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 Asymptotic Behavior in a Nonlinear Cobweb Model with Time Delays Sun, 26 Jul 2015 06:39:41 +0000 http://www.hindawi.com/journals/ddns/2015/312574/ We study the effects of production delays on the local as well as global dynamics of nonlinear cobweb models in a continuous-time framework. After reviewing a single delay model, we proceed to two models with two delays. When the two delays are used to form an expected price or feedback for price adjustment, we have a winding stability switching curve and in consequence obtain repetition of stability losses and gains via Hopf bifurcation. When the two delays are involved in two interrelated markets, we find that the stability switching occurs on straight lines and complicated dynamics can arise in unstable markets. Akio Matsumoto and Ferenc Szidarovszky Copyright © 2015 Akio Matsumoto and Ferenc Szidarovszky. All rights reserved. An Approach to Modeling the Impact of Traffic Incident on Urban Expressway Wed, 22 Jul 2015 06:38:48 +0000 http://www.hindawi.com/journals/ddns/2015/605016/ To identify network bottlenecks of urban expressway effectively is a foundational work for improving network traffic condition and preventing traffic congestion. This study proposes a methodology to estimate the impact of traffic incident on urban expressway on the basis of modified cell transmission model. The metastable state was taken into account in the proposed method to reflect the actual operating state of traffic flow on urban expressway as much as possible. Regarding the location of traffic incident, the method of cell restructuring settings was discussed. We then proceed to introduce a new concept of the effected length in a given time period as the evaluation indicator to directly depict the influence of traffic incident. The proposed method was tested on a 6516-meter urban expressway section of west second ring road in Beijing. The simulation results indicated that the proposed methodology performs well to predict the impact of traffic incident on urban expressway. Yaping Li, Jian Lu, HongWu Li, Huihui Xiao, and Qingchao Liu Copyright © 2015 Yaping Li et al. All rights reserved. Effects of the Interest Rate and Reserve Requirement Ratio on Bank Risk in China: A Panel Smooth Transition Regression Approach Tue, 21 Jul 2015 13:31:19 +0000 http://www.hindawi.com/journals/ddns/2015/571384/ This paper applies the Panel Smooth Transition Regression (PSTR) model to simulate the effects of the interest rate and reserve requirement ratio on bank risk in China. The results reveal the nonlinearity embedded in the interest rate, reserve requirement ratio, and bank risk nexus. Both the interest rate and reserve requirement ratio exert a positive impact on bank risk for the low regime and a negative impact for the high regime. The interest rate performs a significant effect while the reserve requirement ratio shows an insignificant effect on bank risk on a statistical basis for both the high and low regimes. Zhongyuan Geng and Xue Zhai Copyright © 2015 Zhongyuan Geng and Xue Zhai. All rights reserved. Design of Feedback Control for Networked Finite-Distributed Delays Systems with Quantization and Packet Dropout Compensation Thu, 16 Jul 2015 14:27:52 +0000 http://www.hindawi.com/journals/ddns/2015/158972/ This paper investigates the feedback control for networked discrete-time finite-distributed delays with quantization and packet dropout, and systems induce the control problem. The compensation scheme occurs in a random way. The quantization of system state or output signal is in front of being communicated. It is shown that the design of both a state feedback controller and an observer-based output feedback controller can be achieved, which ensure the asymptotical stability as well as a prescribed performance of the resulting closed-loop system satisfying dependence on the size of the discrete and distributed delays. Numerical examples are given to illustrate the effectiveness and applicability of the design method in this paper. Wen-Chiung Hsu, Lian-Wang Lee, Kuan-Hsuan Tseng, Chien-Yu Lu, Chin-Wen Liao, and Ho-Nien Shou Copyright © 2015 Wen-Chiung Hsu et al. All rights reserved. On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem Thu, 16 Jul 2015 09:22:02 +0000 http://www.hindawi.com/journals/ddns/2015/121437/ This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented. Ozgur Yildirim and Meltem Uzun Copyright © 2015 Ozgur Yildirim and Meltem Uzun. All rights reserved. Multiperiod Coordination Models of Coal-Electricity Supply Chain with Double Price Regulations Wed, 15 Jul 2015 07:10:52 +0000 http://www.hindawi.com/journals/ddns/2015/789597/ Using game models, we study multiperiod coordination contract and model of coal-electricity supply chain under the condition of double price regulations to alleviate the price conflicts of coal and electricity enterprises. The study reveals that, in boom seasons of coal demand, the multiperiod coordination mechanism may not only reduce the price of thermal coal but also increase the fulfillment rate of thermal coal. Meanwhile, the ordering quantity of thermal coal is increased and the shortage probability of electricity supply is decreased. Thereby, the conflicts between coal and electricity are also alleviated effectively. Hongjun Peng, Meihua Zhou, and Fudong Wang Copyright © 2015 Hongjun Peng et al. All rights reserved. An Impulsively Controlled Three-Species Prey-Predator Model with Stage Structure and Birth Pulse for Predator Tue, 14 Jul 2015 10:24:49 +0000 http://www.hindawi.com/journals/ddns/2015/380492/ We investigate the dynamic behaviors of a two-prey one-predator system with stage structure and birth pulse for predator. By using the Floquet theory of linear periodic impulsive equation and small amplitude perturbation method, we show that there exists a globally asymptotically stable two-prey eradication periodic solution when the impulsive period is less than some critical value. Further, we study the permanence of the investigated model. Our results provide valuable strategy for biological economics management. Numerical analysis is also inserted to illustrate the results. Yanyan Hu, Mei Yan, and Zhongyi Xiang Copyright © 2015 Yanyan Hu et al. All rights reserved. Active Control of Nonlinear Suspension System Using Modified Adaptive Supertwisting Controller Tue, 14 Jul 2015 09:35:41 +0000 http://www.hindawi.com/journals/ddns/2015/408623/ The suspension system is faced with nonlinearities from the spring, damper, and external excitations from the road surface. The objective of any control action provided to the suspension is to improve ride comfort while ensuring road holding for the vehicle. In this work, a robust higher order sliding mode algorithm combining the merits of the modified supertwisting algorithm and the adaptive supertwisting algorithm has been proposed for the nonlinear active suspension system. The proposed controller is robust to linearly growing perturbations and bounded uncertainties. Simulations have been performed for different classes of road excitations and the results are presented. Jagat J. Rath, Kalyana C. Veluvolu, and Michael Defoort Copyright © 2015 Jagat J. Rath et al. All rights reserved. Stability Analysis of One-Leg Methods for Nonlinear Neutral Delay Integrodifferential Equations Tue, 14 Jul 2015 07:29:39 +0000 http://www.hindawi.com/journals/ddns/2015/325364/ This paper is concerned with the numerical solution of nonlinear neutral delay integrodifferential equations (NDIDEs). The adaptation of one-leg methods is considered. It is proved that an A-stable one-leg method can preserve the global stability and a strongly A-stable one-leg method can preserve the asymptotic stability of the analytical solution of nonlinear NDIDEs. Numerical tests are given to confirm the theoretical results. Yuexin Yu and Liping Wen Copyright © 2015 Yuexin Yu and Liping Wen. All rights reserved. A Modified Cellular Automaton Approach for Mixed Bicycle Traffic Flow Modeling Mon, 13 Jul 2015 11:49:23 +0000 http://www.hindawi.com/journals/ddns/2015/213204/ Several previous studies have used the Cellular Automaton (CA) for the modeling of bicycle traffic flow. However, previous CA models have several limitations, resulting in differences between the simulated and the observed traffic flow features. The primary objective of this study is to propose a modified CA model for simulating the characteristics of mixed bicycle traffic flow. Field data were collected on physically separated bicycle path in Shanghai, China, and were used to calibrate the CA model using the genetic algorithm. Traffic flow features between simulations of several CA models and field observations were compared. The results showed that our modified CA model produced more accurate simulation for the fundamental diagram and the passing events in mixed bicycle traffic flow. Based on our model, the bicycle traffic flow features, including the fundamental diagram, the number of passing events, and the number of lane changes, were analyzed. We also analyzed the traffic flow features with different traffic densities, traffic components on different travel lanes. Results of the study can provide important information for understanding and simulating the operations of mixed bicycle traffic flow. Xiaonian Shan, Zhibin Li, Xiaohong Chen, and Jianhong Ye Copyright © 2015 Xiaonian Shan et al. All rights reserved. Joint Ordering and Pricing Decisions for New Repeat-Purchase Products Thu, 09 Jul 2015 14:26:54 +0000 http://www.hindawi.com/journals/ddns/2015/461959/ This paper studies ordering and pricing problems for new repeat-purchase products. We incorporate the repeat-purchase rate and price effects into the Bass model to characterize the demand pattern. We consider two decision models: (1) two-stage decision model, in which the sales division chooses a price to maximize the gross profit and the purchasing division determines an optimal ordering decision to minimize the total cost under a given demand subsequently, and (2) joint decision model, in which the firm makes ordering and pricing decisions simultaneously to maximize the profit. We combine the generalized Bass model with dynamic lot sizing model to formulate the joint decision model. We apply both models to a specific imported food provided by an online fresh produce retailer in Central China, solve them by Gaussian Random-Walk and Wagner-Whitin based algorithms, and observe three results. First, joint pricing and ordering decisions bring more significant profits than making pricing and ordering decisions sequentially. Second, a great initiative in adoption significantly increases price premium and profit. Finally, the optimal price shows a U-shape (i.e., decreases first and increases later) relationship and the profit increases gradually with the repeat-purchase rate when it is still not very high. Xiang Wu and Jinlong Zhang Copyright © 2015 Xiang Wu and Jinlong Zhang. All rights reserved. Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces Thu, 09 Jul 2015 09:43:56 +0000 http://www.hindawi.com/journals/ddns/2015/532725/ The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. Mujahid Abbas, Manuel De la Sen, and Talat Nazir Copyright © 2015 Mujahid Abbas et al. All rights reserved. The Pricing of Vulnerable Options in a Fractional Brownian Motion Environment Thu, 09 Jul 2015 07:50:02 +0000 http://www.hindawi.com/journals/ddns/2015/579213/ Under the assumption of the stock price, interest rate, and default intensity obeying the stochastic differential equation driven by fractional Brownian motion, the jump-diffusion model is established for the financial market in fractional Brownian motion setting. With the changes of measures, the traditional pricing method is simplified and the general pricing formula is obtained for the European vulnerable option with stochastic interest rate. At the same time, the explicit expression for it comes into being. Chao Wang, Shengwu Zhou, and Jingyuan Yang Copyright © 2015 Chao Wang et al. All rights reserved. A Novel Method of Interestingness Measures for Association Rules Mining Based on Profit Thu, 09 Jul 2015 05:46:37 +0000 http://www.hindawi.com/journals/ddns/2015/868634/ Association rules mining is an important topic in the domain of data mining and knowledge discovering. Some papers have presented several interestingness measure methods; the most typical are Support, Confidence, Lift, Improve, and so forth. But their limitations are obvious, like no objective criterion, lack of statistical base, disability of defining negative relationship, and so forth. This paper proposes three new methods, Bi-lift, Bi-improve, and Bi-confidence, for Lift, Improve, and Confidence, respectively. Then, on the basis of utility function and the executing cost of rules, we propose interestingness function based on profit (IFBP) considering subjective preferences and characteristics of specific application object. Finally, a novel measure framework is proposed to improve the traditional one through experimental analysis. In conclusion, the new methods and measure framework are prior to the traditional ones in the aspects of objective criterion, comprehensive definition, and practical application. Chunhua Ju, Fuguang Bao, Chonghuan Xu, and Xiaokang Fu Copyright © 2015 Chunhua Ju et al. All rights reserved. On Fractional Orthonormal Polynomials of a Discrete Variable Wed, 08 Jul 2015 08:51:00 +0000 http://www.hindawi.com/journals/ddns/2015/141325/ A fractional analogue of classical Gram or discrete Chebyshev polynomials is introduced. Basic properties as well as their relation with the fractional analogue of Legendre polynomials are presented. I. Area, J. D. Djida, J. Losada, and Juan J. Nieto Copyright © 2015 I. Area et al. All rights reserved. Study on the Queue-Length Distribution in Queue with Working Vacations Mon, 06 Jul 2015 08:42:20 +0000 http://www.hindawi.com/journals/ddns/2015/160697/ This paper analyzes a finite buffer size discrete-time queue with multiple working vacations and different input rate. Using supplementary variable technique and embedded Markov chain method, the queue-length distribution solution in the form of formula at arbitrary epoch is obtained. Some performance measures associated with operating cost are also discussed based on the obtained queue-length distribution. Then, several numerical experiments follow to demonstrate the effectiveness of the obtained formulae. Finally, a state-dependent operating cost function is constructed to model an express logistics service center. Regarding the service rate during working vacation as a control variable, the optimization analysis on the cost function is carried out by using parabolic method. Chuanyi Luo, Jiangyi Li, and Yinghui Tang Copyright © 2015 Chuanyi Luo et al. All rights reserved. On Some Fixed Point Results for -Type Contraction Mappings in Metric Spaces Mon, 06 Jul 2015 08:18:10 +0000 http://www.hindawi.com/journals/ddns/2015/914158/ We prove some fixed point theorems for -type multivalued contractive mappings in the setting of Banach spaces and metric spaces. The results provided allow recovering different well-known results. Hemant Kumar Pathak and Rosana Rodríguez-López Copyright © 2015 Hemant Kumar Pathak and Rosana Rodríguez-López. All rights reserved. New Results on Reachable Set Estimation and Controller Design for Linear Systems with Mixed Delays via Triple Integral Functionals Thu, 02 Jul 2015 09:25:55 +0000 http://www.hindawi.com/journals/ddns/2015/935920/ This paper is concerned with the problem of reachable set estimation and controller design for a class of linear systems with mixed delays and bounded disturbance inputs. By constructing a newly augmented Lyapunov-Krasovskii functional, combining with triple integral technique and reciprocally convex approach, some new reachable set estimation conditions are derived in terms of linear matrix inequalities. Based on these conditions, a state-feedback controller has been designed to ensure the reachable set of the closed-loop system bounded by a given ellipsoid. Finally, two numerical examples are given to illustrate the effectiveness of the proposed analysis and designed method. Wei Kang and Shouming Zhong Copyright © 2015 Wei Kang and Shouming Zhong. All rights reserved. Impulsive Multiorders Riemann-Liouville Fractional Differential Equations Sun, 28 Jun 2015 12:26:18 +0000 http://www.hindawi.com/journals/ddns/2015/603893/ Impulsive multiorders fractional differential equations are studied. Existence and uniqueness results are obtained for first- and second-order impulsive initial value problems by using Banach’s fixed point theorem in an appropriate weighted space. Examples illustrating the main results are presented. Weera Yukunthorn, Sotiris K. Ntouyas, and Jessada Tariboon Copyright © 2015 Weera Yukunthorn et al. All rights reserved. Dynamic Analysis of General Integrated Pest Management Model with Double Impulsive Control Sun, 28 Jun 2015 08:09:16 +0000 http://www.hindawi.com/journals/ddns/2015/839097/ A general predator-prey model with disease in the prey and double impulsive control is proposed and investigated for the purpose of integrated pest management. By using the Floquet theory, the comparison theorem of impulsive differential equations, and the persistence theory of dynamical systems, we obtain that if threshold value , then the susceptible pest eradication periodic solution is globally asymptotically stable and if , then the model is permanent. The numerical examples not only illustrate the theoretical results, but also show that when the model is permanent, then it may possess a unique globally attractive -periodic solution. Yingke Li, Zhidong Teng, Kai Wang, and Ahmadjan Muhammadhaji Copyright © 2015 Yingke Li et al. All rights reserved. A PD-Type Iterative Learning Control for a Class of Switched Discrete-Time Systems with Model Uncertainties and External Noises Thu, 25 Jun 2015 10:57:28 +0000 http://www.hindawi.com/journals/ddns/2015/410292/ A PD-type iterative learning control algorithm is applied to a class of linear discrete-time switched systems for tracking desired trajectories. The application is based on assumption that the switched systems repetitively operate over a finite time interval and the switching rules are arbitrarily prespecified. By taking advantage of the super-vector approach, a sufficient condition of the monotone convergence of the algorithm is deduced when both the model uncertainties and the external noises are absent. Then the robust monotone convergence is analyzed when the model uncertainties are present and the robustness against the bounded external noises is discussed. The analysis manifests that the proposed PD-type iterative learning control algorithm is feasible and effective when it is imposed on the linear switched systems specified by the arbitrarily preset switching rules. The attached simulations support the feasibility and the effectiveness. Xuan Yang Copyright © 2015 Xuan Yang. All rights reserved. Fuzzy Availability Assessment for a Repairable Multistate Series-Parallel System Thu, 25 Jun 2015 10:45:32 +0000 http://www.hindawi.com/journals/ddns/2015/156059/ This paper considers a repairable multistate series-parallel system (RMSSPS) with fuzzy parameters. It is assumed that the system components are independent, and their state transition rates and performance rates are fuzzy values. The fuzzy universal generating function technique is adopted to determine fuzzy state probability and fuzzy performance rate of the system. On the basis of α-cut approach and the extension principle, parametric programming technique is employed to obtain the α-cuts of some indices for the system. The system fuzzy availability is defined as the ability of the system to satisfy fuzzy consumer demand. A special assessment approach is developed for evaluating the fuzzy steady-state availability of the system with the fuzzy demand. A flow transmission system with three components is presented to demonstrate the validity of the proposed method. Linmin Hu, Dequan Yue, and Ruiling Tian Copyright © 2015 Linmin Hu et al. All rights reserved. The Effect of Pulse Vaccination and Treatment on SIR Epidemic Model with Media Impact Thu, 25 Jun 2015 07:13:18 +0000 http://www.hindawi.com/journals/ddns/2015/532494/ We propose a novel SIR epidemic dynamical control model with media impact, where the state dependent pulse vaccination and medication treatment control strategies are being introduced to prevent the spread of disease at different control threshold values. By using the geometry theory of differential equation and method of successor function, the existence of positive order-1 periodic solution is studied. Further, some sufficient conditions of the orbitally asymptotical stability for positive order-1 periodic solution are given by the analog Poincaré criterion. Furthermore, numerical simulations are carried to illustrate the feasibility of our main results presented here. Zhi-Long He and Lin-Fei Nie Copyright © 2015 Zhi-Long He and Lin-Fei Nie. All rights reserved. Stabilization of the FO-BLDCM Chaotic System in the Sense of Lyapunov Tue, 23 Jun 2015 05:57:17 +0000 http://www.hindawi.com/journals/ddns/2015/750435/ Based on an integer-order Brushless DC motors (IO-BLDCM) system, we give a fractional-order Brushless DC motors (FO-BLDCM) system in this paper. There exists a chaotic attractor for fractional-order in the FO-BLDCM system. Furthermore, using the Lyapunov direct method for fractional-order system, a control scheme is proposed to stabilize the FO-BLDCM chaotic system in the sense of Lyapunov. Numerical simulation shows that the control scheme in this paper is valid for the FO-BLDCM chaotic system. Ping Zhou, Rongji Bai, and Hao Cai Copyright © 2015 Ping Zhou et al. All rights reserved. Simulation of a Vibrant Membrane Using a 2-Dimensional Cellular Automaton Thu, 18 Jun 2015 11:51:16 +0000 http://www.hindawi.com/journals/ddns/2015/542507/ This paper proposes a 2-dimensional cellular automaton (CA) model and how to derive the model evolution rule to simulate a two-dimensional vibrant membrane. The resulting model is compared with the analytical solution of a two-dimensional hyperbolic partial differential equation (PDE), linear and homogeneous. This models a vibrant membrane with specific conditions, initial and boundary. The frequency spectrum is analysed as well as the error between the data produced by the CA model. Then it is compared to the data provided by the solution evaluation to the differential equation. This shows how the CA obtains a behavior similar to the PDE. Moreover, it is possible to simulate nonclassical initial conditions for which there is no exact solution using PDE. Very interesting information could be obtained from the CA model such as the fundamental frequency. I. Huerta-Trujillo, J. C. Chimal-Eguía, L. Muñoz-Salazar, and J. A. Martinez-Nuño Copyright © 2015 I. Huerta-Trujillo et al. All rights reserved. Random Vibration Analysis of Train Moving over Slab Track on Bridge under Track Irregularities and Earthquakes by Pseudoexcitation Method Wed, 17 Jun 2015 12:55:59 +0000 http://www.hindawi.com/journals/ddns/2015/436567/ This paper investigates the random vibration and the dynamic reliability of operation stability of train moving over slab track on bridge under track irregularities and earthquakes by the pseudoexcitation method (PEM). Each vehicle is modeled by multibody dynamics. The track and bridge is simulated by a rail-slab-girder-pier interaction finite element model. The coupling equations of motion are established based on the wheel-rail interaction relationship. The random excitations of the track irregularities and seismic accelerations are transformed into a series of deterministic pseudoexcitations by PEM. The time-dependent power spectral densities (PSDs) of the random vibration of the system are obtained by step-by-step integration method, and the corresponding dynamic reliability is estimated based on the first-passage failure criterion. A case study is then presented in which a high-speed train moves over a slab track resting on a simply supported girder bridge. The PSD characteristics of the random vibration of the bridge and train are analyzed, the influence of the wheel-rail-bridge interaction models on the random vibration of the bridge and train is discussed, and furthermore the influence of train speed, earthquake intensity, and pier height on the dynamic reliability of train operation stability is studied. Zhiping Zeng, Kunteng Zhu, Xianfeng He, Wentao Xu, Lingkun Chen, and Ping Lou Copyright © 2015 Zhiping Zeng et al. All rights reserved. A Mathematical Model of the Formation of Lanes in Crowds of Pedestrians Moving in Opposite Directions Wed, 17 Jun 2015 12:48:32 +0000 http://www.hindawi.com/journals/ddns/2015/872807/ In crowded environments, pedestrians moving in opposite directions segregate into lanes of individuals moving in the same direction. It is believed that this formation of lanes that facilitates the flow results from the individuals acting on their behalf, responding to local stimuli, without the intention of benefiting the crowd as a whole. We give evidence that this is true by developing and analyzing a simple mathematical model. Our results suggest that the simple behavior of moving out of the way to avoid imminent collisions leads to the formation of lanes of individuals moving in the same direction. Guillermo H. Goldsztein Copyright © 2015 Guillermo H. Goldsztein. All rights reserved. Multilevel Bloom Filters for P2P Flows Identification Based on Cluster Analysis in Wireless Mesh Network Tue, 16 Jun 2015 09:40:50 +0000 http://www.hindawi.com/journals/ddns/2015/801934/ With the development of wireless mesh networks and distributed computing, lots of new P2P services have been deployed and enrich the Internet contents and applications. The rapid growth of P2P flows brings great pressure to the regular network operation. So the effective flow identification and management of P2P applications become increasingly urgent. In this paper, we build a multilevel bloom filters data structure to identify the P2P flows through researches on the locality characteristics of P2P flows. Different level structure stores different numbers of P2P flow rules. According to the characteristics values of the P2P flows, we adjust the parameters of the data structure of bloom filters. The searching steps of the scheme traverse from the first level to the last level. Compared with the traditional algorithms, our method solves the drawbacks of previous schemes. The simulation results demonstrate that our algorithm effectively enhances the performance of P2P flows identification. Then we deploy our flow identification algorithm in the traffic monitoring sensors which belong to the network traffic monitoring system at the export link in the campus network. In the real environment, the experiment results demonstrate that our algorithm has a fast speed and high accuracy to identify the P2P flows; therefore, it is suitable for actual deployment. Xia-an Bi, Xiaohui Wang, Luyun Xu, Sheng Chen, and Hong Liu Copyright © 2015 Xia-an Bi et al. All rights reserved. Stabilizing Solution for a Discrete-Time Modified Algebraic Riccati Equation in Infinite Dimensions Tue, 16 Jun 2015 08:24:12 +0000 http://www.hindawi.com/journals/ddns/2015/293930/ We provide necessary and sufficient conditions for the existence of stabilizing solutions for a class of modified algebraic discrete-time Riccati equations (MAREs) defined on ordered Banach spaces of sequences of linear and bounded operators. These MAREs arise in the study of linear quadratic (LQ) optimal control problems for infinite-dimensional discrete-time linear systems (DTLSs) affected simultaneously by multiplicative white noise (MN) and Markovian jumps (MJs). Unlike most of the previous works, where the detectability and observability notions are key tools for studying the global solvability of MAREs, in this paper the conditions of existence of mean-square stabilizing solutions are given directly in terms of system parameters. The methods we have used are based on the spectral theory of positive operators and the properties of trace class and compact operators. Our results generalise similar ones obtained for finite-dimensional MAREs associated with stochastic DTLSs without MJs. Also they complete and extend (in the autonomous case) former investigations concerning the existence of certain global solutions (as minimal, maximal, and stabilizing solutions) for generalized discrete-time Riccati type equations defined on infinite-dimensional ordered Banach spaces. Viorica Mariela Ungureanu Copyright © 2015 Viorica Mariela Ungureanu. All rights reserved. Multiscale Discrete Simulation of Complex Systems Tue, 16 Jun 2015 08:08:44 +0000 http://www.hindawi.com/journals/ddns/2015/383084/ Qingang Xiong, Jingsen Ma, Hao Zhou, and Giulio Lorenzini Copyright © 2015 Qingang Xiong et al. All rights reserved.