Discrete Dynamics in Nature and Society http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2017 , Hindawi Publishing Corporation . All rights reserved. Novel Concepts of Bipolar Fuzzy BCK-Submodules Mon, 23 Jan 2017 10:04:52 +0000 http://www.hindawi.com/journals/ddns/2017/2084191/ Translations and multiplications of bipolar fuzzy BCK-submodules are discussed. Extensions of bipolar fuzzy BCK-submodules are introduced. Relations between translations and multiplications of bipolar fuzzy BCK-submodules are presented. M. A. Alghamdi, N. M. Muthana, and N. O. Alshehri Copyright © 2017 M. A. Alghamdi et al. All rights reserved. Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model Mon, 23 Jan 2017 09:34:27 +0000 http://www.hindawi.com/journals/ddns/2017/9275474/ A discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. The numerical simulations not only illustrate the consistence with the theoretical analysis, but also exhibit other complex dynamical behaviors, such as bifurcation diagrams, Maximum Lyapunov exponents, and phase portraits. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point by using the feedback control method. Xueli Chen and Lishun Ren Copyright © 2017 Xueli Chen and Lishun Ren. All rights reserved. Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations Mon, 23 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/8630895/ In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent. Qingxue Huang, Fuqiang Zhao, Jiaquan Xie, Lifeng Ma, Jianmei Wang, and Yugui Li Copyright © 2017 Qingxue Huang et al. All rights reserved. Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems Sun, 22 Jan 2017 14:20:35 +0000 http://www.hindawi.com/journals/ddns/2017/2741326/ This paper is devoted to the estimates for weak solutions to nonlinear degenerate parabolic systems related to Hörmander’s vector fields. The reverse Hölder inequalities for degenerate parabolic system under the controllable growth conditions and natural growth conditions are established, respectively, and an important multiplicative inequality is proved; finally, we obtain the estimates for the weak solutions by combining the results of Gianazza and the Caccioppoli inequality. Na Wei, Xiangyu Ge, Yonghong Wu, and Leina Zhao Copyright © 2017 Na Wei et al. All rights reserved. Certain Nonlinear Integral Inequalities and Their Applications Thu, 19 Jan 2017 12:03:35 +0000 http://www.hindawi.com/journals/ddns/2017/8290906/ Several new retarded integral inequalities of Gronwall-Bellman-Pachpatte type are presented which generalize the inequalities to the more general nonlinear case in the literature and provide explicit bounds on unknown functions. These results include many existing ones as special cases and can be used as tools in the qualitative analysis of certain classes of integrodifferential equations. Yazhou Tian, Min Fan, and Yuangong Sun Copyright © 2017 Yazhou Tian et al. All rights reserved. Dynamics of a Higher-Order System of Difference Equations Thu, 19 Jan 2017 11:30:22 +0000 http://www.hindawi.com/journals/ddns/2017/4312640/ Consider the following system of difference equations: , , , , , ; where is a positive integer, , , and the initial conditions , are positive real numbers. We obtain the expressions of the positive solutions of the system and then give a precise description of the convergence of the positive solutions. Finally, we give some numerical results. Qi Wang, Qinqin Zhang, and Qirui Li Copyright © 2017 Qi Wang et al. All rights reserved. A Frame-Based Conjugate Gradients Direct Search Method with Radial Basis Function Interpolation Model Thu, 19 Jan 2017 07:28:22 +0000 http://www.hindawi.com/journals/ddns/2017/4082432/ In this paper, we propose a new hybrid direct search method where a frame-based PRP conjugate gradients direct search algorithm is combined with radial basis function interpolation model. In addition, the rotational minimal positive basis is used to reduce the computation work at each iteration. Numerical results for solving the CUTEr test problems show that the proposed method is promising. Xiaowei Fang and Qin Ni Copyright © 2017 Xiaowei Fang and Qin Ni. All rights reserved. Pricing Mining Concessions Based on Combined Multinomial Pricing Model Wed, 18 Jan 2017 08:42:18 +0000 http://www.hindawi.com/journals/ddns/2017/2196702/ A combined multinomial pricing model is proposed for pricing mining concession in which the annualized volatility of the price of mineral products follows a multinomial distribution. First, a combined multinomial pricing model is proposed which consists of binomial pricing models calculated according to different volatility values. Second, a method is provided to calculate the annualized volatility and the distribution. Third, the value of convenience yields is calculated based on the relationship between the futures price and the spot price. The notion of convenience yields is used to adjust our model as well. Based on an empirical study of a Chinese copper mine concession, we verify that our model is easy to use and better than the model with constant volatility when considering the changing annualized volatility of the price of the mineral product. Chang Xiao and Jinsheng Zhou Copyright © 2017 Chang Xiao and Jinsheng Zhou. All rights reserved. Manufacturer’s R&D Investment Strategy and Pricing Decisions in a Decentralized Supply Chain Wed, 18 Jan 2017 08:08:57 +0000 http://www.hindawi.com/journals/ddns/2017/9879874/ Consider that a manufacturer Stackelberg supply chain consists of an upstream supplier and a downstream manufacturer. The manufacturer purchases a component from the supplier and then transforms it into a final product which is sold in a price and quality sensitive market. The manufacturer considers to make R&D investment to improve the product quality and reduce the production cost. We first investigate and derive the optimal investment strategy and pricing decisions by establishing a three-stage game model. We show that the optimal investment strategy and pricing decisions in the decentralized model may deviate from those in the centralized model. We then propose a mechanism to coordinate the decentralized supply chain, by introducing a profit sharing policy, a production cost sharing policy, and an investment cost sharing policy. Finally, we show that both the supplier and the manufacturer can benefit from participating in the proposed coordination mechanism. Hengyun Zhang and Dingjun Hong Copyright © 2017 Hengyun Zhang and Dingjun Hong. All rights reserved. New JLS-Factor Model versus the Standard JLS Model: A Case Study on Chinese Stock Bubbles Wed, 18 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/8017510/ In this paper, we extend the Johansen-Ledoit-Sornette (JLS) model by introducing fundamental economic factors in China (including the interest rate and deposit reserve rate) and the historical volatilities of targeted and US equity indices into the original model, which is a flexible tool to detect bubbles and predict regime changes in financial markets. We then derive a general method to incorporate these selected factors in addition to the log-periodic power law signature of herding and compare the prediction accuracy of the critical time between the original and the new JLS models (termed the JLS-factor model) by applying these two models to fit two well-known Chinese stock indices in three bubble periods. The results show that the JLS-factor model with Chinese characteristics successfully depicts the evolutions of bubbles and “antibubbles” and constructs efficient end-of-bubble signals for all bubbles in Chinese stock markets. In addition, the results of standard statistical tests demonstrate the excellent explanatory power of these additive factors and confirm that the new JLS model provides useful improvements over the standard JLS model. Zongyi Hu and Chao Li Copyright © 2017 Zongyi Hu and Chao Li. All rights reserved. Pricing and Warranty Decisions of Substitutable Products for a Fuzzy Two-Echelon Supply Chain Mon, 16 Jan 2017 09:09:32 +0000 http://www.hindawi.com/journals/ddns/2017/8476516/ This paper considers the optimal decisions of pricing and warranty level for substitutable products in a fuzzy supply chain environment, where the consumer demands, manufacturing costs, and warranty costs are characterized as fuzzy variables. Expected value manufacturer-leader Stackelberg models and two chance-constrained programming models, that is, the -optimistic and -pessimistic manufacturer-leader Stackelberg models, are established. The corresponding closed-form solutions are obtained by using the game-theoretical approach and fuzzy theory. Finally, numerical examples are presented to illustrate the effectiveness of the models and to provide managerial insights for decision makers. The results show that it would be beneficial for the whole supply chain when the warranty services are introduced into the market, and the firm which provides the warranty service has the advantage in holding more dominant position. Yongzhao Wang Copyright © 2017 Yongzhao Wang. All rights reserved. Mixed Carbon Policies Based on Cooperation of Carbon Emission Reduction in Supply Chain Thu, 12 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/4379124/ This paper established cooperation decision model for a mixed carbon policy of carbon trading-carbon tax (environmental tax) in a two-stage - supply chain. For three different cooperative abatement situations, we considered the supplier driven model, the manufacturer driven model, and the equilibrium game model. We investigated the influence of mixed carbon policy with constraint of reduction targets on supply chain price, productivity, profits, carbon emissions reduction rate, and so on. The results showed that () high-strength carbon policies do not necessarily encourage enterprises to effectively reduce emissions, and increasing market acceptance of low carbon products or raising the price of carbon quota can promote the benign reduction; () perfect competitive carbon market has a higher carbon reduction efficiency than oligarch carbon market, but their optimal level of cooperation is the same and the realized reduction rate is in line with the intensity of carbon policy; () the policy sensitivity of the carbon trading mechanism is stronger than the carbon tax; “paid quota mechanism” can subsidize the cost of abatement and improve reduction initiative. Finally, we use a numerical example to solve the optimal decisions under different market situations, validating the effectiveness of model and the conclusions. Yongwei Cheng, Dong Mu, and Yi Zhang Copyright © 2017 Yongwei Cheng et al. All rights reserved. Nonlinear Reduced-Order Observer-Based Predictive Control for Diving of an Autonomous Underwater Vehicle Tue, 03 Jan 2017 09:38:57 +0000 http://www.hindawi.com/journals/ddns/2017/4394571/ The attitude control and depth tracking issue of autonomous underwater vehicle (AUV) are addressed in this paper. By introducing a nonsingular coordinate transformation, a novel nonlinear reduced-order observer (NROO) is presented to achieve an accurate estimation of AUV’s state variables. A discrete-time model predictive control with nonlinear model online linearization (MPC-NMOL) is applied to enhance the attitude control and depth tracking performance of AUV considering the wave disturbance near surface. In AUV longitudinal control simulation, the comparisons have been presented between NROO and full-order observer (FOO) and also between MPC-NMOL and traditional NMPC. Simulation results show the effectiveness of the proposed method. Xuliang Yao, Guangyi Yang, and Yu Peng Copyright © 2017 Xuliang Yao et al. All rights reserved. On the Stochastic Dynamics of a Social Epidemics Model Mon, 02 Jan 2017 09:48:50 +0000 http://www.hindawi.com/journals/ddns/2017/6297074/ Alcohol abuse is a major social problem, which has caused a lot of damages or hidden dangers to the individual and the society. In this paper, with random factors of alcoholism considered in mortality rate of compartment populations, we formulate a stochastic alcoholism model according to compartment theory of infectious disease. Based on this model, we investigate the long-term stochastic dynamics behaviors of two equilibria of the corresponding deterministic model and point out the effect of random disturbance on the stability of the system. We find that when , we get the estimation between the trajectory of stochastic system and in the average in time with respect to the disturbance intensity, while when , stochastic system is ergodic and has the unique stationary distribution. Finally, we carry out numerical simulations to support the corresponding theoretical results. Xun-Yang Wang, Peng-Zhan Zhang, and Qing-Shan Yang Copyright © 2017 Xun-Yang Wang et al. All rights reserved. Consensus Analysis of Fractional-Order Multiagent Systems with Double-Integrator Mon, 02 Jan 2017 06:55:53 +0000 http://www.hindawi.com/journals/ddns/2017/9256532/ In nature, many phenomena can be explained by coordinated behavior of agents with fractional-order dynamics. In this paper, the consensus problem of fractional-order multiagent systems with double-integrator is studied, where the fractional-order satisfies . Based on the fractional-order stability theory, Mittag-Leffler function, and Laplace transform, a necessary and sufficient condition is obtained under the assumption that the directed graph for the communication network contains a directed spanning tree. Finally, an example with simulation is presented to illustrate the theoretical results. Chunde Yang, Wenjing Li, and Wei Zhu Copyright © 2017 Chunde Yang et al. All rights reserved. Neimark-Sacker Bifurcation in Demand-Inventory Model with Stock-Level-Dependent Demand Sun, 01 Jan 2017 13:33:54 +0000 http://www.hindawi.com/journals/ddns/2017/8162865/ An analysis of dynamics of demand-inventory model with stock-level-dependent demand formulated as a three-dimensional system of difference equations with four parameters is considered. By reducing the model to the planar system with five parameters, an analysis of one-parameter bifurcation of equilibrium points is presented. By the analytical method, we prove that nondegeneracy conditions for the existence of Neimark-Sacker bifurcation for the planar system are fulfilled. To check the sign of the first Lyapunov coefficient of Neimark-Sacker bifurcation, we use numerical simulations. We give phase portraits of the planar system to confirm the previous analytical results and show new interesting complex dynamical behaviours emerging in it. Finally, the economical interpretation of the system is given. Piotr Hachuła, Magdalena Nockowska-Rosiak, and Ewa Schmeidel Copyright © 2017 Piotr Hachuła et al. All rights reserved. A Nonhomogeneous Dirichlet Problem for a Nonlinear Pseudoparabolic Equation Arising in the Flow of Second-Grade Fluid Thu, 29 Dec 2016 12:09:30 +0000 http://www.hindawi.com/journals/ddns/2016/3875324/ We study the following initial-boundary value problem − + = , , ; , ; , where are given constants and and are given functions. In Part 1, we use the Galerkin method and compactness method to prove the existence of a unique weak solution of the problem above on for every In Part 2, we investigate asymptotic behavior of the solution as In Part 3, we prove the existence and uniqueness of a weak solution of problem − + = , , ; , associated with a “-periodic condition” , where is given constant. Le Thi Phuong Ngoc, Truong Thi Nhan, and Nguyen Thanh Long Copyright © 2016 Le Thi Phuong Ngoc et al. All rights reserved. Worst-Case Investment and Reinsurance Optimization for an Insurer under Model Uncertainty Tue, 27 Dec 2016 06:55:37 +0000 http://www.hindawi.com/journals/ddns/2016/9693419/ In this paper, we study optimal investment-reinsurance strategies for an insurer who faces model uncertainty. The insurer is allowed to acquire new business and invest into a financial market which consists of one risk-free asset and one risky asset whose price process is modeled by a Geometric Brownian motion. Minimizing the expected quadratic distance of the terminal wealth to a given benchmark under the “worst-case” scenario, we obtain the closed-form expressions of optimal strategies and the corresponding value function by solving the Hamilton-Jacobi-Bellman (HJB) equation. Numerical examples are presented to show the impact of model parameters on the optimal strategies. Xiangbo Meng, Ximin Rong, Lidong Zhang, and Ziping Du Copyright © 2016 Xiangbo Meng et al. All rights reserved. The European Vulnerable Option Pricing with Jumps Based on a Mixed Model Tue, 27 Dec 2016 06:10:59 +0000 http://www.hindawi.com/journals/ddns/2016/8035746/ In this paper, we combine the reduced-form model with the structural model to discuss the European vulnerable option pricing. We define that the default occurs when the default process jumps or the corporate goes bankrupt. Assuming that the underlying asset follows the jump-diffusion process and the default follows the Vasicek model, we can have the expression of European vulnerable option. Then we use the measure transformation and martingale method to derive the explicit solution of it. Chao Wang, Jianmin He, and Shouwei Li Copyright © 2016 Chao Wang et al. All rights reserved. A Parameter Estimation Method for Nonlinear Systems Based on Improved Boundary Chicken Swarm Optimization Mon, 26 Dec 2016 15:48:16 +0000 http://www.hindawi.com/journals/ddns/2016/3795961/ Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO) has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO) is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems. Shaolong Chen, Renyu Yang, Renhuan Yang, Liu Yang, Xiuzeng Yang, Chuangbiao Xu, Baoguo Xu, Huatao Zhang, Yaosheng Lu, and Weiping Liu Copyright © 2016 Shaolong Chen et al. All rights reserved. On the Periods of Biperiodic Fibonacci and Biperiodic Lucas Numbers Mon, 26 Dec 2016 14:05:09 +0000 http://www.hindawi.com/journals/ddns/2016/7341729/ This paper is concerned with periods of Biperiodic Fibonacci and Biperiodic Lucas sequences taken as modulo prime and prime power. By using Fermat’s little theorem, quadratic reciprocity, many results are obtained. Dursun Tascı and Gul Ozkan Kızılırmak Copyright © 2016 Dursun Tascı and Gul Ozkan Kızılırmak. All rights reserved. Dynamical Analysis of a Computer Virus Propagation Model with Delay and Infectivity in Latent Period Thu, 22 Dec 2016 12:02:59 +0000 http://www.hindawi.com/journals/ddns/2016/3067872/ A delayed SLB computer virus propagation model with infectivity in latent period is proposed in this paper. We establish sufficient conditions for local stability of the positive equilibrium and existence of Hopf bifurcation by analyzing distribution of the roots of the associated characteristic equation and applying the Hopf bifurcation theorem. Furthermore, properties of the Hopf bifurcation are determined by using the normal form theory and the center manifold theorem. Finally, numerical simulations supporting the theoretical analysis are carried out. Zizhen Zhang and Dianjie Bi Copyright © 2016 Zizhen Zhang and Dianjie Bi. All rights reserved. Collaboration and Evolution of E-Commerce and Express Delivery Industry Supply Chain Tue, 20 Dec 2016 14:00:36 +0000 http://www.hindawi.com/journals/ddns/2016/3452037/ Considering the contradictions between the electronic commerce (e-commerce) and its matching express delivery service, this paper investigates a supply chain regarding e-commerce and express delivery industry, in which collaborative operations of enterprises are discussed. The profitability and collaboration capability acting as order parameters and the rest of the influential resources including logistics, fund, information, and commodity are selected with their interrelations being examined based on servo theory of synergetics. Besides, evolutionary model of the e-commerce and express delivery industry is established and analyzed according to self-organization method of system dynamic theory to illustrate order parameters’ role in system evolution, and numerical analyses emerged to intuitively demonstrate the solutions. We conclude the work along with its results of significant references for investigating resource integrations by combining the two closely related businesses in an entire cooperative supply chain and providing guidelines for e-commerce and express delivery enterprises and industries in effective collaboration and system evolution. Ying Xu, Xuemei Zhang, Jian Cao, Ya Chen, and Xuhong Ye Copyright © 2016 Ying Xu et al. All rights reserved. Global Dynamics for a Novel Differential Infectivity Epidemic Model with Stage Structure Mon, 19 Dec 2016 09:41:16 +0000 http://www.hindawi.com/journals/ddns/2016/4823815/ A novel differential infectivity epidemic model with stage structure is formulated and studied. Under biological motivation, the stability of equilibria is investigated by the global Lyapunov functions. Some novel techniques are applied to the global dynamics analysis for the differential infectivity epidemic model. Uniform persistence and the sharp threshold dynamics are established; that is, the reproduction number determines the global dynamics of the system. Finally, numerical simulations are given to illustrate the main theoretical results. Yunguo Jin Copyright © 2016 Yunguo Jin. All rights reserved. Numerical Analysis of Discrete Switching Prey-Predator Model for Integrated Pest Management Thu, 08 Dec 2016 11:20:08 +0000 http://www.hindawi.com/journals/ddns/2016/8627613/ The switching discrete prey-predator model concerning integrated pest management has been proposed, and the switches are guided by the economic threshold (ET). To begin with, the regular and virtual equilibria of switching system have been discussed and the key parameter bifurcation diagrams for the existence of equilibria have been proposed, which reveal the three different regions of equilibria. Besides, numerical bifurcation analyses show that the switching discrete system may have complicated dynamics behavior including chaos and the coexistence of multiple attractors. Finally, the effects of key parameters on the switching frequencies and switching times are discussed and the sensitivity analysis of varying parameter values for mean switching times has also been given. The results proved that economic threshold (ET) and the growth rate () were the key parameters for pest control. Changcheng Xiang, Yi Yang, Zhongyi Xiang, and Wenjie Qin Copyright © 2016 Changcheng Xiang et al. All rights reserved. Global Solutions in the Species Competitive Chemotaxis System with Inequal Diffusion Rates Thu, 08 Dec 2016 07:14:03 +0000 http://www.hindawi.com/journals/ddns/2016/5015246/ This paper is devoted to studying the two-species competitive chemotaxis system with signal-dependent chemotactic sensitivities and inequal diffusion rates , , , , , , under homogeneous Neumann boundary conditions in a bounded and regular domain . If the nonnegative initial date and where the constants , the system possesses a unique global solution that is uniformly bounded under some suitable assumptions on the chemotaxis sensitivity functions , and linear chemical production function . Huaihuo Cao Copyright © 2016 Huaihuo Cao. All rights reserved. Weighted Complex Network Analysis of the Different Patterns of Metro Traffic Flows on Weekday and Weekend Wed, 07 Dec 2016 09:50:09 +0000 http://www.hindawi.com/journals/ddns/2016/9865230/ We present a multilayer model to characterize the weekday and weekend patterns in terms of the spatiotemporal flow size distributions in subway networks, based on trip data and operation timetables obtained from the Beijing Subway System. We also investigate the disparity of incoming and outgoing flows at a given station to describe the different spatial structure performance between transfer and nontransfer stations. In addition, we describe the essential interactions between PFN and TFN by defining an indicator, real load. By comparing with the two patterns on weekday and weekend, we found that the substantial trends have roughly the same form, with noticeable lower sizes of flows on weekend ascribed to the essential characteristics of travel demand. Jia Feng, Xiamiao Li, Baohua Mao, Qi Xu, and Yun Bai Copyright © 2016 Jia Feng et al. All rights reserved. Boundedly Rational User Equilibrium with Restricted Unused Routes Mon, 05 Dec 2016 06:11:00 +0000 http://www.hindawi.com/journals/ddns/2016/9848916/ A boundedly rational user equilibrium model with restricted unused routes (R-BRUE) considering the restrictions of both used route cost and unused route cost is proposed. The proposed model hypothesizes that for each OD pair no traveler can reduce his/her travel time by an indifference band by unilaterally changing route. Meanwhile, no route is unutilized if its travel time is lower than sum of indifference band and the shortest route cost. The largest and smallest used route sets are defined using mathematical expression. We also show that, with the increase of the indifference band, the largest and smallest used route sets will be augmented, and the critical values of indifference band to augment these two path sets are identified by solving the mathematical programs with equilibrium constraints. Based on the largest and smallest used route sets, the R-BRUE route set without paradoxical route is generated. The R-BRUE solution set can then be obtained by assigning all traffic demands to the corresponding generated route set. Various numerical examples are also provided to illustrate the essential ideas of the proposed model and structure of R-BRUE route flow solution set. Chao Sun, Menghui Li, Lin Cheng, Senlai Zhu, and Zhaoming Chu Copyright © 2016 Chao Sun et al. All rights reserved. Identifying the Determinants of CO2 Emission Change in China’s Power Sector Wed, 30 Nov 2016 13:26:55 +0000 http://www.hindawi.com/journals/ddns/2016/2626418/ Power sector is significantly important for China to achieve the CO2 emission reduction targets. In this study, we analyze the features of CO2 emissions and environment effect in China’s power sector, investigate the driving factors of CO2 emission change based on the logarithmic mean Divisia index (LMDI) method, and evaluate the mitigation potential of CO2 emissions in China’s power sector. Results show that CO2 emissions in China’s power sector increased rapidly from 492.00 Mt in 1990 to 3049.88 Mt in 2014 while CO2 emission intensity experienced an unsteady downward trend during the study period. Industrial scale effect is the key contributor to CO2 emission growth in China’s power sector, and its contribution degree reaches 123.97%. Energy intensity effect contributes most to the decrease in CO2 emissions, with a contribution degree of −20.01%. Capital productivity effect is another important factor leading to CO2 emissions increase. The aggregate CO2 emission reduction would reach 17973.86 million tons (Mt) during 2015–2030 in the ideal emission reduction scenario. Finally, policy recommendations are made for future energy-saving and CO2 emission reduction in China’s power sector. Caiqing Zhang, Mi Zhang, and Nan Zhang Copyright © 2016 Caiqing Zhang et al. All rights reserved. Fractal Dimension Analysis of the Julia Sets of Controlled Brusselator Model Wed, 30 Nov 2016 07:43:18 +0000 http://www.hindawi.com/journals/ddns/2016/8234108/ Fractal theory is a branch of nonlinear scientific research, and its research object is the irregular geometric form in nature. On account of the complexity of the fractal set, the traditional Euclidean dimension is no longer applicable and the measurement method of fractal dimension is required. In the numerous fractal dimension definitions, box-counting dimension is taken to characterize the complexity of Julia set since the calculation of box-counting dimension is relatively achievable. In this paper, the Julia set of Brusselator model which is a class of reaction diffusion equations from the viewpoint of fractal dynamics is discussed, and the control of the Julia set is researched by feedback control method, optimal control method, and gradient control method, respectively. Meanwhile, we calculate the box-counting dimension of the Julia set of controlled Brusselator model in each control method, which is used to describe the complexity of the controlled Julia set and the system. Ultimately we demonstrate the effectiveness of each control method. Yuqian Deng, Xiuxiong Liu, and Yongping Zhang Copyright © 2016 Yuqian Deng et al. All rights reserved.