Discrete Dynamics in Nature and Society http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. The Applications of Algebraic Methods on Stable Analysis for General Differential Dynamical Systems with Multidelays Thu, 28 May 2015 14:29:19 +0000 http://www.hindawi.com/journals/ddns/2015/984323/ The distribution of purely imaginary eigenvalues and stabilities of generally singular or neutral differential dynamical systems with multidelays are discussed. Choosing delays as parameters, firstly with commensurate case, we find new algebraic criteria to determine the distribution of purely imaginary eigenvalues by using matrix pencil, linear operator, matrix polynomial eigenvalues problem, and the Kronecker product. Additionally, we get practical checkable conditions to verdict the asymptotic stability and Hopf bifurcation of differential dynamical systems. At last, with more general case, the incommensurate, we mainly study critical delays when the system appears purely imaginary eigenvalue. Jian Ma and Baodong Zheng Copyright © 2015 Jian Ma and Baodong Zheng. All rights reserved. Empirical Bayes Inference for the Parameter of Power Distribution Based on Ranked Set Sampling Thu, 28 May 2015 12:13:47 +0000 http://www.hindawi.com/journals/ddns/2015/760768/ This research is based on ranked set sampling. Through the analysis and proof, the empirical Bayes test rule and asymptotical property for the parameter of power distribution are obtained. Naiyi Li, Yuan Li, Yongming Li, and Yang Liu Copyright © 2015 Naiyi Li et al. All rights reserved. Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms Wed, 27 May 2015 13:53:25 +0000 http://www.hindawi.com/journals/ddns/2015/273026/ We study heterogeneous Cournot oligopolies of variable sizes and compositions, in which the firms have different degrees of rationality, being either rational firms with perfect foresight or naive best response firms with static expectations. Each oligopoly can be described using its size and composition, that is, the fraction of firms that are rational. We take into account two frameworks, one in which the decisional rules are exogenously assigned and the other in which the firms may change their heuristics. We consider a switching mechanism based on a logit rule, where the switching propensity is regulated by a parameter which represents the evolutionary pressure. In the fixed fractions setting, we prove that, in general, the composition has a stabilizing effect, while increasing the oligopoly size leads to instability. However, we show that, for particular parameters settings, stability is not affected by the composition or the firms number. Similarly, in the evolutionary fractions setting, we analytically prove that when marginal costs are identical, increasing the evolutionary pressure has a destabilizing effect. Nevertheless, focusing on particular examples with different marginal costs we are able to show that evolutionary pressure may also have a stabilizing or a neutral role. Fausto Cavalli, Ahmad Naimzada, and Marina Pireddu Copyright © 2015 Fausto Cavalli et al. All rights reserved. Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion Wed, 27 May 2015 07:08:55 +0000 http://www.hindawi.com/journals/ddns/2015/371852/ We consider a delayed predator-prey model with harvesting effort and impulsive diffusion between two patches. By the impulsive comparison theorem and the discrete dynamical system determined by the stroboscopic map, we obtain some sufficient conditions on the existence and global attractiveness of predator-eradicated periodic solution for the system. Furthermore, the permanence of the system is derived. The obtained results will modify and improve the ones in some existing publications and give the estimate for the ultimately low and upper boundedness of the systems. Lingzhi Huang and Zhichun Yang Copyright © 2015 Lingzhi Huang and Zhichun Yang. All rights reserved. Basin of Attraction through Invariant Curves and Dominant Functions Tue, 26 May 2015 11:35:01 +0000 http://www.hindawi.com/journals/ddns/2015/160672/ We study a second-order difference equation of the form , where both and are decreasing. We consider a set of invariant curves at and use it to characterize the behaviour of solutions when and when . The case is related to the Y2K problem. For , we study the stability of the equilibrium solutions and find an invariant region where solutions are attracted to the stable equilibrium. In particular, for certain range of the parameters, a subset of the basin of attraction of the stable equilibrium is achieved by bounding positive solutions using the iteration of dominant functions with attracting equilibria. Ziyad AlSharawi, Asma Al-Ghassani, and A. M. Amleh Copyright © 2015 Ziyad AlSharawi et al. All rights reserved. Analysis of Linkage Effects among Currency Networks Using REER Data Thu, 21 May 2015 11:31:39 +0000 http://www.hindawi.com/journals/ddns/2015/641907/ We modeled the currency networks through the use of REER (real effective exchange rate) instead of a bilateral exchange rate in order to overcome the confusion in selecting base currencies. Based on the MST (minimum spanning tree) approach and the rolling-window method, we constructed time-varying and correlation-based networks with which we investigate the linkage effects among different currencies. In particular, and as the source of empirical data, we chose the monthly REER data for a set of 61 major currencies during the period from 1994 to 2014. The study demonstrated that obvious linkage effects existed among currency networks and the euro (EUR) was confirmed as the predominant world currency. Additionally, we used the rolling-window method to investigate the stability of linkage effects, doing so by calculating the mean correlations and mean distances as well as the normalized tree length and degrees of those currencies. The results showed that financial crises during the study period had a great effect on the currency network’s topology structure and led to more clustered currency networks. Our results suggested that it is more appropriate to estimate the linkage effects among currency networks through the use of REER data. Haishu Qiao, Ying Li, and Yue Xia Copyright © 2015 Haishu Qiao et al. All rights reserved. New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay Wed, 20 May 2015 07:55:59 +0000 http://www.hindawi.com/journals/ddns/2015/480816/ The problem of finite-time stability for linear discrete time systems with state time-varying delay is considered in this paper. Two finite sum inequalities for estimating weighted norms of delayed states are proposed in order to obtain less conservative stability criteria. By using Lyapunov-Krasovskii-like functional with power function, two sufficient conditions of finite-time stability are proposed and expressed in the form of linear matrix inequalities (LMIs), which are dependent on the minimum and maximum delay bounds. The numerical example is presented to illustrate the applicability of the developed results. It was shown that the obtained results are less conservative than some existing ones in the literature. Sreten B. Stojanovic Copyright © 2015 Sreten B. Stojanovic. All rights reserved. A Parallel Spectral Element Method for Fractional Lorenz System Wed, 20 May 2015 07:34:09 +0000 http://www.hindawi.com/journals/ddns/2015/682140/ We provide a parallel spectral element method for the fractional Lorenz system numerically. The detailed construction and implementation of the method are presented. Thanks to the spectral accuracy of the presented method, the storage requirement due to the “global time dependence” can be considerably relaxed. Also, the parareal method combining spectral element method reduces the computing time greatly. Finally, we have tested the chaotic behaviors of fractional Lorenz system. Our numerical results are in excellent agreement with the results from other numerical methods. Yanhui Su Copyright © 2015 Yanhui Su. All rights reserved. Change Point Determination for an Attribute Process Using an Artificial Neural Network-Based Approach Wed, 20 May 2015 05:50:27 +0000 http://www.hindawi.com/journals/ddns/2015/892740/ The change point identification has played a vital role in process improvement for an attribute process. This identification is able to effectively help process personnel to quickly determine the corresponding root causes and significantly improve the underlying process. Although many studies have focused on identifying the change point of a process, a generic identification approach has not been developed. The typical maximum likelihood estimator (MLE) approach has limitations: particularly, the known prior process distribution and mathematical difficulties. These deficiencies are commonly encountered in practice. Accordingly, this study proposes an artificial neural network (ANN) mechanism to overcome the difficulties of typical MLE approach in determining the change point of an attribute process. Specifically, the performance among the statistical process control (SPC) chart alone, the typical MLE approach, and the proposed ANN mechanism are investigated for the following cases: (1) a known attribute process distribution with the associated MLE being available to be used, (2) an unknown attribute process distribution with the MLE being unable to be used, and (3) an unknown attribute process distribution with the MLE being misused. The superior results and the performance of the proposed approach are reported and discussed. Yuehjen E. Shao and Ke-Shan Lin Copyright © 2015 Yuehjen E. Shao and Ke-Shan Lin. All rights reserved. Coping with Loss Aversion in the Newsvendor Model Mon, 18 May 2015 13:38:12 +0000 http://www.hindawi.com/journals/ddns/2015/851586/ We introduce loss aversion into the decision framework of the newsvendor model. By introducing the loss aversion coefficient , we propose a novel utility function for the loss-averse newsvendor. First, we obtain the optimal order quantity to maximize the expected utility for the loss-averse newsvendor who is risk-neutral. It is found that this optimal order quantity is smaller than the expected profit maximization order quantity in the classical newsvendor model, which may help to explain the decision bias in the classical newsvendor model. Then, to reduce the risk which originates from the fluctuation in the market demand, we achieve the optimal order quantity to maximize CVaR about utility for the loss-averse newsvendor who is risk-averse. We find that this optimal order quantity is smaller than the optimal order quantity to maximize the expected utility above and is decreasing in the confidence level . Further, it is proved that the expected utility under this optimal order quantity is decreasing in the confidence level , which verifies that low risk implies low return. Finally, a numerical example is given to illustrate the obtained results and some management insights are suggested for the loss-averse newsvendor model. Jianwu Sun and Xinsheng Xu Copyright © 2015 Jianwu Sun and Xinsheng Xu. All rights reserved. A Correlated Model for Evaluating Performance and Energy of Cloud System Given System Reliability Mon, 18 May 2015 06:53:08 +0000 http://www.hindawi.com/journals/ddns/2015/497048/ The serious issue of energy consumption for high performance computing systems has attracted much attention. Performance and energy-saving have become important measures of a computing system. In the cloud computing environment, the systems usually allocate various resources (such as CPU, Memory, Storage, etc.) on multiple virtual machines (VMs) for executing tasks. Therefore, the problem of resource allocation for running VMs should have significant influence on both system performance and energy consumption. For different processor utilizations assigned to the VM, there exists the tradeoff between energy consumption and task completion time when a given task is executed by the VMs. Moreover, the hardware failure, software failure and restoration characteristics also have obvious influences on overall performance and energy. In this paper, a correlated model is built to analyze both performance and energy in the VM execution environment given the reliability restriction, and an optimization model is presented to derive the most effective solution of processor utilization for the VM. Then, the tradeoff between energy-saving and task completion time is studied and balanced when the VMs execute given tasks. Numerical examples are illustrated to build the performance-energy correlated model and evaluate the expected values of task completion time and consumed energy. Hongli Zhang, Panpan Li, and Zhigang Zhou Copyright © 2015 Hongli Zhang et al. All rights reserved. Nonlinear Dynamics in Epidemic Systems Sun, 17 May 2015 12:57:21 +0000 http://www.hindawi.com/journals/ddns/2015/703695/ Li Li, Zhen Jin, Sanling Yuan, Kaifa Wang, Alexander B. Medvinsky, and Bai-Lian Li Copyright © 2015 Li Li et al. All rights reserved. Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity Sun, 17 May 2015 06:36:49 +0000 http://www.hindawi.com/journals/ddns/2015/654507/ We formulate a ()-dimensional viral infection model with humoral immunity, classes of uninfected target cells and   classes of infected cells. The incidence rate of infection is given by nonlinear incidence rate, Beddington-DeAngelis functional response. The model admits discrete time delays describing the time needed for infection of uninfected target cells and virus replication. By constructing suitable Lyapunov functionals, we establish that the global dynamics are determined by two sharp threshold parameters: and . Namely, a typical two-threshold scenario is shown. If , the infection-free equilibrium is globally asymptotically stable, and the viruses are cleared. If , the immune-free equilibrium is globally asymptotically stable, and the infection becomes chronic but with no persistent antibody immune response. If , the endemic equilibrium is globally asymptotically stable, and the infection is chronic with persistent antibody immune response. Xinxin Tian and Jinliang Wang Copyright © 2015 Xinxin Tian and Jinliang Wang. All rights reserved. Influence of Dynamical Change of Edges on Clustering Coefficients Thu, 14 May 2015 13:56:26 +0000 http://www.hindawi.com/journals/ddns/2015/172720/ Clustering coefficient is a very important measurement in complex networks, and it describes the average ratio between the actual existent edges and probable existent edges in the neighbor of one vertex in a complex network. Besides, in a complex networks, the dynamic change of edges can trigger directly the evolution of network and further affect the clustering coefficients. As a result, in this paper, we investigate the effects of the dynamic change of edge on the clustering coefficients. It is illustrated that the increase and decrease of the clustering coefficient can be effectively controlled by adding or deleting several edges of the network in the evolution of complex networks. Yuhong Ruan and Anwei Li Copyright © 2015 Yuhong Ruan and Anwei Li. All rights reserved. Improved Results on Reachable Set Bounding for Linear Delayed Systems with Polytopic Uncertainties Thu, 14 May 2015 12:14:20 +0000 http://www.hindawi.com/journals/ddns/2015/895412/ This paper focuses on bound of reachable sets for delayed linear systems with polytopic uncertainties. Based on Lyapunov-Krasovskii functional theory, delay decomposition technique, and reciprocally convex method, some new results expressed in the form of linear matrix inequalities are derived. It should be noted that triple integral functionals are first to be introduced for reachable set analysis. Consequently, a tighter bound of the reachable set is obtained. Four numerical examples are given to illustrate the effectiveness and advantage of the proposed results comparing with the existing criteria. Hao Chen Copyright © 2015 Hao Chen. All rights reserved. Transient Analysis of a -out-of- System with -Policy, Repairmen’s Multiple Vacations, and Redundant Dependency Thu, 14 May 2015 12:06:43 +0000 http://www.hindawi.com/journals/ddns/2015/209653/ This paper analyzes a -out-of-: repairable system with -policy, repairmen’s multiple synchronous vacations, and redundant dependency. When there is no failed component in the system, the repairmen leave for a vacation, the duration of which follows a phase type distribution. Upon returning from vacation, they should take another vacation if there are less than failed components waiting in the system. This pattern continues until at least failed components are waiting. Moreover, the redundant dependency which is a special kind of failure dependency is taken into account in the multicomponent system. Under such assumptions, the availability, the rate of occurrence of failures, and the reliability of the system are derived in transient regime by applying the quasi-birth-and-death process. Furthermore, the Runge-Kutta method is carried out to numerically discuss the time-dependent behavior of the system reliability measures. Finally, a special case of the system is presented to show the validity of our model. Wenqing Wu and Yinghui Tang Copyright © 2015 Wenqing Wu and Yinghui Tang. All rights reserved. Stability Analysis for a Fractional HIV Infection Model with Nonlinear Incidence Thu, 14 May 2015 11:12:09 +0000 http://www.hindawi.com/journals/ddns/2015/563127/ We introduce the fractional-order derivatives into an HIV infection model with nonlinear incidence and show that the established model in this paper possesses nonnegative solution, as desired in any population dynamics. We also deal with the stability of the infection-free equilibrium, the immune-absence equilibrium, and the immune-presence equilibrium. Numerical simulations are carried out to illustrate the results. Linli Zhang, Gang Huang, Anping Liu, and Ruili Fan Copyright © 2015 Linli Zhang et al. All rights reserved. Analysis of a Viral Infection Model with Delayed Nonlytic Immune Response Thu, 14 May 2015 08:40:19 +0000 http://www.hindawi.com/journals/ddns/2015/235420/ We investigate the dynamical behavior of a virus infection model with delayed nonlytic immune response. By analyzing corresponding characteristic equations, the local stabilities of two boundary equilibria are established. By using suitable Lyapunov functional and LaSalle’s invariance principle, we establish the global stability of the infection-free equilibrium. We find that the infection free equilibrium is globally asymptotically stable when , and the infected equilibrium without immunity is local asymptotically stable when . Under the condition we obtain the sufficient conditions to the local stability of the infected equilibrium with immunity . We show that the time delay can change the stability of and lead to the existence of Hopf bifurcations. The stabilities of bifurcating periodic solutions are studied and numerical simulations to our theorems are provided. Mengye Chen, Liang You, Jie Tang, Shasha Su, and Ruiming Zhang Copyright © 2015 Mengye Chen et al. All rights reserved. Positive Periodic Solutions of a Neutral Impulsive Predator-Prey Model Thu, 14 May 2015 07:45:30 +0000 http://www.hindawi.com/journals/ddns/2015/818506/ We investigate a ratio-dependent predator-prey model with Holling type III functional response based on system of neutral impulsive differential equations. Sufficient conditions for existence of positive periodic solutions are obtained by applying continuation theorem. Our main results demonstrate that under the suitable periodic impulse perturbations, the neutral impulsive system preserves the periodicity of the corresponding neutral system without impulse. In addition, our results can be applied to the corresponding system without impulsive effect, and thus, extend previous results. Guirong Liu and Xiaojuan Song Copyright © 2015 Guirong Liu and Xiaojuan Song. All rights reserved. Modeling and Analyzing the Spread of Flash Disk Worms via Multiple Subnets Thu, 14 May 2015 07:44:56 +0000 http://www.hindawi.com/journals/ddns/2015/941862/ The Flash Disk worms, spreading via both Web-based scanning and removable devices between multiple subnets, have become a serious threat to the Internet, especially those physically isolated subnets. We present a model which incorporates specific features of these worms in this paper. Then, we analyze the dynamic behaviors of the model when one subnet is considered. Analytical result shows that the Flash Disk worm can self-perpetuate when and will die out otherwise. When multiple subnets are considered, we get that once a computer is infected by the Flash Disk worms, other computers in that subnet will be infected in a short time. Thus, for any subnet, to contain the Flash Disk worms, the most effective way is to prevent the first infected individual by improving the users’ security awareness of using removed devices. Our results are illustrated by numerical simulation. Guihua Li, Zhenzhen Peng, and Lipeng Song Copyright © 2015 Guihua Li et al. All rights reserved. On the Stability and Equilibrium Points of Multistaged Epidemic Models Thu, 14 May 2015 06:56:27 +0000 http://www.hindawi.com/journals/ddns/2015/379576/ This paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as -model to study its stability. The model includes successive stages of infectious subpopulations, each one acting at the exposed subpopulation of the next infectious stage in a cascade global disposal where each infectious population acts as the exposed subpopulation of the next infectious stage. The model also has internal delays which characterize the time intervals of the coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages. Since the susceptible subpopulation is common, and then unique, to all the infectious stages, its coupled dynamic action on each of those stages is modeled with an increasing delay as the infectious stage index increases from 1 to . The physical interpretation of the model is that the dynamics of the disease exhibits different stages in which the infectivity and the mortality rates vary as the individual numbers go through the process of recovery, each stage with a characteristic average time. Raul Nistal, Manuel de la Sen, Santiago Alonso-Quesada, Asier Ibeas, and Aitor J. Garrido Copyright © 2015 Raul Nistal et al. All rights reserved. Stability of an HIV/AIDS Treatment Model with Different Stages Thu, 14 May 2015 06:42:10 +0000 http://www.hindawi.com/journals/ddns/2015/630503/ An HIV/AIDS treatment model with different stages is proposed in this paper. The stage of the HIV infection is divided into two stages, that is, HIV-positive in the asymptomatic stage of HIV infection and HIV-positive individuals in the pre-AIDS stage. The fact that some individuals with HIV-positive individuals after the treatment can be transformed into the compartment of HIV-positive individuals in the asymptomatic stage of HIV infection, the compartment of HIV-positive individuals in the pre-AIDS stage, or the compartment of individuals with full-blown AIDS is also considered. Mathematical analyses establish the idea that the global dynamics of the HIV/AIDS model are determined by the basic reproduction number . The disease-free equilibrium is globally asymptotically stable if . The endemic equilibrium is globally asymptotically stable if for a special case. Numerical simulations are also conducted to support the analytic results. Hai-Feng Huo and Rui Chen Copyright © 2015 Hai-Feng Huo and Rui Chen. All rights reserved. Dynamical Analysis of SIR Epidemic Model with Nonlinear Pulse Vaccination and Lifelong Immunity Thu, 14 May 2015 06:27:21 +0000 http://www.hindawi.com/journals/ddns/2015/848623/ SIR epidemic model with nonlinear pulse vaccination and lifelong immunity is proposed. Due to the limited medical resources, vaccine immunization rate is considered as a nonlinear saturation function. Firstly, by using stroboscopic map and fixed point theory of difference equations, the existence of disease-free periodic solution is discussed, and the globally asymptotical stability of disease-free periodic solution is proven by using Floquet multiplier theory and differential impulsive comparison theorem. Moreover, by using the bifurcation theorem, sufficient condition for the existence of positive periodic solution is obtained by choosing impulsive vaccination period as a bifurcation parameter. Lastly, some simulations are given to validate the theoretical results. Wencai Zhao, Juan Li, and Xinzhu Meng Copyright © 2015 Wencai Zhao et al. All rights reserved. Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa Thu, 14 May 2015 06:26:11 +0000 http://www.hindawi.com/journals/ddns/2015/842792/ The Ebola virus is currently one of the most virulent pathogens for humans. The latest major outbreak occurred in Guinea, Sierra Leone, and Liberia in 2014. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method. Amira Rachah and Delfim F. M. Torres Copyright © 2015 Amira Rachah and Delfim F. M. Torres. All rights reserved. Rank One Strange Attractors in Periodically Kicked Lorenz System with Time-Delay Tue, 12 May 2015 07:10:59 +0000 http://www.hindawi.com/journals/ddns/2015/915614/ Rank one strange attractor in periodically kicked Lorenz system with time-delay is investigated. Our discussion is based on the theory of rank one maps formulated by Wang and Young. First, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when periodically kicked delayed system undergoes a generic Hopf bifurcation. Then we use the theory to the periodically kicked Lorenz system with delay, and derivation of conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations are presented. Wenjie Yang, Yiping Lin, and Yunxian Dai Copyright © 2015 Wenjie Yang et al. All rights reserved. Supply Chain Bilateral Coordination with Option Contracts under Inflation Scenarios Mon, 11 May 2015 07:20:52 +0000 http://www.hindawi.com/journals/ddns/2015/502021/ There exist obvious changes in price and demand during the inflationary period, both of which are regarded as the key factors leading to supply chain uncertainty. In this paper, we focus our discussion on price increase and demand contraction caused by inflation, integrate the effect of inflation and option contracts within the model framework, and analyze how to use option contracts to achieve supply chain coordination under inflation scenarios. We consider a one-period two-stage supply chain consisting of one supplier and one retailer and explore the effect of inflation on the optimal ordering and production decisions under three different types of contracts: wholesale price contracts, option contracts, and portfolio contracts. Moreover, we explore the impact of option contracts on the supply chain through using wholesale price contracts model as the benchmark. We find that the retailer prefers adopting portfolio contracts, but the supplier prefers providing option contracts under inflation scenarios. Ultimately, option contracts will be implemented owing to the supplier’s market dominant position. In addition, we discuss the supply chain bilateral coordination mechanism with option contracts from the perspectives of two members and derive that option contracts can coordinate the supply chain and achieve Pareto improvement under inflation scenarios. Nana Wan and Xu Chen Copyright © 2015 Nana Wan and Xu Chen. All rights reserved. Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant Thu, 07 May 2015 09:34:10 +0000 http://www.hindawi.com/journals/ddns/2015/612354/ The rhizosphere microbe plays an important role in removing the pollutant generated from industrial and agricultural production. To investigate the dynamics of the microbial degradation, a nonlinear mathematical model of the rhizosphere microbial degradation is proposed based on impulsive state feedback control. The sufficient conditions for existence of the positive order-1 or order-2 periodic solution are obtained by using the geometrical theory of the semicontinuous dynamical system. We show the impulsive control system tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the process of the microbial degradation. Furthermore, mathematical results are justified by some numerical simulations. Zhong Zhao, Liuyong Pang, Zhanping Zhao, and Chengguang Luo Copyright © 2015 Zhong Zhao et al. All rights reserved. Modeling and Simulation Based on the Hybrid System of Leasing Equipment Optimal Allocation Tue, 05 May 2015 12:30:15 +0000 http://www.hindawi.com/journals/ddns/2015/459381/ Modeling of the hybrid system of leasing equipment optimal allocation and its optimal control methods are put forward based on the hybrid characteristics of succession and dispersion. After studying equipment unit’s hybrid automata model (the hybrid and basic structure), the hybrid system facing manufacture demand can be considered as the synthesis of some hybrid and basic structures, which efficiently avoid combination explosion of models due to the increase of systematic scale. On this basis, we study the hybrid and optimal control methods that meet the demand for some equipment and achieve the usage rate maximization. Following that, calculating methods of performance optimization and simulation are put forward based on the first- and second-order subsection linear model. At last, we also have made the numerical simulating calculation on the equipment’s optimal matching of some leasing company. Ying Tian and Wei-qing Zhong Copyright © 2015 Ying Tian and Wei-qing Zhong. All rights reserved. Codimension-Two Grazing Bifurcations in Three-Degree-of-Freedom Impact Oscillator with Symmetrical Constraints Tue, 05 May 2015 11:39:38 +0000 http://www.hindawi.com/journals/ddns/2015/353581/ This paper investigates the codimension-two grazing bifurcations of a three-degree-of-freedom vibroimpact system with symmetrical rigid stops since little research can be found on this important issue. The criterion for existence of double grazing periodic motion is presented. Using the classical discontinuity mapping method, the Poincaré mapping of double grazing periodic motion is obtained. Based on it, the sufficient condition of codimension-two bifurcation of double grazing periodic motion is formulated, which is simplified further using the Jacobian matrix of smooth Poincaré mapping. At the end, the existence regions of different types of periodic-impact motions in the vicinity of the codimension-two grazing bifurcation point are displayed numerically by unfolding diagram and phase diagrams. Qunhong Li, Pu Chen, and Jieqiong Xu Copyright © 2015 Qunhong Li et al. All rights reserved. Bifurcation Analysis for Nonlinear Recurrence Relations with Threshold Control and -Periodic Coefficients Wed, 22 Apr 2015 07:33:43 +0000 http://www.hindawi.com/journals/ddns/2015/610345/ A nonlinear recurrence involving a piecewise constant McCulloch-Pitts function and -periodic coefficient sequences is investigated. By allowing the threshold parameter to vary from 0 to , we work out a complete bifurcation analysis for the asymptotic behaviors of the corresponding solutions. Among other things, we show that each solution tends towards one of four different limits. Furthermore, the accompanying initial regions for each type of solutions can be determined. It is hoped that our analysis will provide motivation for further results for recurrent McCulloch-Pitts type neural networks. Liping Dou, Chengmin Hou, and Sui Sun Cheng Copyright © 2015 Liping Dou et al. All rights reserved.