http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/971534By constructing a Lyapunov function, a new instability result is established, which guarantees that the trivial solution of a certain nonlinear vector differential equation of the fifth order is unstable. An example is also given to illustrate the importance of the result obtained. By this way, our findings improve an instability result related to a scalar differential equation in the literature to instability of the trivial solution to the afore-mentioned differential equation.Cemil Tunç and Melike Karta© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/981952Spanish unemployment is characterized by three distinct regimes of low, medium, and high unemployment and by a fast transition between them. This paper presents a simple nonlinear dynamic model that is able to explain this behavior with multiple equilibria and jumps describing the transition between equilibria. The model has only a small number of parameters capturing the fundamentals of labor markets and macroeconomic and institutional factors. The model is capable of generating unemployment dynamics that encompass the “unique” natural rate hypothesis, the structuralist hypothesis, and the hysteresis hypothesis.João Ricardo Faria and Miguel A. León-Ledesma© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/792632The set of all rational functions with any fixed denominator that simultaneously nullify in the infinite point is parametrized by means of a well-known integrable system: a finite dimensional version of the discrete KP hierarchy. This type of study was originated in Y. Nakamura's works who used others integrable systems. Our work proves that the finite discrete KP hierarchy completely parametrizes the space RatΛ(n) of rational functions of the form f(x)=q(x)/zn, where q(x) is a polynomial of order n−1 with nonzero independent coefficent. More exactly, it is proved that there exists a bijection from RatΛ(n) to the moduli space of solutions of the finite discrete KP hierarchy and a compatible linear system.Raúl Felipe and Nancy López© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/243291We study the asymptotic behavior of positive solutions to the difference equation xn=max{A/xn-1α,B/xn−2β}, n=0,1,…, where 0<α, β<1, A,B>0. We prove that every positive solution to this equation converges to x∗=max{A1/(α+1),B1/(β+1)}.Fangkuan Sun© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/257680Several existence theorems of twin positive solutions are established for a nonlinear m-point boundary value problem of third-order p-Laplacian dynamic equations on time scales by using a fixed point theorem. We present two theorems and four corollaries which generalize the results of related literature. As an application, an example to demonstrate our results is given. The obtained conditions are different from some known results.Wei Han and Guang Zhang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/524945This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the T-periodic Logistic system with time-varying generating operators and T0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed T-periodic system with time-varying generating operators and T0-periodic impulsive perturbations are given. It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable when T and T0 are rational dependent and its period must be nT0 for some n∈N. At last, an example is given for demonstration.JinRong Wang, X. Xiang, W. Wei, and Qian Chen© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/592950This paper is devoted to the study of a generalized modified version of the well-known Beverton-Holt equation in ecology. The proposed model describes the population evolution of some species in a certain habitat driven by six parametrical sequences, namely, the intrinsic growth rate (associated with the reproduction capability), the degree of sympathy of the species with the habitat (described by a so-called environment carrying capacity), a penalty term to deal with overpopulation levels, the harvesting (fishing or hunting) regulatory quota, or related to use of pesticides when fighting damaging plagues, and the independent consumption which basically quantifies predation. The independent consumption is considered as a part of a more general additive disturbance which also potentially includes another extra additive disturbance term which might be attributed to net migration from or to the habitat or modeling measuring errors. Both potential contributions are included for generalization purposes in the proposed modified generalized Beverton-Holt equation. The properties of stability and boundedness of the solution sequences, equilibrium points of the stationary model, and the existence of oscillatory solution sequences are investigated. A numerical example for a population of aphids is investigated with the theoretical tools developed in the paper.M. De La Sen© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/219653We consider the dynamics of a stochastic cobweb model with linear demand and a backward-bending supply curve. In our model, forward-looking expectations and backward-looking ones are assumed, in fact we assume that the representative agent chooses the backward predictor with probability q_,__0_q_1, and the forward predictor with probability (1−q), so that the expected price at time t is a random variable and consequently the dynamics describing the price evolution in time is governed by a stochastic dynamical system. The dynamical system becomes a Markov process when the memory rate vanishes. In particular, we study the Markov chain in the cases of discrete and continuous time. Using a mixture of analytical tools and numerical methods, we show that, when prices take discrete values, the corresponding Markov chain is asymptotically stable. In the case with continuous prices and nonnecessarily zero memory rate, numerical evidence of bounded price oscillations is shown. The role of the memory rate is studied through numerical experiments, this study confirms the stabilizing effects of the presence of resistant memory.Serena Brianzoni, Cristiana Mammana, Elisabetta Michetti, and Francesco Zirilli© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/706154A delayed predator-prey model with diffusion and competition is proposed. Some sufficient conditions on uniform persistence of the model have been obtained. By applying Liapunov-Razumikhin technique, we will point out, under almost periodic circumstances, a set of sufficient conditions that assure the existence and uniqueness of the positive almost periodic solution which is globally asymptotically stable.Qiong Liu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/312870We present a framework to characterize terrestrial functions—surficial and bottom topographic regions that are represented, respectively, as raster digital elevation models (DEMs) and digital bathymetric models (DBMs)—through analysis of flow fields that are simulated via geodesic morphology. Characterization of such functions is done via a new descriptor. Computation of this new descriptor involves the following steps: (i) basin in digital form representing topographic fluctuations as an input, (ii) threshold decomposition of basin—that consists of channelized and nonchannelized regions—into sets, (iii) proper indexing of these sets to decide the marker set(s) and its (their) corresponding mask set(s), (iv) performing geodesic propagation that provides basic flow field structures, and (v) finally providing a new basin descriptor—geodesic spectrum. We demonstrated this five-step framework on five different synthetic and/or realistic DEMs and/or DBMs. This study provides potentially invaluable insights to further study the travel-time flood propagation within basins of both fluvial and tidal systems.Sin Liang Lim and B. S. Daya Sagar© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/945109The permanence of a single-species population discrete model with feedback control is considered. We found that if we use the method of comparison theorem, then the additional condition, to some extent, is necessary. But for the system itself, this condition may not be necessary. Here, we use new methods instead of the comparison theorem to get the permanence of the system in consideration; the additional condition in Chen's paper (2007) is deleted.Yong-Hong Fan and Lin-Lin Wang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/820629We investigate the periodic nature of solutions of the max difference equation xn+1=max⁡{xn,A}/(xnxn−1), n=0,1,…, where A is a positive real parameter, and the initial conditions x−1=Ar−1 and x0=Ar0 such that r−1 and r0 are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005).Ali Gelisken, Cengiz Cinar, and Ibrahim Yalcinkaya© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/590142Based on Ruch's concept of diagram lattices formed by Young diagrams we investigated the possibility to transform incomparable diagrams into comparable ones by means of vector catalysis. Ruch's diagram lattices allow a very general description of comparing frequency distributions by their mixing-character as an order relation which is equivalent to majorisation in the mathematical theory of inequalities. Dealing with Young diagrams or vectors containing only integer components, respectively, vector catalysis is strongly related to entanglement catalysis in quantum informatics. In a very systematic way the diagram lattices of the partitions up to the number n=20 have been searched for incomparable pairs which can be catalysed. This concept opens the opportunity for regarding vector catalysis as a universal phenomenon which is not restricted to the quantum mechanical idea of entanglement catalysis. Such a general approach offers the possibility to compare vector catalysis with chemical ideas of catalysis and autocatalysis in a very fundamental sense. We emphasize that vector catalysis is a universally valid procedure for classification purposes, where incomparable sequences of symbols are transformed into comparable ones in a much higher dimensional space ignoring any physical interpretation of these symbols.Ernst-Christoph Haß, Sonja Sauerbrei, and Peter Jörg Plath© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/252876Several existence theorems of positive solutions are established for nonlinear m-point boundary value problem for the following dynamic equations on time scales (ϕ(uΔ))∇+a(t)f(t,u(t))=0, t∈(0,T), ϕ(uΔ(0))=∑i=1m−2aiϕ(uΔ(ξi)), u(T)=∑i=1m−2biu(ξi), where ϕ:R→R is an increasing homeomorphism and homomorphism and ϕ(0)=0. As an application, an example to demonstrate our results is given.Yanbin Sang, Hua Su, and Yafeng Xiao© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/138547The purpose of this paper is to propose a version of causality testing that focuses on how the sign of the returns affects the causality results. We replace the traditional VAR specification used in the Granger causality test by a discrete-time bivariate noisy Mackey glass model. Our test reveals interesting and previously unexplored relationships in US economic series, including inflation, metal, and stock returns.D. Hristu-Varsakelis and C. Kyrtsou© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/867623We consider nonlinear difference equations of unbounded order of the form xi=bi−∑j=0iai,jfi−j(xj),  i=0,1,2,…, where fj(x)  (j=0,…,i) are suitable functions. We establish sufficient conditions for the boundedness and the convergence of xi as i→+∞. Some of these conditions are interesting mainly for studying stability of numerical methods for Volterra integral equations.E. Messina, Y. Muroya, E. Russo, and A. Vecchio© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/526734This study attempts to characterize and predict stock returns series in Shanghai stock exchange using the concepts of nonlinear dynamical theory. Surrogate data method of multivariate time series shows that all the stock returns time series exhibit nonlinearity. Multivariate nonlinear prediction methods and univariate nonlinear prediction method, all of which use the concept of phase space reconstruction, are considered. The results indicate that multivariate nonlinear prediction model outperforms univariate nonlinear prediction model, local linear prediction method of multivariate time series outperforms local polynomial prediction method, and BP neural network method. Multivariate nonlinear prediction model is a useful tool for stock price prediction in emerging markets.Junhai Ma and Lixia Liu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/375452The purpose of this paper is to assess the statistical characterization of weighted networks in terms of the generalization of the relevant parameters, namely, average path length, degree distribution, and clustering coefficient. Although the degree distribution and the average path length admit straightforward generalizations, for the clustering coefficient several different definitions have been proposed in the literature. We examined the different definitions and identified the similarities and differences between them. In order to elucidate the significance of different definitions of the weighted clustering coefficient, we studied their dependence on the weights of the connections. For this purpose, we introduce the relative perturbation norm of the weights as an index to assess the weight distribution. This study revealed new interesting statistical regularities in terms of the relative perturbation norm useful for the statistical characterization of weighted graphs.I. E. Antoniou and E. T. Tsompa© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/262475We show that (1) there exist almost periodic orbits in T2-spaces of which the closures are not minimal sets; (2) there exist minimal sets in locally compact T1-spaces which are not compact; (3) there exist almost periodic orbits in T2-spaces of which the closures contain not only almost periodic points. These give answers to the three problems given by Mai and Sun in (2007).Jie-Hua Mai and Xin-He Liu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/140548In this paper the classical strong laws of large number of Kolmogorov, Chung, and Teicher for independent random variables were generalized on the case of ρ∗-mixing sequence. The main result was applied to obtain a Marcinkiewicz SLLN.Anna Kuczmaszewska© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/435787This paper proposes an alternative approach to economic growth with money. The production side is the same as the Solow model, the Ramsey model, and the Tobin model. But we deal with behavior of consumers differently from the traditional approaches. The model is influenced by the money-in-the-utility (MIU) approach in monetary economics. It provides a mechanism of endogenous saving which the Solow model lacks and avoids the assumption of adding up utility over a period of time upon which the Ramsey approach is based.Wei-Bin Zhang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/389727We consider a periodic time-dependent predator-prey system with stage structure and impulsive harvesting, in which the prey has a life history that takes them through two stages, immature and mature. A set of sufficient and necessary conditions which guarantee the permanence of the system are obtained. Finally, we give a brief discussion of our results.Kaiyuan Liu and Lansun Chen© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/263785This paper is concerned with the existence of unique and multiple solutions to the boundary value problem of a second-order difference equation with a parameter, which is a complement of the work by J. S. Yu and Z. M. Guo in 2006.Xi-Lan Liu and Jian-Hua Wu© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/746951A delayed SEIRS epidemic model with pulse vaccination and nonlinear incidence rate is proposed. We analyze the dynamical behaviors of this model and point out that there exists an infection-free periodic solution which is globally attractive if R1<1, R2>1, and the disease is permanent. Our results indicate that a short period of pulse or a large pulse vaccination rate is the sufficient condition for the eradication of the disease. The main feature of this paper is to introduce time delay and impulse into SEIRS model and give pulse vaccination strategies.Chunjin Wei and Lansun Chen© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/149267We propose a discrete predator-prey systems with Beddington-DeAngelis functional response and feedback controls. By applying the comparison theorem of difference equation, sufficient conditions are obtained for the permanence of the system.Xuepeng Li and Wensheng Yang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/47264We study the behaviour of the solutions of the following difference equation with the max operator: xn+1=max{1/xn,Axn−1}, n∈ℕ0, where parameter A∈ℝ and initial values x−1 and x0 are nonzero real numbers. In the most of the cases we determine the behaviour of the solutions in the terms of the initial values x−1 and x0 and the parameter A.I. Yalçinkaya, B. D. Iričanin, and C. Çinar© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2007/73849We prove that all positive solutions of the autonomous difference equation xn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, where k,m∈ℕ, and f is a continuous function satisfying the condition β min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um} for some β∈(0,1), converge to the positive equilibrium x¯=(α−1)/(β+1) if α>1.Bratislav D. Iričanin© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/193872Part-metric-related (PMR) inequality chains are elegant and are useful in the study of difference equations. In this paper, we establish a new PMR inequality chain, which is then applied to show the global asymptotic stability of a class of rational difference equations.Xiaofan Yang, Fangkuan Sun, and Yuan Yan Tang© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/265609This work is concerned with the monotone iterative technique for partial dynamic equations of first order on time scales and for this purpose, the existence, uniqueness, and comparison results are also established.Peiguang Wang and Ping Li© 2008, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/591261The asymptotic stability of discrete-time interval system with delay is discussed. A new sufficient condition for preserving the asymptotic stability of the system is presented by means of the inequality techniques. By mathematical analysis, the stability criterion is less conservative than that in previous result. Finally, one example is given to demonstrate the applicability of the present scheme.Wei Zhu© 2008, Hindawi Publishing Corporation. All rights reserved.