http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2012/752950/This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.Yingqi Zhang, Caixia Liu, and Xiaowu MuCopyright © 2012 Yingqi Zhang et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/418091/Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.Zhishuai Ding, Guifang Cheng, and Xiaowu MuCopyright © 2012 Zhishuai Ding et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/418564/The dynamics of an impulsively controlled three-species food chain system with the Beddington-DeAngelis functional response are investigated using the Floquet theory and a comparison method. In the system, three species are prey, mid-predator, and top-predator. Under an integrated control strategy in sense of biological and chemical controls, the condition for extinction of the prey and the mid-predator is investigated. In addition, the condition for extinction of only the mid-predator is examined. We provide numerical simulations to substantiate the theoretical results.Younghae Do, Hunki Baek, and Dongseok KimCopyright © 2012 Younghae Do et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/296136/This paper investigates the stability of stochastic delay differential systems with two kinds of impulses, that is, destabilizing impulses and stabilizing impulses. Both the pth moment and almost sure exponential stability criteria are established by using the average impulsive interval. When the impulses are regarded as disturbances, a lower bound of average impulsive interval is obtained; it means that the impulses should not happen too frequently. On the other hand, when the impulses are used to stabilize the system, an upper bound of average impulsive interval is derived; namely, enough impulses are needed to stabilize the system. The effectiveness of the proposed results is illustrated by two examples.Xiaotai Wu, Litan Yan, Wenbing Zhang, and Liang ChenCopyright © 2012 Xiaotai Wu et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/745697/A discrete time two-nation arms race model involving a piecewise constant nonlinear control function is formulated and studied. By elementary but novel arguments, we are able to give a complete analysis of its asymptotic behavior when the threshold parameter in the control function varies from 0+ to ∞. We show that all solutions originated from positive initial values tend to limit one or two cycles. An implication is that when devastating weapons are involved, “terror equilibrium” can be achieved and escalated race avoided. It is hoped that our analysis will provide motivation for further studying of discrete-time equations with piecewise smooth nonlinearities.Chengmin Hou and Sui Sun ChengCopyright © 2012 Chengmin Hou and Sui Sun Cheng. All rights reserved.http://www.hindawi.com/journals/ddns/2012/684280/We investigate formulas for closely related series of the forms: ∑n=0∞1/(Uan+b+c), ∑n=0∞(-1)nUan+b/(Uan+b+c)2, ∑n=0∞U2(an+b)/(Uan+b2+c)2 for certain values of a, b, and c.Neşe ÖmürCopyright © 2012 Neşe Ömür. All rights reserved.http://www.hindawi.com/journals/ddns/2012/327437/We study the behavior of the well-defined solutions of the max type difference equation xn+1=max 1/xn,Anxn-1, n=0,1,…, where the initial conditions are arbitrary nonzero real numbers and {An} is a period-two sequence of real numbers with An∈[0,∞).İbrahim YalçınkayaCopyright © 2012 İbrahim Yalçınkaya. All rights reserved.http://www.hindawi.com/journals/ddns/2011/732164/Our aim in this paper is to establish some explicit bounds of the unknown function in a certain class of nonlinear dynamic inequalities in two independent variables on time scales which are unbounded above. These on the one hand generalize and on the other hand furnish a handy tool for the study of qualitative as well as quantitative properties of solutions of partial dynamic equations on time scales. Some examples are considered to demonstrate the applications of the results.S. H. SakerCopyright © 2011 S. H. Saker. All rights reserved.http://www.hindawi.com/journals/ddns/2011/516418/Based on the theory of a falling shadow which was first formulated by Wang (1985), a theoretical approach of the ideal structure in d-algebras is established. The notions of a falling d-subalgebra, a falling d-ideal, a falling BCK-ideal, and a falling d♯-ideal of a d-algebra are introduced. Some fundamental properties are investigated. Relations among a falling d-subalgebra, a falling d-ideal, a falling BCK-ideal, and a falling d♯-ideal are stated. Characterizations of falling d-ideals and falling d♯-ideals are discussed. A relation between a fuzzy d-subalgebra and a falling d-subalgebra is provided.Young Bae Jun, Sun Shin Ahn, and Kyoung Ja LeeCopyright © 2011 Young Bae Jun et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/325371/This paper deals with the problem of delay-dependent stability criterion of uncertain periodic switched recurrent neural networks with time-varying delays. When uncertain discrete-time recurrent neural network is a periodic system, it is expressed as switched neural network for the finite switching state. Based on the switched quadratic Lyapunov functional approach (SQLF) and free-weighting matrix approach (FWM), some linear matrix inequality criteria are found to guarantee the delay-dependent asymptotical stability of these systems. Two examples illustrate the exactness of the proposed criteria.Xing Yin, Jun Li, Weigen Wu, and Qiranrong TanCopyright © 2011 Xing Yin et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/201274/We propose a class of virus dynamics models with multitarget cells and multiple intracellular delays and study their global properties. The first model is a 5-dimensional system of nonlinear delay differential equations (DDEs) that describes the interaction of the virus with two classes of target cells. The second model is a (2n+1)-dimensional system of nonlinear DDEs that describes the dynamics of the virus, n classes of uninfected target cells, and n classes of infected target cells. The third model generalizes the second one by assuming that the incidence rate of infection is given by saturation functional response. Two types of discrete time delays are incorporated into these models to describe (i) the latent period between the time the target cell is contacted by the virus particle and the time the virus enters the cell, (ii) the latent period between the time the virus has penetrated into a cell and the time of the emission of infectious (mature) virus particles. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of these models. We have proven that if the basic reproduction number R0 is less than unity, then the uninfected steady state is globally asymptotically stable, and if R0>1 (or if the infected steady state exists), then the infected steady state is globally asymptotically stable.A. M. Elaiw and M. A. AlghamdiCopyright © 2011 A. M. Elaiw and M. A. Alghamdi. All rights reserved.http://www.hindawi.com/journals/ddns/2011/285809/Consideration is given to the free drainage of an Oldroyd four-constant liquid from a vertical porous surface. The governing systems of quasilinear partial differential equations are solved by the Fourier-Galerkin spectral method. It is shown that Fourier-Galerkin approximations are convergent with spectral accuracy. An efficient and accurate algorithm based on the Fourier-Galerkin approximations for the governing system of quasilinear partial differential equations is developed and implemented. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented. The effect of the material parameters, elasticity, and porous medium constant on the centerline velocity and drainage rate is discussed.F. Talay Akyildiz, Mehmet Emir Koksal, and Nurhan KaplanCopyright © 2011 F. Talay Akyildiz et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/178483/We are concerned with a kind of three-dimensional system of rational difference equations, given by Kurbanli (2011). A new expression of solution of the system is presented, and the asymptotical behavior is described. At the same time, we also consider a different system and obtain some results, which expand the study of such a kind of difference equations and the method can be applied to other systems.Liu Keying, Zhao Zhongjian, Li Xiaorui, and Li PengCopyright © 2011 Liu Keying et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/271928/Based on a predator-prey differential system with continuously distributed delays, we derive a corresponding difference version by using the method of a discretization technique. A good understanding of permanence of system and global attractivity of positive solutions of system is gained. An example and its numerical simulations are presented to substantiate our theoretical results.Lili Liu and Zhijun LiuCopyright © 2011 Lili Liu and Zhijun Liu. All rights reserved.http://www.hindawi.com/journals/ddns/2011/174376/We first study how to make use of the Marotto theory to prove rigorously the existence of the Li-Yorke chaos in diffusively coupled map lattices with open boundary conditions (i.e., a high-dimensional discrete dynamical system). Then, the recent 0-1 test for chaos is applied to confirm our theoretical claim. In addition, we control the chaotic motions to a fixed point with delay feedback method. Numerical results support the theoretical analysis.Li-Guo Yuan and Qi-Gui YangCopyright © 2011 Li-Guo Yuan and Qi-Gui Yang. All rights reserved.http://www.hindawi.com/journals/ddns/2011/841324/Complex dynamical features are explored in a discrete interregional macrodynamic model proposed by Asada et al., using numerical methods. The model is five-dimensional with four parameters. The results demonstrate patterns of dynamical behaviour, such as bifurcation processes and coexistence of attractors, generated by high-dimensional discrete systems. In three cases of two-dimensional parameter subspaces the stability of equilibrium region is determined and its boundaries, the flip and Neimark-Hopf bifurcation curves, are identified by means of necessary coefficient criteria. In the first case closed invariant curves (CICs) are found to occur through 5D-crater-type bifurcations, and for certain ranges of parameter values a stable equilibrium coexists with an unstable CIC associated with the subcritical bifurcation, as well as with an outer stable CIC. A remarkable feature of the second case is the coexistence of two attracting CICs outside the stability region. In both these cases the related hysteresis effects are illustrated by numerical simulations. In the third case a remarkable feature is the apparent unfolding of an attracting CIC before it evolves to a chaotic attractor. Examples of CICs and chaotic attractors are given in subspaces of phase space.Toichiro Asada and Panagiotis MarkellosCopyright © 2011 Toichiro Asada and Panagiotis Markellos. All rights reserved.http://www.hindawi.com/journals/ddns/2011/163541/This paper investigates a dynamic mathematical model of fish algae consumption with an impulsive control strategy analytically. It is proved that the system has a globally asymptotically stable algae-eradication periodic solution and is permanent by using the theory of impulsive equations and small-amplitude perturbation techniques. Numerical results for impulsive perturbations demonstrate the rich dynamic behavior of the system. Further, we have also compared biological control with chemical control. All these results may be useful in controlling eutrophication.Jin Yang and Min ZhaoCopyright © 2011 Jin Yang and Min Zhao. All rights reserved.http://www.hindawi.com/journals/ddns/2011/856132/We give some new identities on the Bernoulli and Euler numbers by using the bosonic p-adic integral on Zp and reflection symmetric properties of Bernoulli and Euler polynomials.Dae San Kim, Taekyun Kim, Sang-Hun Lee, D. V. Dolgy, and Seog-Hoon RimCopyright © 2011 Dae San Kim et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/360583/We prove that if a continuous, Lyapunov stable map f from a compact metric space X into itself is topologically transitive and has the asymptotic average shadowing property, then X is consisting of one point. As an application, we prove that the identity map iX:X→X does not have the asymptotic average shadowing property, where X is a compact metric space with at least two points.Risong Li and Xiaoliang ZhouCopyright © 2011 Risong Li and Xiaoliang Zhou. All rights reserved.http://www.hindawi.com/journals/ddns/2011/284261/By considering Melham's sums (Melham, 2004), we compute various more general nonalternating sums, alternating sums, and sums that alternate according to (-1)(n+12) involving the generalized Fibonacci and Lucas numbers.E. Kılıç, N. Ömür, and Y. T. UlutaşCopyright © 2011 E. Kılıç et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/724697/A brain computer interface BCI enables direct communication between a brain and a computer translating brain activity into computer commands using preprocessing, feature extraction, and classification operations. Feature extraction is crucial, as it has a substantial effect on the classification accuracy and speed. While fractal dimension has been successfully used in various domains to characterize data exhibiting fractal properties, its usage in motor imagery-based BCI has been more recent. In this study, commonly used fractal dimension estimation methods to characterize time series Katz's method, Higuchi's method, rescaled range method, and Renyi's entropy were evaluated for feature extraction in motor imagery-based BCI by conducting offline analyses of a two class motor imagery dataset. Different classifiers fuzzy k-nearest neighbours FKNN, support vector machine, and linear discriminant analysis were tested in combination with these methods to determine the methodology with the best performance. This methodology was then modified by implementing the time-dependent fractal dimension TDFD, differential fractal dimension, and differential signals methods to determine if the results could be further improved. Katz's method with FKNN resulted in the highest classification accuracy of 85%, and further improvements by 3% were achieved by implementing the TDFD method.Chu Kiong Loo, Andrews Samraj, and Gin Chong LeeCopyright © 2011 Chu Kiong Loo et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/572062/Using the fixed point method, we investigate the stability of the systems of quadratic-cubic and additive-quadratic-cubic functional equations with constant coefficients form r-divisible groups into Ŝerstnev probabilistic Banach spaces.M. Eshaghi Gordji, Y. J. Cho, M. B. Ghaemi, and H. MajaniCopyright © 2011 M. Eshaghi Gordji et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/917892/A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs) driven by Poisson processes. A general framework for mean-square convergence of the methods is provided. It is shown that under certain conditions global error estimates for a method can be inferred from estimates on its local error. The applicability of the mean-square convergence theory is illustrated by the stochastic θ-methods and the balanced implicit methods. It is derived from Theorem 3.1 that the order of the mean-square convergence of both of them for NSDDEs with jumps is 1/2. Numerical experiments illustrate the theoretical results. It is worth noting that the results of mean-square convergence of the stochastic θ-methods and the balanced implicit methods are also new.Lin Hu and Siqing GanCopyright © 2011 Lin Hu and Siqing Gan. All rights reserved.http://www.hindawi.com/journals/ddns/2011/653937/We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorously mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals.Hui Cao, Yicang Zhou, and Baojun SongCopyright © 2011 Hui Cao et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/730783/We investigate a delayed eco-epidemiological model with disease in predator and saturation incidence. First, by comparison arguments, the permanence of the model is discussed. Then, we study the local stability of each equilibrium of the model by analyzing the corresponding characteristic equations and find that Hopf bifurcation occurs when the delay τ passes through a sequence of critical values. Next, by means of an iteration technique, sufficient conditions are derived for the global stability of the disease-free planar equilibrium and the positive equilibrium. Numerical examples are carried out to illustrate the analytical results.Shuxue Mao, Rui Xu, Zhe Li, and Yunfei LiCopyright © 2011 Shuxue Mao et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/628369/We consider a discrete Internet model with a single link accessed by a single source, which responds to congestion signals from the network. Firstly, the stability of the equilibria of the system is investigated by analyzing the characteristic equation. By choosing the time delay as a bifurcation parameter, we prove that Neimark-Sacker bifurcations occur when the delay passes a sequence of critical values. Then, the explicit algorithm for determining the direction of the Neimark-Sacker bifurcations and the stability of the bifurcating periodic solutions is derived. Finally, some numerical simulations are given to verify the theoretical analysis.Yingguo LiCopyright © 2011 Yingguo Li. All rights reserved.http://www.hindawi.com/journals/ddns/2011/210261/The second-order one-dimensional linear hyperbolic equation with time and space variable coefficients and nonlocal boundary conditions is solved by using stable operator-difference schemes. Two new second-order difference schemes recently appeared in the literature are compared numerically with each other and with the rather old first-order difference scheme all to solve abstract Cauchy problem for hyperbolic partial differential equations with time-dependent unbounded operator coefficient. These schemes are shown to be absolutely stable, and the numerical results are presented to compare the accuracy and the execution times. It is naturally seen that the second-order difference schemes are much more advantages than the first-order ones. Although one of the second-order difference scheme is less preferable than the other one according to CPU (central processing unit) time consideration, it has superiority when the accuracy weighs more importance.Mehmet Emir KoksalCopyright © 2011 Mehmet Emir Koksal. All rights reserved.http://www.hindawi.com/journals/ddns/2011/902014/A dynamic triopoly game characterized by firms with different expectations is modeled by three-dimensional nonlinear difference equations, where the market has quadratic inverse demand function and the firm possesses cubic total cost function. The local stability of Nash equilibrium is studied. Numerical simulations are presented to show that the triopoly game model behaves chaotically with the variation of the parameters. We obtain the fractal dimension of the strange attractor, bifurcation diagrams, and Lyapunov exponents of the system.Junhai Ma and Xiaosong PuCopyright © 2011 Junhai Ma and Xiaosong Pu. All rights reserved.http://www.hindawi.com/journals/ddns/2011/262349/We consider a method for driving general complex networks into prescribed cluster synchronization patterns by using pinning control. The coupling between the vertices of the network is nonlinear, and sufficient conditions are derived analytically for the attainment of cluster synchronization. We also propose an effective way of adapting the coupling strengths of complex networks. In addition, the critical combination of the control strength, the number of pinned nodes and coupling strength in each cluster are given by detailed analysis cluster synchronization of a special topological structure complex network. Our theoretical results are illustrated by numerical simulations.Jianwen Feng, Jingyi Wang, Chen Xu, and Francis AustinCopyright © 2011 Jianwen Feng et al. All rights reserved.http://www.hindawi.com/journals/ddns/2011/476381/Recently, the modified q-Bernoulli numbers and polynomials are introduced in (D. V. Dolgy et al., in press). These numbers are valuable to study the weighted q-zeta and L-functions. In this paper, we study the weighted q-zeta functions and weighted L-functions from the modified q-Bernoulli numbers and polynomials with weight α.T. Kim, S. H. Lee, Hyeon-Ho Han, and C. S. RyooCopyright © 2011 T. Kim et al. All rights reserved.