http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Wed, 19 Jun 2013 15:39:59 +0000 http://www.hindawi.com/journals/ddns/2013/398750/ Financial risk is objective in modern financial activity. Management and measurement of the financial risks have become key abilities for financial institutions in competition and also make the major content in finance engineering and modern financial theories. It is important and necessary to model and forecast financial risk. We know that nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, specially in finance risk measure and management. Under the nonlinear expectation framework, however, the related statistical models and statistical inferences have not yet been well established. In this paper, a sublinear expectation nonlinear regression is defined, and its identifiability is obtained. Several parameter estimations and model predictions are suggested, and the asymptotic normality of the estimation and the mini-max property of the prediction are obtained. Finally, simulation study and real data analysis are carried out to illustrate the new model and methods. In this paper, the notions and methodological developments are nonclassical and original, and the proposed modeling and inference methods establish the foundations for nonlinear expectation statistics. Yunquan Song and Lu Lin Copyright © 2013 Yunquan Song and Lu Lin. All rights reserved. Wed, 19 Jun 2013 08:17:04 +0000 http://www.hindawi.com/journals/ddns/2013/358930/ A predator-prey system with generalized group defense and impulsive control strategy is investigated. By using Floquet theorem and small amplitude perturbation skills, a local asymptotically stable prey-eradication periodic solution is obtained when the impulsive period is less than some critical value. Otherwise, the system is permanent if the impulsive period is larger than the critical value. By using bifurcation theory, we show the existence and stability of positive periodic solution when the pest eradication lost its stability. Numerical examples show that the system considered has more complicated dynamics, including (1) high-order quasiperiodic and periodic oscillation, (2) period-doubling and halving bifurcation, (3) nonunique dynamics (meaning that several attractors coexist), and (4) chaos and attractor crisis. Further, the importance of the impulsive period, the released amount of mature predators and the degree of group defense effect are discussed. Finally, the biological implications of the results and the impulsive control strategy are discussed. Shunyi Li Copyright © 2013 Shunyi Li. All rights reserved. Wed, 12 Jun 2013 15:25:47 +0000 http://www.hindawi.com/journals/ddns/2013/917835/ A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure that -dimensional Cohen-Grossberg neural networks with -level discontinuous activation functions can have equilibrium points or periodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results. Yanke Du, Yanlu Li, and Rui Xu Copyright © 2013 Yanke Du et al. All rights reserved. Wed, 12 Jun 2013 13:25:41 +0000 http://www.hindawi.com/journals/ddns/2013/368176/ This paper is devoted to periodic Gause-type ratio-dependent predator-prey systems with monotonic or nonmonotonic numerical responses on time scales. By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of periodic solutions. In particular, our results improve and generalize some known ones. Xiaoquan Ding, Hongyuan Liu, and Fengye Wang Copyright © 2013 Xiaoquan Ding et al. All rights reserved. Mon, 10 Jun 2013 11:22:28 +0000 http://www.hindawi.com/journals/ddns/2013/491359/ Nonlinear fractional partial differential equations have been solved with the help of the extended trial equation method. Based on the fractional derivative in the sense of modified Riemann-Liouville derivative and traveling wave transformation, the fractional partial differential equation can be turned into the nonlinear nonfractional ordinary differential equation. For illustrating the reliability of this approach, we apply it to the generalized third order fractional KdV equation and the fractional equation according to the complete discrimination system for polynomial method. As a result, some new exact solutions to these nonlinear problems are successfully constructed such as elliptic integral function solutions, Jacobi elliptic function solutions, and soliton solutions. Yusuf Pandir, Yusuf Gurefe, and Emine Misirli Copyright © 2013 Yusuf Pandir et al. All rights reserved. Thu, 06 Jun 2013 14:41:24 +0000 http://www.hindawi.com/journals/ddns/2013/489521/ This paper is concerned with the general solution of linear fractional neutral differential difference equations. The exponential estimates of the solution and the variation of constant formula for linear fractional neutral differential difference equations are derived by using the Gronwall integral inequality and the Laplace transform method, respectively. The obtained results extend the corresponding ones of integer order linear ordinary differential equations and delay differential equations. Hai Zhang, Jinde Cao, and Wei Jiang Copyright © 2013 Hai Zhang et al. All rights reserved. Wed, 05 Jun 2013 10:15:46 +0000 http://www.hindawi.com/journals/ddns/2013/259730/ Using a new fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to nonlinear two-point boundary value problems for second-order impulsive differential equations with concave or convex nonlinearities. Lingling Zhang and Chengbo Zhai Copyright © 2013 Lingling Zhang and Chengbo Zhai. All rights reserved. Tue, 04 Jun 2013 14:44:58 +0000 http://www.hindawi.com/journals/ddns/2013/720818/ In 2001, Friedman et al. conjectured the existence of a “firewall effect” in which individuals who are infected with HIV, but remain in a state of low infectiousness, serve to prevent the virus from spreading. To evaluate this historical conjecture, we develop a new graph-theoretic measure that quantifies the extent to which Friedman’s firewall hypothesis (FH) holds in a risk network. We compute this new measure across simulated trajectories of a stochastic discrete dynamical system that models a social network of 25,000 individuals engaging in risk acts over a period of 15 years. The model’s parameters are based on analyses of data collected in prior studies of the real-world risk networks of people who inject drugs (PWID) in New York City. Analysis of system trajectories reveals the structural mechanisms by which individuals with mature HIV infections tend to partition the network into homogeneous clusters (with respect to infection status) and how uninfected clusters remain relatively stable (with respect to infection status) over long stretches of time. We confirm the spontaneous emergence of network firewalls in the system and reveal their structural role in the nonspreading of HIV. Bilal Khan, Kirk Dombrowski, Mohamed Saad, Katherine McLean, and Samuel Friedman Copyright © 2013 Bilal Khan et al. All rights reserved. Mon, 03 Jun 2013 09:02:52 +0000 http://www.hindawi.com/journals/ddns/2013/705318/ This paper defines two different ways of the process of the opinion formation and focuses on the effect of the proportion of the two strategies of process and the structure of the network. A multiopinion model is proposed in this paper, which includes two strategies of opinion formation. At the first part, the change of the structured network and the change of the single node are used as two strategies of the process of the opinion formation. We focus on how the proportion of the two strategies can affect the outcome of the process. At the second part, as the proportion of the two strategies is fixed, the edges are dense in the community and sparse outside. Thus we can construct a bifurcation diagram to be verified through experimental study. The phase transition is studied in the network which contains more than four opinions and two strategies of process. Our results show that the size of the group and the dense of edges are the two important features for the process of opinion formation. Cheng Ju, Yang Cao, and Pengcheng Zhou Copyright © 2013 Cheng Ju et al. All rights reserved. Sun, 02 Jun 2013 11:36:24 +0000 http://www.hindawi.com/journals/ddns/2013/281395/ Blanchard and Huang introduced the notion of weakly mixing subset, and Oprocha and Zhang gave the concept of transitive subset and studied its basic properties. In this paper our main goal is to discuss the weakly mixing subsets and transitive subsets in set-valued discrete systems. We prove that a set-valued discrete system has a transitive subset if and only if original system has a weakly mixing subset. Moreover, we give an example showing that original system has a transitive subset, which does not imply set-valued discrete system has a transitive subset. Lei Liu Copyright © 2013 Lei Liu. All rights reserved. Tue, 28 May 2013 10:35:15 +0000 http://www.hindawi.com/journals/ddns/2013/162128/ This study proposes a nonlinear min-cost-pursued swapping dynamic (NMSD) system to model the evolution of selfish routing games on traffic network where travelers only swap from previous costly routes to the least costly ones. NMSD is a rational behavior adjustment process with stationary link flow pattern being the Wardrop user equilibrium. NMSD is able to prevent two behavioral deficiencies suffered by the existing min-cost-oriented models and keep solution invariance. NMSD relaxes the homogeneous user assumption, and the continuous-time NMSD (CNMSD) and discrete-time NMSD (DNMSD) share the same revision protocol. Moreover, CNMSD is Lyapunov-stable. Two numerical examples are conducted. The first one is designed to characterize the NMSD-conducted network traffic evolution and test the stability of day-to-day NMSD. The second one aims to explore the impacts of network scale on the stability of route-swaps conducted by pairwise and min-cost-pursed swapping behaviors. Wenyi Zhang, Wei Guan, Jihui Ma, and Tao Wang Copyright © 2013 Wenyi Zhang et al. All rights reserved. Mon, 27 May 2013 13:10:24 +0000 http://www.hindawi.com/journals/ddns/2013/784279/ Using a generalized Riccati transformation and the general integral means technique, some new interval oscillation criteria for the linear matrix Hamiltonian system , , are obtained. These results generalize and improve the oscillation criteria due to Zheng (2008). An example is given to dwell upon the importance of our results. Jing Shao and Fanwei Meng Copyright © 2013 Jing Shao and Fanwei Meng. All rights reserved. Mon, 27 May 2013 13:09:41 +0000 http://www.hindawi.com/journals/ddns/2013/152069/ We investigate the zero distribution of -shift difference polynomials of meromorphic functions with zero order and obtain some results that extend previous results of K. Liu et al. Yong Liu, Yinhong Cao, Xiaoguang Qi, and Hongxun Yi Copyright © 2013 Yong Liu et al. All rights reserved. Sun, 26 May 2013 16:57:05 +0000 http://www.hindawi.com/journals/ddns/2013/829535/ We give divisibility properties of the generalized Fibonacci sequence by matrix methods. We also present new recursive identities for the generalized Fibonacci and Lucas sequences. Aynur Yalçiner Copyright © 2013 Aynur Yalçiner. All rights reserved. Mon, 20 May 2013 15:13:34 +0000 http://www.hindawi.com/journals/ddns/2013/104173/ In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives. The second approach is by iterating the derivative and then defining a fractional order by making use of the binomial theorem to obtain Grünwald-Letnikov fractional derivatives. In this paper we formulate the delta and nabla discrete versions for left and right fractional integrals and derivatives representing the second approach. Then, we use the discrete version of the Q-operator and some discrete fractional dual identities to prove that the presented fractional differences and sums coincide with the discrete Riemann ones describing the first approach. Thabet Abdeljawad, Dumitru Baleanu, Fahd Jarad, and Ravi P. Agarwal Copyright © 2013 Thabet Abdeljawad et al. All rights reserved. Mon, 20 May 2013 11:56:27 +0000 http://www.hindawi.com/journals/ddns/2013/179401/ We focus on a system of a rational -order difference equation , , , where . We investigate the dynamical behavior of positive solution for the system. Banyat Sroysang Copyright © 2013 Banyat Sroysang. All rights reserved. Sun, 19 May 2013 13:56:41 +0000 http://www.hindawi.com/journals/ddns/2013/681689/ Social distancing, vaccination, and medical treatments have been extensively studied and widely used to control the spread of infectious diseases. However, it is still a difficult task for health administrators to determine the optimal combination of these strategies when confronting disease outbreaks with limited resources, especially in the case of interconnected populations, where the flow of individuals is usually restricted with the hope of avoiding further contamination. We consider two coupled populations and examine them independently under two variants of well-known discrete time disease models. In both examples we compute approximations for the control levels necessary to minimize costs and quickly contain outbreaks. The main technique used is simulated annealing, a stochastic search optimization tool that, in contrast with traditional analytical methods, allows easy implementation to any number of patches with different kinds of couplings and internal dynamics. Geisel Alpízar and Luis F. Gordillo Copyright © 2013 Geisel Alpízar and Luis F. Gordillo. All rights reserved. Sun, 19 May 2013 11:28:12 +0000 http://www.hindawi.com/journals/ddns/2013/816382/ Xiang Li, Chen Zhou, and Xiaochen Sun Copyright © 2013 Xiang Li et al. All rights reserved. Thu, 16 May 2013 18:03:43 +0000 http://www.hindawi.com/journals/ddns/2013/474852/ We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem. We tackle the problem using duality concept, differently from traditional approaches. Our method is based on Lagrangian relaxation. Lagrange multipliers transform the problem, keeping the optimality as well as decreasing the complexity. However, it is not easy to find Lagrange multipliers nearest to the capacity constraints of the problem. Through empirical investigation of Lagrangian space, we can see the potentiality of using a memetic algorithm. So we use a memetic algorithm to find the optimal Lagrange multipliers. We show the efficiency of the proposed method by the experiments on well-known benchmark data. Yourim Yoon and Yong-Hyuk Kim Copyright © 2013 Yourim Yoon and Yong-Hyuk Kim. All rights reserved. Wed, 15 May 2013 16:40:49 +0000 http://www.hindawi.com/journals/ddns/2013/183420/ Combining the exponential dichotomy of evolution family, composition theorems for almost automorphic functions with Banach fixed point theorem, we establish new existence and uniqueness theorems for almost automorphic mild solutions to neutral parabolic nonautonomous evolution equations with nondense domain. A unified framework is set up to investigate the existence and uniqueness of almost automorphic mild solutions to some classes of parabolic partial differential equations and neutral functional differential equations. Zhanrong Hu and Zhen Jin Copyright © 2013 Zhanrong Hu and Zhen Jin. All rights reserved. Wed, 15 May 2013 12:03:52 +0000 http://www.hindawi.com/journals/ddns/2013/943961/ This paper is devoted to introduce a new approach to investigate the existence of solutions for a three-point boundary value problem of fractional difference equations as fllows: , , and = We present an existence result at resonance case. The proof relies on coincidence degree theory. Zhongmin Huang and Chengmin Hou Copyright © 2013 Zhongmin Huang and Chengmin Hou. All rights reserved. Wed, 15 May 2013 10:23:01 +0000 http://www.hindawi.com/journals/ddns/2013/864707/ The investigations are made on the exponential synchronization of the stochastic Lur'e system with nonlinear coupling and impulsive disturbance. The impulsive effects in complex networks could play a positive or a negative role for synchronization. For the sake of simplification and efficiency, a single impulsive controller is designed to realize the synchronization of the impulsive dynamical network with respect to stabilizing and destabilizing impulsive effects. Sufficient conditions are derived to guarantee the realization of the exponential synchronization for all initial values by means of the Lyapunov stability theorem, the comparison principle, and the linear matrix inequalities (LMIs). Numerical simulations are given to support the validity of the analytical results. Yi Zhao, Ze Tang, and Jianwen Feng Copyright © 2013 Yi Zhao et al. All rights reserved. Tue, 14 May 2013 19:13:52 +0000 http://www.hindawi.com/journals/ddns/2013/841764/ This study is based on an early brain tumor growth that is modeled as a hybrid system such as (A): , where the parameters , and denote positive numbers, and are negative numbers and is the integer part of . Equation (A) explains a brain tumor growth, where is embedded to show the drug effect on the tumor and is a rate that causes a negative effect by the immune system on the tumor population. Using (A), we have constructed two models of a tumor growth: one is (A) and the other one is a population model at low density by incorporating an Allee function to (A) at time . To consider the global behavior of (A), we investigate the discrete solutions of (A). Examination of the characterization of the stability shows that increase of the population growth rate decreases the local stability of the positive equilibrium point of (A). The simulations give a detailed description of the behavior of solutions of (A) with and without Allee effect. F. Bozkurt Copyright © 2013 F. Bozkurt. All rights reserved. Tue, 14 May 2013 17:34:33 +0000 http://www.hindawi.com/journals/ddns/2013/903593/ We deal with the form of the solutions for the following systems of rational difference equations , , with nonzero real numbers initial conditions. Also we investigate some properties of the obtained solutions and present some numerical examples. H. El-Metwally Copyright © 2013 H. El-Metwally. All rights reserved. Mon, 13 May 2013 12:08:34 +0000 http://www.hindawi.com/journals/ddns/2013/495838/ We investigate the global convergence, boundedness, and periodicity of solutions of the recursive sequence , where the parameters and are positive real numbers, and the initial conditions and are positive real numbers where . M. M. El-Dessoky Copyright © 2013 M. M. El-Dessoky. All rights reserved. Sun, 12 May 2013 14:45:54 +0000 http://www.hindawi.com/journals/ddns/2013/604105/ By introducing new definitions of convex and concave quasioperator and quasilower and quasiupper, by means of the monotone iterative techniques without any compactness conditions, we obtain the iterative unique solution of nonlinear mixed monotone Fredholm-type integral equations in Banach spaces. Our results are even new to convex and concave quasi operator, and then we apply these results to the two-point boundary value problem of second-order nonlinear ordinary differential equations in the ordered Banach spaces. Hua Su Copyright © 2013 Hua Su. All rights reserved. Sun, 12 May 2013 13:18:05 +0000 http://www.hindawi.com/journals/ddns/2013/408904/ We propose a price game model of irrigation water in a coastal irrigation district. Then, we discuss the stability and codimension-two period-doubling (flip) bifurcation. Then, the MATLAB package Cl_MatContM is employed to illustrate its numerical bifurcations-based continuation methods. Lastly, the 0-1 test algorithm is used to compute the median value of correlation coefficient which can indicate whether the underlying dynamics is regular or chaotic. Baogui Xin and Yuting Li Copyright © 2013 Baogui Xin and Yuting Li. All rights reserved. Sun, 12 May 2013 07:58:11 +0000 http://www.hindawi.com/journals/ddns/2013/385419/ We study the bifurcation of limit cycles from periodic orbits of a four-dimensional system when the perturbation is piecewise linear with two switching boundaries. Our main result shows that when the parameter is sufficiently small at most, six limit cycles can bifurcate from periodic orbits in a class of asymmetric piecewise linear perturbed systems, and, at most, three limit cycles can bifurcate from periodic orbits in another class of asymmetric piecewise linear perturbed systems. Moreover, there are perturbed systems having six limit cycles. The main technique is the averaging method. Yanyan Cheng Copyright © 2013 Yanyan Cheng. All rights reserved. Thu, 09 May 2013 15:20:50 +0000 http://www.hindawi.com/journals/ddns/2013/756251/ We consider a single-machine scheduling problem with upper bounded actual processing time and upper bounded maintenance time under deteriorating effect. The actual processing time of a job is a position-dependent power function. If the actual processing time of a job exceeds the upper bound, tardiness penalty of the job should be paid. And if the maintenance time exceeds the corresponding upper bound, tardiness penalty of the maintenance should also be paid. The maintenance duration studied in the paper is a position-dependent exponential function. The objective is to find jointly the optimal maintenance frequency and the optimal job sequence to minimize the total cost, which is a linear function of the makespan and the total tardiness. We show that the studied scheduling problem can be transformed as a classic assignment problem to solve. There is also shown that a special case of the scheduling problem can be optimally solved by a lower order algorithm. Pengfei Xue and Yulin Zhang Copyright © 2013 Pengfei Xue and Yulin Zhang. All rights reserved. Thu, 09 May 2013 15:10:21 +0000 http://www.hindawi.com/journals/ddns/2013/480560/ Being inspired by the Hopfield neural networks (Hopfield (1982) and Hopfield and Tank (1985)) and the nonlinear sigmoid power control algorithm for cellular radio systems in Uykan and Koivo (2004), in this paper, we present a novel discrete recurrent nonlinear system and extend the results in Uykan (2009), which are for autonomous linear systems, to nonlinear case. The proposed system can be viewed as a discrete-time realization of a recently proposed continuous-time network in Uykan (2013). In this paper, we focus on discrete-time analysis and provide various novel key results concerning the discrete-time dynamics of the proposed system, some of which are as follows: (i) the proposed system is shown to be stable in synchronous and asynchronous work mode in discrete time; (ii) a novel concept called Pseudo-SINR (pseudo-signal-to-interference-noise ratio) is introduced for discrete-time nonlinear systems; (iii) it is shown that when the system states approach an equilibrium point, the instantaneous Pseudo-SINRs are balanced; that is, they are equal to a target value. The simulation results confirm the novel results presented and show the effectiveness of the proposed discrete-time network as applied to various associative memory systems and clustering problems. Zekeriya Uykan Copyright © 2013 Zekeriya Uykan. All rights reserved.