Discrete Dynamics in Nature and Society https://www.hindawi.com The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Cross-Shareholdings Structural Characteristic and Evolution Analysis Based on Complex Network Mon, 27 Feb 2017 06:48:04 +0000 http://www.hindawi.com/journals/ddns/2017/5801386/ This study depicts the network morphology of firms which establish ties through cross-shareholdings by the theory of complex network analysis method. It calculates some complex network properties of the cross-shareholdings network and analyzes the evolution law of network structure in nearly 7 years. The network clearly displays small world properties and scale-free properties. The cross-shareholdings network average path length and clustering coefficient is with a small amplitude fluctuation; the network structure is relatively stable. Such a study is of practical importance and could provide opportunities for policy makers to improve the performance of the cross-shareholdings network. Xiaohong Chang and Haiyun Wang Copyright © 2017 Xiaohong Chang and Haiyun Wang. All rights reserved. An Identity in Commutative Rings with Unity with Applications to Various Sums of Powers Mon, 27 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/9092515/ Let be a commutative ring of characteristic ( may be equal to ) with unity and zero 0. Given a positive integer and the so-called -symmetric set such that for each , define the th power sum as , for We prove that for each positive integer there holds As an application, we obtain two new Pascal-like identities for the sums of powers of the first positive integers. Miomir Andjić and Romeo Meštrović Copyright © 2017 Miomir Andjić and Romeo Meštrović. All rights reserved. An Improved Unscented Kalman Filter for Discrete Nonlinear Systems with Random Parameters Sun, 26 Feb 2017 07:52:05 +0000 http://www.hindawi.com/journals/ddns/2017/7905690/ This paper investigates the nonlinear unscented Kalman filtering (UKF) problem for discrete nonlinear dynamic systems with random parameters. We develop an improved unscented transformation by incorporating the random parameters into the state vector to enlarge the number of sigma points. The theoretical analysis reveals that the approximated mean and covariance via the improved unscented transformation match the true values correctly up to the third order of Taylor series expansion. Based on the improved unscented transformation, an improved UKF method is proposed to expand the application of the UKF for nonlinear systems with random parameters. An application to the mobile source localization with time difference of arrival (TDOA) measurements and sensor position uncertainties is provided where the simulation results illustrate that the improved UKF method leads to a superior performance in comparison with the normal UKF method. Yue Wang, Zhijian Qiu, and Xiaomei Qu Copyright © 2017 Yue Wang et al. All rights reserved. Classical and Impulse Stochastic Control on the Optimization of Dividends with Residual Capital at Bankruptcy Thu, 23 Feb 2017 07:15:04 +0000 http://www.hindawi.com/journals/ddns/2017/2693568/ In this paper, we consider the optimization problem of dividends for the terminal bankruptcy model, in which some money would be returned to shareholders at the state of terminal bankruptcy, while accounting for the tax rate and transaction cost for dividend payout. Maximization of both expected total discounted dividends before bankruptcy and expected discounted returned money at the state of terminal bankruptcy becomes a mixed classical-impulse stochastic control problem. In order to solve this problem, we reduce it to quasi-variational inequalities with a nonzero boundary condition. We explicitly construct and verify solutions of these inequalities and present the value function together with the optimal policy. Peimin Chen and Bo Li Copyright © 2017 Peimin Chen and Bo Li. All rights reserved. Existence and Exponential Stability of Solutions to Stochastic Neutral Functional Differential Equations Wed, 22 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2623035/ In this paper we consider the existence and stability of solutions to stochastic neutral functional differential equations with finite delays. Under suitable conditions, the existence and exponential stability of solutions were obtained by using the semigroup approach and Banach fixed point theorem. Ling Hu, Zheng Wu, Zhangzhi Wei, and Lianglong Wang Copyright © 2017 Ling Hu et al. All rights reserved. Ticket Fare Optimization for China’s High-Speed Railway Based on Passenger Choice Behavior Tue, 21 Feb 2017 08:57:21 +0000 http://www.hindawi.com/journals/ddns/2017/6237642/ Although China’s high-speed railway (HSR) is maturing after more than ten years of construction and development, the load factor and revenue of HSR could still be improved by optimizing the ticket fare structure. Different from the present unitary and changeless fare structure, this paper explores the application of multigrade fares to China’s HSR. On the premise that only one fare grade can be offered for each origin-destination (O-D) at the same time, this paper addresses the questions of how to adjust ticket price over time to maximize the revenue. First, on the basis of piecewise pricing strategy, a ticket fare optimization model is built, which could be transformed to convex program to be solved. Then, based on the analysis of passenger arrival regularity using historical ticket data of Beijing-Shanghai HSR line, several experiments are performed using the method proposed in the paper to explore the properties of the optimal multigrade fare scheme. Jinzi Zheng, Jun Liu, and David B. Clarke Copyright © 2017 Jinzi Zheng et al. All rights reserved. On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease Sun, 19 Feb 2017 12:54:39 +0000 http://www.hindawi.com/journals/ddns/2017/4232971/ This paper studies the nonnegativity and local and global stability properties of the solutions of a newly proposed SEIADR model which incorporates asymptomatic and dead-infective subpopulations into the standard SEIR model and, in parallel, it incorporates feedback vaccination plus a constant term on the susceptible and feedback antiviral treatment controls on the symptomatic infectious subpopulation. A third control action of impulsive type (or “culling”) consists of the periodic retirement of all or a fraction of the lying corpses which can become infective in certain diseases, for instance, the Ebola infection. The three controls are allowed to be eventually time varying and contain a total of four design control gains. The local stability analysis around both the disease-free and endemic equilibrium points is performed by the investigation of the eigenvalues of the corresponding Jacobian matrices. The global stability is formally discussed by using tools of qualitative theory of differential equations by using Gauss-Stokes and Bendixson theorems so that neither Lyapunov equation candidates nor the explicit solutions are used. It is proved that stability holds as a parallel property to positivity and that disease-free and the endemic equilibrium states cannot be simultaneously either stable or unstable. The periodic limit solution trajectories and equilibrium points are analyzed in a combined fashion in the sense that the endemic periodic solutions become, in particular, equilibrium points if the control gains converge to constant values and the control gain for culling the infective corpses is asymptotically zeroed. M. De la Sen, A. Ibeas, S. Alonso-Quesada, and R. Nistal Copyright © 2017 M. De la Sen et al. All rights reserved. An Improved Apriori Algorithm Based on an Evolution-Communication Tissue-Like P System with Promoters and Inhibitors Sun, 19 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/6978146/ Apriori algorithm, as a typical frequent itemsets mining method, can help researchers and practitioners discover implicit associations from large amounts of data. In this work, a fast Apriori algorithm, called ECTPPI-Apriori, for processing large datasets, is proposed, which is based on an evolution-communication tissue-like P system with promoters and inhibitors. The structure of the ECTPPI-Apriori algorithm is tissue-like and the evolution rules of the algorithm are object rewriting rules. The time complexity of ECTPPI-Apriori is substantially improved from that of the conventional Apriori algorithms. The results give some hints to improve conventional algorithms by using membrane computing models. Xiyu Liu, Yuzhen Zhao, and Minghe Sun Copyright © 2017 Xiyu Liu et al. All rights reserved. Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance Wed, 15 Feb 2017 09:53:46 +0000 http://www.hindawi.com/journals/ddns/2017/9730312/ In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs) subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC) is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC) law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO) is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach. Xiaohui Mo, Huawei Niu, and Qixun Lan Copyright © 2017 Xiaohui Mo et al. All rights reserved. Factor Analysis Model Based on the Theory of the TOPSIS in the Application Research Tue, 14 Feb 2017 10:13:00 +0000 http://www.hindawi.com/journals/ddns/2017/9173460/ In view of the existing literature panel data factor analysis model in practical application of the deficiency, this paper established the model of factor analysis based on TOPSIS method, which is applied to the analysis of the panel data factor in practice. Compared with the generalized dynamic factor analysis model, the model does not need to satisfy the 4 assumptions of the generalized dynamic factor analysis model at the same time. The model is calculated with regard to every year’s cross section data factor composite scores the highest and lowest, respectively, for the best and worst vector. By TOPSIS theory, the optimal factor scheme approach degree of each research object is obtained. Take the development of China’s service industry as an example; use the optimal factor scheme proximity of model degree to depict the eastern, central, and western development of service industry. The study found that the development of service industry in eastern provinces and in central and western regions differs greatly. In total, China’s service industry has a great development space. Guowang Luo, Yanmin Liu, and Xiaoling Mo Copyright © 2017 Guowang Luo et al. All rights reserved. Global Dynamics and Optimal Control of a Viral Infection Model with Generic Nonlinear Infection Rate Mon, 13 Feb 2017 11:19:47 +0000 http://www.hindawi.com/journals/ddns/2017/7571017/ This paper is devoted to exploring the combined impact of a generic nonlinear infection rate and infected removable storage media on viral spread. For that purpose, a novel dynamical model with an external compartment is proposed, and the explanations of the main model assumptions (especially the generic nonlinear infection rate) are also examined. The existence and global stability of the unique equilibrium of the model are fully investigated, from which it can be seen that computer virus would persist. On this basis, a next-best approach to controlling the level of infected computers is suggested, and the theoretical analysis of optimal control of the model is also performed. Additionally, some numerical examples are given to illustrate the main results. Chenquan Gan, Maobin Yang, Zufan Zhang, and Wanping Liu Copyright © 2017 Chenquan Gan et al. All rights reserved. Simulation-Based Dynamic Passenger Flow Assignment Modelling for a Schedule-Based Transit Network Mon, 13 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2890814/ The online operation management and the offline policy evaluation in complex transit networks require an effective dynamic traffic assignment (DTA) method that can capture the temporal-spatial nature of traffic flows. The objective of this work is to propose a simulation-based dynamic passenger assignment framework and models for such applications in the context of schedule-based rail transit systems. In the simulation framework, travellers are regarded as individual agents who are able to obtain complete information on the current traffic conditions. A combined route selection model integrated with pretrip route selection and entrip route switch is established for achieving the dynamic network flow equilibrium status. The train agent is operated strictly with the timetable and its capacity limitation is considered. A continuous time-driven simulator based on the proposed framework and models is developed, whose performance is illustrated through a large-scale network of Beijing subway. The results indicate that more than 0.8 million individual passengers and thousands of trains can be simulated simultaneously at a speed ten times faster than real time. This study provides an efficient approach to analyze the dynamic demand-supply relationship for large schedule-based transit networks. Xiangming Yao, Baomin Han, Dandan Yu, and Hui Ren Copyright © 2017 Xiangming Yao et al. All rights reserved. Global Attractivity in a Discrete Mutualism Model with Infinite Deviating Arguments Sun, 12 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2912147/ A set of sufficient conditions is obtained for the global attractivity of the following two-species discrete mutualism model with infinite deviating arguments: and , where , , are all positive constants, , and . Our results generalize the main result of Yang et al. (2014). Xiangdong Xie, Yalong Xue, and Runxin Wu Copyright © 2017 Xiangdong Xie et al. All rights reserved. Hartman-Wintner-Type Inequality for a Fractional Boundary Value Problem via a Fractional Derivative with respect to Another Function Sun, 12 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/5123240/ We consider a fractional boundary value problem involving a fractional derivative with respect to a certain function . A Hartman-Wintner-type inequality is obtained for such problem. Next, several Lyapunov-type inequalities are deduced for different choices of the function . Moreover, some applications to eigenvalue problems are presented. Mohamed Jleli, Mokhtar Kirane, and Bessem Samet Copyright © 2017 Mohamed Jleli et al. All rights reserved. Research on Modeling Intrahousehold Interactions from the Perspective of Space-Time Constraints Thu, 09 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/2917106/ Interactions among family members can yield valuable information for interpreting individual travel decisions. Typically, each family member plays a set role and travel decisions are made by considering the combined needs of household members. This study investigates both multiactivity and multiperson interactions in urban nuclear families and proposes the novel concepts of “activity-restriction degree” and “activity-constraint niche” to quantify the degree of space-time constraints within time geography. A structural equation model is employed to analyze intrahousehold interactions based on individual activity-travel patterns during the workday. The results indicate that the links between family members reflect behavioral responses (with constraints) between individuals and other family members. Household interaction constraints not only influence individual travel decisions but also affect the realization of the household activity for everyone. These interactions lead to reasonable adjustments and mutual support and to the identification of efficient activity patterns that meet the demands of the entire household. Liangpeng Gao, Yanjie Ji, Yang Liu, and Baohong He Copyright © 2017 Liangpeng Gao et al. All rights reserved. Centralized Data-Sampling Approach for Global Synchronization of Fractional-Order Neural Networks with Time Delays Thu, 09 Feb 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/6157292/ In this paper, the global synchronization problem is investigated for a class of fractional-order neural networks with time delays. Taking into account both better control performance and energy saving, we make the first attempt to introduce centralized data-sampling approach to characterize the synchronization design strategy. A sufficient criterion is given under which the drive-response-based coupled neural networks can achieve global synchronization. It is worth noting that, by using centralized data-sampling principle, fractional-order Lyapunov-like technique, and fractional-order Leibniz rule, the designed controller performs very well. Two numerical examples are presented to illustrate the efficiency of the proposed centralized data-sampling scheme. Jin-E Zhang Copyright © 2017 Jin-E Zhang. All rights reserved. A Dynamic Stackelberg Game of Supply Chain for a Corporate Social Responsibility Thu, 02 Feb 2017 08:37:52 +0000 http://www.hindawi.com/journals/ddns/2017/8656174/ In this paper, we establish a dynamic game to allocate CSR (Corporate Social Responsibility) to the members of a supply chain. We propose a model of a supply chain in a decentralized state which includes a supplier and a manufacturer. For analyzing supply chain performance in decentralized state and the relationships between the members of the supply chain, we formulate a model that crosses through multiperiods with the help of a dynamic discrete Stackelberg game which is made under two different information structures. We obtain an equilibrium point at which both the profits of members and the level of CSR taken up by supply chains are maximized. Massimiliano Ferrara, Mehrnoosh Khademi, Mehdi Salimi, and Somayeh Sharifi Copyright © 2017 Massimiliano Ferrara et al. All rights reserved. Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs Wed, 01 Feb 2017 13:57:17 +0000 http://www.hindawi.com/journals/ddns/2017/6079450/ The hyper-Zagreb index is an important branch in the Zagreb indices family, which is defined as , where is the degree of the vertex in a graph . In this paper, the monotonicity of the hyper-Zagreb index under some graph transformations was studied. Using these nice mathematical properties, the extremal graphs among -vertex trees (acyclic), unicyclic, and bicyclic graphs are determined for hyper-Zagreb index. Furthermore, the sharp upper and lower bounds on the hyper-Zagreb index of these graphs are provided. Wei Gao, Muhammad Kamran Jamil, Aisha Javed, Mohammad Reza Farahani, Shaohui Wang, and Jia-Bao Liu Copyright © 2017 Wei Gao et al. All rights reserved. A Perspective of Evolution for Carbon Emissions Trading Market: The Dilemma between Market Scale and Government Regulation Wed, 01 Feb 2017 08:05:12 +0000 http://www.hindawi.com/journals/ddns/2017/1432052/ Which means are more effective for reducing carbon emission? Our paper argues the effect of the government regulation and the market trading on the carbon emission. Based on our model, we obtain three conclusions as follows. First, government strengthened regulation can encourage firms to participate in the trading market for carbon emission. Second, there is the negative relation of supervision cost to trading price. Third, there is an alternative relationship between the scale economy level of the supervisory authority and that of the carbon emissions market. Meanwhile, our numerical simulations also confirm our results for our model analyses. Qi Zhu Copyright © 2017 Qi Zhu. All rights reserved. Finite-Time Bounded Synchronization of the Growing Complex Network with Nondelayed and Delayed Coupling Mon, 30 Jan 2017 14:18:24 +0000 http://www.hindawi.com/journals/ddns/2017/6501583/ The objective of this paper is to discuss finite-time bounded synchronization for a class of the growing complex network with nondelayed and delayed coupling. In order to realize finite-time synchronization of complex networks, a new finite-time stable theory is proposed; effective criteria are developed to realize synchronization of the growing complex dynamical network in finite time. Moreover, the error of two growing networks is bounded simultaneously in the process of finite-time synchronization. Finally, some numerical examples are provided to verify the theoretical results established in this paper. Yuhua Xu, Jincheng Zhang, Wuneng Zhou, and Dongbing Tong Copyright © 2017 Yuhua Xu et al. All rights reserved. An Enhanced Supervisory Control Strategy for Periodicity Mutual Exclusions in Discrete Event Systems Based on Petri Nets Mon, 30 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/1395142/ Mutual exclusion problems widely exist in discrete event systems in which several processes will compete for the common resource for maintaining their normal running. This competition is mutually exclusive. However, a special behavior, that is, periodic mutual exclusion behavior, is important for many discrete event systems. Once a process obtains the common resource, it will consecutively obtain the common resource in the following several competitions. The other processes should wait for the release of the common resource. All processes will compete for the common resource again after the common resource is released. These competitions have obvious periodicity. In this paper, a methodology is proposed to design periodic mutual exclusion supervisors to control the periodic mutual exclusion behavior in discrete event systems. Moreover, two original structural conversion concepts, called -derivation and -convergence processes, are proposed to construct the periodic mutual exclusion supervisors. The discussion results show that many undesirable execution sequences are forbidden since the periodic mutual exclusion behavior is controlled by the proposed periodic mutual exclusion supervisors. Finally, an example is used to illustrate the proposed methodology. Zhongyuan Jiang, Huan Wang, Xiaoliang Chen, Mingwei Tang, and Jianhong Ye Copyright © 2017 Zhongyuan Jiang et al. All rights reserved. Differential Games and Discrete Dynamics in Applied Sciences Tue, 24 Jan 2017 09:20:40 +0000 http://www.hindawi.com/journals/ddns/2017/6023140/ Massimiliano Ferrara, Gafurjan Ibragimov, and Vincenzo Scalzo Copyright © 2017 Massimiliano Ferrara et al. All rights reserved. The Total Return Swap Pricing Model under Fuzzy Random Environments Tue, 24 Jan 2017 08:17:37 +0000 http://www.hindawi.com/journals/ddns/2017/9762841/ This paper models the jump amplitude and frequency of random parameters of asset value as a triangular fuzzy interval. In other words, we put forward a new double exponential jump diffusion model with fuzziness, express the parameters in terms of total return swap pricing, and derive a fuzzy form pricing formula for the total return swap. Following simulation, we find that the more the fuzziness in financial markets, the more the possibility of fuzzy credit spreads enlarging. On the other hand, when investors exhibit stronger subjective beliefs, fuzzy credit spreads diminish. Using fuzzy information and random analysis, one can consider more uncertain sources to explain how the asset price jump process works and the subjective judgment of investors in financial markets under a variety of fuzzy conditions. An appropriate price range will give investors more flexibility in making a choice. Liang Wu, Jun-tao Wang, Jie-fang Liu, and Ya-ming Zhuang Copyright © 2017 Liang Wu et al. All rights reserved. Qualitative Stability Analysis of an Obesity Epidemic Model with Social Contagion Tue, 24 Jan 2017 00:00:00 +0000 http://www.hindawi.com/journals/ddns/2017/1084769/ We study an epidemiological mathematical model formulated in terms of an ODE system taking into account both social and nonsocial contagion risks of obesity. Analyzing first the case in which the model presents only the effect due to social contagion and using qualitative methods of the stability analysis, we prove that such system has at the most three equilibrium points, one disease-free equilibrium and two endemic equilibria, and also that it has no periodic orbits. Particularly, we found that when considering (the basic reproductive number) as a parameter, the system exhibits a backward bifurcation: the disease-free equilibrium is stable when and unstable when , whereas the two endemic equilibria appear from (a specific positive value reached by and less than unity), one being asymptotically stable and the other unstable, but for values, only the former remains inside the feasible region. On the other hand, considering social and nonsocial contagion and following the same methodology, we found that the dynamic of the model is simpler than that described above: it has a unique endemic equilibrium point that is globally asymptotically stable. Enrique Lozano-Ochoa, Jorge Fernando Camacho, and Cruz Vargas-De-León Copyright © 2017 Enrique Lozano-Ochoa et al. 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.