www.hindawi.com/journals/ddns/2017/5730295/ This paper examines the interval forecasting of carbon futures prices in one of the most important carbon futures market. Specifically, the purpose of this study is to present a novel hybrid approach, which is composed of multioutput support vector regression (MSVR) and particle swarm optimization (PSO), in the task of forecasting the highest and lowest prices of carbon futures on the next trading day. Furthermore, we set out to investigate if considering some potential predictors, which have strong influence on carbon futures prices, in modeling process is useful for achieving better prediction performance. Aiming at testing its effectiveness, we benchmark the forecasting performance of our approach against four competitors. The daily interval prices of carbon futures contracts traded in the Intercontinental Futures Exchange from August 12, 2010, to November 13, 2014, are used as the experiment dataset. The statistical significance of the interval forecasts is examined. The proposed hybrid approach is found to demonstrate the higher forecasting performance relative to all other competitors. Our application offers practitioners a promising set of results with interval forecasting in carbon futures market. Lu Zhang, Junbiao Zhang, Tao Xiong, and Chiao Su Copyright © 2017 Lu Zhang et al. All rights reserved. Dynamics of Endomorphism of Finite Abelian Groups Tue, 08 Aug 2017 08:47:48 +0000 http://www.hindawi.com/journals/ddns/2017/6295430/ We study the dynamics of endomorphisms on a finite abelian group. We obtain the automorphism group for these dynamical systems. We also give criteria and algorithms to determine whether it is a fixed point system. Zhao Jinxing and Nan Jizhu Copyright © 2017 Zhao Jinxing and Nan Jizhu. All rights reserved. A PLS Approach to Measuring Investor Sentiment in Chinese Stock Market Sun, 06 Aug 2017 09:24:33 +0000 http://www.hindawi.com/journals/ddns/2017/2387543/ We select five objective sentiment indicators and one subjective sentiment indicator to build investor sentiment composite index in Chinese stock market by using the partial least squares. The reason why we do that is to improve the shortcomings of the principal component analysis, which was adopted to build investor sentiment composite index in the pioneering research. Moreover, due to the large proportion of individual investors in Chinese stock market and the rapid change of investor sentiment, we innovatively use the weekly data with smaller information granularity and higher frequency. Through empirical tests for its reasonability and market’s predictive capability, we find that this index appears to fit the data better and improves prediction. Gang He, Shuzhen Zhu, and Haifeng Gu Copyright © 2017 Gang He et al. All rights reserved. Nonstationary and Chaotic Dynamics in Age-Structured Population Models Sun, 06 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/1964286/ The dynamics from nonlinear discrete age-structured population models is under consideration. Focus is on bifurcations, as well as nonstationary and chaotic dynamics. We also explore different mechanisms which may lead to periodic phenomena. Some new results are also presented, in particular from models where both fecundity and survival terms contain nonlinear elements. Arild Wikan and Ørjan Kristensen Copyright © 2017 Arild Wikan and Ørjan Kristensen. All rights reserved. An Optimization Model and Modified Harmony Search Algorithm for Microgrid Planning with ESS Thu, 03 Aug 2017 08:27:34 +0000 http://www.hindawi.com/journals/ddns/2017/8425458/ To solve problems such as the high cost of microgrids (MGs), balance between supply and demand, stability of system operation, and optimizing the MG planning model, the energy storage system (ESS) and harmony search algorithm (HSA) are proposed. First, the conventional MG planning optimization model is constructed and the constraint conditions are defined: the supply and demand balance and reserve requirements. Second, an ESS is integrated into the optimal model of MG planning. The model with an ESS can solve and identify parameters such as the optimal power, optimal capacity, and optimal installation year. Third, the convergence speed and robustness of the ESS are optimized and improved. A case study comprising three different cases concludes the paper. The results show that the modified HSA (MHSA) can effectively improve the stability and economy of MG operation with an ESS. Yang Jiao, Jing Wu, Qing-kun Tan, Zhong-fu Tan, and Guan Wang Copyright © 2017 Yang Jiao et al. All rights reserved. Socioeconomic Drivers of Environmental Pollution in China: A Spatial Econometric Analysis Thu, 03 Aug 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/4673262/ This paper studies the environmental pollution and its impacts in China using prefecture-level cities and municipalities data. Moran’s I, the widely used spatial autocorrelation index, provides a fairly strong pattern of spatial clustering of environmental pollution and suggests a fairly high stability of the positive spatial correlation. To investigate the driving forces of environmental pollution and explore the relationship between fiscal decentralization, economic growth, and environmental pollution, spatial Durbin model is used for this analysis. The result shows that fiscal decentralization of local unit plays a significant role in promoting the environmental pollution and the feedback effect of fiscal decentralization on environmental pollution is also positive, though it is not significant. The relationship of GDP per capita and environmental pollution shows inverted U-shaped curve. Due to the scale effect of secondary industry, the higher the level of secondary industry development in a unit is, the easier it is to attract the secondary industry in adjacent units, which mitigates the environmental pollution in adjacent units. Densely populated areas tend to deteriorate local environment, but environmental regulation in densely populated areas is often tighter than other areas, which reduces environmental pollution to a certain extent. Jianmin Liu, Xia Chen, and Runchu Wei Copyright © 2017 Jianmin Liu et al. All rights reserved. Complexity and Application of Tobacco Manufacturer Pricing Game considering Market Segments Mon, 31 Jul 2017 12:05:00 +0000 http://www.hindawi.com/journals/ddns/2017/6701286/ This paper considers price as a strategy using two methods of market segmentation through game theory based on the collected data of several typical cities in Shandong province. Three oligarchs are discussed to analyze the complexity of the market in tobacco system. The effect of different factors on the equilibrium price of Nash equilibrium is discussed. What is more, the variation of parameters drives the system to change to uncertain status, even to bifurcation or chaos. We also discuss the model under normal circumstances, when the three parties jointly take chaos control measures, and its impact on the system. Finally, we clarify chaos control of economic significance. The results indicate that only reasonable pricing strategy is a critical point to achieve maximized profit and maintain orderly operation at the same time, which is a constructive suggestion for tobacco companies’ operational strategy. Shubing Guo, Junhai Ma, and Xueli Zhan Copyright © 2017 Shubing Guo et al. All rights reserved. Two New Approximations for Variable-Order Fractional Derivatives Mon, 31 Jul 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/1586249/ We introduced a parameter which was related to ; then two numerical schemes for variable-order Caputo fractional derivatives were derived; the second-order numerical approximation to variable-order fractional derivatives and -order approximation for are established. For the given parameter , the error estimations of formulas were proven, which were higher than some recently derived schemes. Finally, some numerical examples with exact solutions were studied to demonstrate the theoretical analysis and verify the efficiency of the proposed methods. Ruilian Du and Zongqi Liang Copyright © 2017 Ruilian Du and Zongqi Liang. All rights reserved.