http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ddns/2012/435402/The stability for the switched Cohen-Grossberg neural networks with mixed time delays and α-inverse Hölder activation functions is investigated under the switching rule with the average dwell time property. By applying multiple Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique, a delay-dependent sufficient criterion is achieved to ensure such switched neural networks to be globally exponentially stable in terms of LMIs, and the exponential decay estimation is explicitly developed for the states too. Two illustrative examples are given to demonstrate the validity of the theoretical results.Huaiqin Wu, Guohua Xu, Chongyang Wu, Ning Li, Kewang Wang, and Qiangqiang GuoCopyright © 2012 Huaiqin Wu et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/362526/We will prove some new dynamic inequalities of Opial's type on time scales. The results not only extend some results in the literature but also improve some of them. Some continuous and discrete inequalities are derived from the main results as special cases. The results will be applied on second-order half-linear dynamic equations on time scales to prove several results related to the spacing between consecutive zeros of solutions and the spacing between zeros of a solution and/or its derivative. The results also yield conditions for disfocality of these equations.Samir H. SakerCopyright © 2012 Samir H. Saker. All rights reserved.http://www.hindawi.com/journals/ddns/2012/713740/Managing multiple project is a complex task involving the unrelenting pressures of time and cost. Many studies have proposed various tools and techniques for single-project scheduling; however, the literature further considering multimode or multiproject issues occurring in the real world is rather scarce. In this paper, design structure matrix (DSM) and an improved artificial immune network algorithm (aiNet) are developed to solve a multi-mode resource-constrained scheduling problem. Firstly, the DSM is used to simplify the mathematic model of multi-project scheduling problem. Subsequently, aiNet algorithm comprised of clonal selection, negative selection, and network suppression is adopted to realize the local searching and global searching, which will assure that it has a powerful searching ability and also avoids the possible combinatorial explosion. Finally, the approach is tested on a set of randomly cases generated from ProGen. The computational results validate the effectiveness of the proposed algorithm comparing with other famous metaheuristic algorithms such as genetic algorithm (GA), simulated annealing algorithm (SA), and ant colony optimization (ACO).Chunhua Ju and Tinggui ChenCopyright © 2012 Chunhua Ju and Tinggui Chen. All rights reserved.http://www.hindawi.com/journals/ddns/2012/956564/This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. By using the super- and subsolution techniques, the critical exponent of the system is determined. That is, if Pc=p1q1−(m−p2)(n−q2)<0, then every nonnegative solution is global, whereas if Pc>0, there are solutions that blowup and others that are global according to the size of initial values u0(x) and v0(x). When Pc=0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain large enough that is, if it contains a sufficiently large ball, there is no global solution.Ling Zhengqiu and Wang ZejiaCopyright © 2012 Ling Zhengqiu and Wang Zejia. All rights reserved.http://www.hindawi.com/journals/ddns/2012/843735/The dynamic behaviors in a droop model for phytoplankton growth in a chemostat with nutrient periodically pulsed input are studied. A series of new criteria on the boundedness, permanence, extinction, existence of positive periodic solution, and global attractivity for the model are established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.Kai Wang, Zhidong Teng, and Xueliang ZhangCopyright © 2012 Kai Wang et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/961642/Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai)=D(a1)a22⋯an2+a12D(a2)a32⋯an2+⋯+a12a22⋯an−12D(an) for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.Madjid Eshaghi Gordji, Badrkhan Alizadeh, Young Whan Lee, and Gwang Hui KimCopyright © 2012 Madjid Eshaghi Gordji et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/863931/We investigate the moving average process such that Xn=∑i=1∞aiYi+n, n≥1, where ∑i=1∞|ai|<∞ and {Yi, 1≤i<∞} is a sequence of asymptotically almost negatively associated (AANA) random variables. The complete convergence, complete moment convergence, and the existence of the moment of supermum of normed partial sums are presented for this moving average process.Wenzhi Yang, Xuejun Wang, Nengxiang Ling, and Shuhe HuCopyright © 2012 Wenzhi Yang et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/840986/The tracking problem for continuous-time systems is investigated. It is assumed that the states of the systems are not available. An observer is firstly designed to estimate the states by using the ℋ∞ method. The control action is consist of a state-feedback control, an integral component, and a feedforward loop. The linear-matrix-inequality region is used to constrain the eigenvalue location for the closed-loop systems. The control gains can be obtained by solving a sequence of linear matrix inequalities (LMIs) which can guarantee the mixed ℋ2/ℋ∞ performance for the closed-loop systems.Huxiong LiCopyright © 2012 Huxiong Li. All rights reserved.http://www.hindawi.com/journals/ddns/2012/734754/This paper investigates the guaranteed cost control of chaos problem in 4D Lorenz-Stenflo (LS) system via Takagi-Sugeno (T-S) fuzzy method approach. Based on Lyapunov stability theory and linear matrix inequality (LMI) technique, a state feedback controller is proposed to stabilize the 4D Lorenz-Stenflo chaotic system. An illustrative example is provided to verify the validity of the results developed in this paper.Yi-You Hou, Meei-Ling Hung, and Jui-Sheng LinCopyright © 2012 Yi-You Hou et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/872385/The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property. In order to further prove its integrality, we give its bilinear form and construct its bilinear Bäcklund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form.Yali Shen, Fengqin Zhang, and Xiaomei FengCopyright © 2012 Yali Shen et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/138178/This work concerns the modeling of evolvement of trading behavior in stock markets which can cause significant impact on the movements of prices and volatilities. Based on the assumption of the investors' limited rationality, the evolution mechanism of trading behavior is modeled according to peer effect in network, that investors are prone to imitate their neighbors' activity through comprehensive analysis on the neighboring preferred degree, self-psychological preference, and the network topology of the relationship among them. We investigate by mean-field analysis and extensive simulations the evolution of investors' trading behavior in various typical networks under different characteristics of peer effect. Our results indicate that the evolution of investors' behavior is affected by the network structure of stock market and the effect of neighboring preferred degree; the stability of equilibrium states of investors' behavior dynamics is directly related with the concavity and convexity of the peer effect function; connectivity and heterogeneity of the network play an important role in the evolution of the investment behavior in stock market.Yue-Tang Bian, Lu Xu, Jin-Sheng Li, Jian-Min He, and Ya-Ming ZhuangCopyright © 2012 Yue-Tang Bian et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/652928/This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and two-step BDF method are of order p=0 when applied to impulsive differential equations. An improved linear multistep method is proposed. Convergence and stability conditions of the improved methods are given in the paper. Numerical experiments are given in the end to illustrate the conclusion.X. Liu, M. H. Song, and M. Z. LiuCopyright © 2012 X. Liu et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/618058/We consider the existence for eventually positive solutions of high-order nonlinear neutral differential equations with distributed delay. We use Lebesgue's dominated convergence theorem to obtain new necessary and sufficient condition for the existence of eventually positive solutions.Huanhuan Zhao, Youjun Liu, and Jurang YanCopyright © 2012 Huanhuan Zhao et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/148942/We investigate the stability property for the predator-free equilibrium point of predator-prey systems with a class of functional response and prey refuges by using the analytical approach. Under some very weakly assumption, we show that conditions that ensure the locally asymptotically stable of the predator-free equilibrium point are consistent with that of the globally asymptotically stable ones. Our result supplements the corresponding result of Ma et al., 2009.Fengde Chen, Yumin Wu, and Zhaozhi MaCopyright © 2012 Fengde Chen et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/416789/This paper furnishes a guide for the study of 2-dimensional evolutionary games in discrete time. Evolutionarily stable strategies are identified and nonlinear outcomes are explored. Besides the baseline payoffs of the established strategic interaction, the following elements are also vital to determine the dynamic outcome of a game: the initial fitness of each agent and the rule of motion that describes how individuals switch between strategies. In addition to the dynamic rule commonly used in evolutionary games, the replicator dynamics, we propose another rule, which acknowledges the role of expectations and sophisticates the replicator mechanism.Orlando GomesCopyright © 2012 Orlando Gomes. All rights reserved.http://www.hindawi.com/journals/ddns/2012/724014/The dynamic complexities of a prey-predator system in the presence of alternative prey with impulsive state feedback control are studied analytically and numerically. By using the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions can be obtained. Furthermore, the corresponding bifurcation diagrams and phase diagrams are investigated by means of numerical simulations which illustrate the feasibility of the main results.Chuanjun Dai and Min ZhaoCopyright © 2012 Chuanjun Dai and Min Zhao. All rights reserved.http://www.hindawi.com/journals/ddns/2012/529849/In this paper, a novel digital image denoising algorithm called generalized fractional integral filter is introduced based on the generalized Srivastava-Owa fractional integral operator. The structures of n×n fractional masks of this algorithm are constructed. The denoising performance is measured by employing experiments according to visual perception and PSNR values. The results demonstrate that apart from enhancing the quality of filtered image, the proposed algorithm also reserves the textures and edges present in the image. Experiments also prove that the improvements achieved are competent with the Gaussian smoothing filter.Hamid A. Jalab and Rabha W. IbrahimCopyright © 2012 Hamid A. Jalab and Rabha W. Ibrahim. All rights reserved.http://www.hindawi.com/journals/ddns/2012/786404/The existence and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.Wen-Xue Zhou and Jigen PengCopyright © 2012 Wen-Xue Zhou and Jigen Peng. All rights reserved.http://www.hindawi.com/journals/ddns/2012/652947/A class of Beddington-DeAngelis functional response predator-prey model is considered. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are given.Changjin Xu and Peiluan LiCopyright © 2012 Changjin Xu and Peiluan Li. All rights reserved.http://www.hindawi.com/journals/ddns/2012/904815/We develop an optimization model for risk management in a virtual enterprise environment based on a novel multiswarm particle swarm optimizer called PS2O. The main idea of PS2O is to extend the single population PSO to the interacting multiswarms model by constructing hierarchical interaction topology and enhanced dynamical update equations. With the hierarchical interaction topology, a suitable diversity in the whole population can be maintained. At the same time, the enhanced dynamical update rule significantly speeds up the multiswarm to converge to the global optimum. With five mathematical benchmark functions, PS2O is proved to have considerable potential for solving complex optimization problems. PS2O is then applied to risk management in a virtual enterprise environment. Simulation results demonstrate that the PS2O algorithm is more feasible and efficient than the PSO algorithm in solving this real-world problem.Yichuan Shao, Xingjia Yao, Liwei Tian, and Hanning ChenCopyright © 2012 Yichuan Shao et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/373904/Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in C∗-algebras and Lie C∗-algebras and of derivations on non-Archimedean C∗-algebras and Non-Archimedean Lie C∗-algebras for an m-variable additive functional equation.Yeol Je Cho, Reza Saadati, and Javad VahidiCopyright © 2012 Yeol Je Cho et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/937670/We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problem u‴(t)+λa(t)f(u(t))=0, 0<t<1, u(0)=u′(0)=0, u″(1)=∝u″(η), where λ is a positive parameter, ∝∈(0,1), η∈(0,1), f:(0,∞)→(0,∞), a:(0,1)→(0,∞) are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.Xiaojie Lin and Zhengmin FuCopyright © 2012 Xiaojie Lin and Zhengmin Fu. All rights reserved.http://www.hindawi.com/journals/ddns/2012/579431/Differential transform method is adopted, for the first time, for solving linear singularly perturbed two-point boundary value problems. Four numerical examples are given to demonstrate the effectiveness of the present method. Results show that the numerical scheme is very effective and convenient for solving a large number of linear singularly perturbed two-point boundary value problems with high accuracy.Nurettin Doğan, Vedat Suat Ertürk, and Ömer AkınCopyright © 2012 Nurettin Doğan et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/480196/Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world and social institutions. Where there is a hierarchy with cascade structure, there is a Zipf's rank-size distribution, and vice versa. However, we have no theory to explain the spatial dynamics associated with Zipf's law of cities. In this paper, a new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random distribution of cities. The hierarchical structure can be described with a set of exponential functions that are identical in form to Horton-Strahler's laws on rivers and Gutenberg-Richter's laws on earthquake energy. From the exponential models, we can derive four power laws including Zipf's law indicative of fractals and scaling symmetry. A card-shuffling model is built to interpret the relation between Zipf's law and hierarchy of cities. This model can be expanded to illuminate the general empirical power-law distributions across the individual physical and social sciences, which are hard to be comprehended within the specific scientific domains. This research is useful for us to understand how complex systems such as networks of cities are self-organized.Yanguang ChenCopyright © 2012 Yanguang Chen. All rights reserved.http://www.hindawi.com/journals/ddns/2012/840345/We define the incomplete bivariate Fibonacci and Lucas p-polynomials. In the case x=1, y=1, we obtain the incomplete Fibonacci and Lucas p-numbers. If x=2, y=1, we have the incomplete Pell and Pell-Lucas p-numbers. On choosing x=1, y=2, we get the incomplete generalized Jacobsthal number and besides for p=1 the incomplete generalized Jacobsthal-Lucas numbers. In the case x=1, y=1, p=1, we have the incomplete Fibonacci and Lucas numbers. If x=1, y=1, p=1, k=⌊(n-1)/(p+1)⌋, we obtain the Fibonacci and Lucas numbers. Also generating function and properties of the incomplete bivariate Fibonacci and Lucas p-polynomials are given.Dursun Tasci, Mirac Cetin Firengiz, and Naim TugluCopyright © 2012 Dursun Tasci et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/894207/Spatial cluster analysis is an important data-mining task. Typical techniques include CLARANS, density- and gravity-based clustering, and other algorithms based on traditional von Neumann’s computing architecture. The purpose of this paper is to propose a technique for spatial cluster analysis based on DNA computing and a grid technique. We will adopt the Adleman-Lipton model and then design a flexible grid algorithm. Examples are given to show the effect of the algorithm. The new clustering technique provides an alternative for traditional cluster analysis.Xiyu Liu, Laisheng Xiang, and Xin WangCopyright © 2012 Xiyu Liu et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/125197/This paper studies multispecies nonautonomous Lotka-Volterra competitive systems with delays and fixed-time impulsive effects. The sufficient conditions of integrable form on the permanence of species are established.Xiaomei Feng, Fengqin Zhang, Kai Wang, and Xiaoxia LiCopyright © 2012 Xiaomei Feng et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/328151/This paper considers a rumor transmission model with incubation that incorporates constant recruitment and has infectious force in the latent period and infected period. By carrying out a global analysis of the model and studying the stability of the rumor-free equilibrium and the rumor-endemic equilibrium, we use the geometric approach for ordinary differential equations which is based on the use of higher-order generalization of Bendixson’s criterion. It shows that either the number of rumor infective individuals tends to zero as time evolves or the rumor persists. We prove that the transcritical bifurcation occurs at R0 crosses the bifurcation threshold R0=1 by projecting the flow onto the extended center manifold. Since the rumor endemic level at the equilibrium is a continuous function of R0, as a consequence for successful eradication of the rumor, one should simply reduce R0 continuously below the threshold value 1. Finally, the obtained results are numerically validated and then discussed from both the mathematical and the sociological perspectives.Liang'an Huo, Peiqing Huang, and Chun-xiang GuoCopyright © 2012 Liang'an Huo et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/258309/Wolfram divided the 256 elementary cellular automata rules informally into four classes using dynamical concepts like periodicity, stability, and chaos. Rule 14, which is Bernoulli στ-shift rule and is a member of Wolfram’s class II, is said to be simple as periodic before. Therefore, it is worthwhile studying dynamical behaviors of rule 14, whether it possesses chaotic attractors or not. In this paper, the complex dynamical behaviors of rule 14 of one-dimensional cellular automata are investigated from the viewpoint of symbolic dynamics. We find that rule 14 is chaotic in the sense of both Li-Yorke and Devaney on its attractor. Then, we prove that there exist fixed points in rule 14. Finally, we use diagrams to explain the attractor of rule 14, where characteristic function is used to describe that all points fall into Bernoulli-shift map after two iterations under rule 14.Qi Han, Xiaofeng Liao, and Chuandong LiCopyright © 2012 Qi Han et al. All rights reserved.http://www.hindawi.com/journals/ddns/2012/184918/An epidemiological model of TB with infectivity in latent period and imperfect treatment is introduced. As presented, sustained oscillations are not possible and the endemic proportions either approach the disease-free equilibrium or an endemic equilibrium. The expanded model that stratified the infectious individuals according to their time-since-infection θ is also carried out. The global asymptotic stability of the infection-free state is established as well as local asymptotic stability of the endemic equilibrium. At the end, numerical simulations are presented to illustrate the results.Juan Wang, Sha-Sha Gao, and Xue-Zhi LiCopyright © 2012 Juan Wang et al. All rights reserved.