Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion Thu, 17 Apr 2014 08:00:41 +0000 http://www.hindawi.com/journals/aaa/2014/130851/ Predator-prey models describe biological phenomena of pursuit-evasion interaction. And this interaction exists widely in the world for the necessary energy supplement of species. In this paper, we have investigated a ratio-dependent spatially extended food chain model. Based on the bifurcation analysis (Hopf and Turing), we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point , and find that the model dynamics exhibits complex pattern replication. For fixed parameters, on increasing the control parameter , the sequence “holes holes-stripe mixtures stripes spots-stripe mixtures spots” pattern is observed. And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication. Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point , and find that the model dynamics exhibits stripes-spots pattern replication. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems. Lei Zhang Copyright © 2014 Lei Zhang. All rights reserved. Existence and Uniqueness of Almost Periodic Solutions for Neural Networks with Neutral Delays Thu, 17 Apr 2014 06:08:55 +0000 http://www.hindawi.com/journals/aaa/2014/642685/ A class of neural networks system with neutral delays is investigated. The existence and uniqueness of almost periodic solution for the system are obtained by using fixed point theorem; we extend some results in the references. Min Xu, Zengji Du, and Kaige Zhuang Copyright © 2014 Min Xu et al. All rights reserved. The Local Stability of Solutions for a Nonlinear Equation Thu, 17 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/781813/ The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space by assuming that the initial value only lies in the space . Haibo Yan and Ls Yong Copyright © 2014 Haibo Yan and Ls Yong. All rights reserved. Stability to a Kind of Functional Differential Equations of Second Order with Multiple Delays by Fixed Points Thu, 17 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/413037/ We discuss the stability of solutions to a kind of scalar Liénard type equations with multiple variable delays by means of the fixed point technique under an exponentially weighted metric. By this work, we improve some related results from one delay to multiple variable delays. Cemil Tunç and Emel Biçer Copyright © 2014 Cemil Tunç and Emel Biçer. All rights reserved. Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems Thu, 17 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/486509/ We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM) that is based on the homotopy perturbation method (HPM) and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM). At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves. Daniel Olvera and Alex Elías-Zúñiga Copyright © 2014 Daniel Olvera and Alex Elías-Zúñiga. All rights reserved. LP Well-Posedness for Bilevel Vector Equilibrium and Optimization Problems with Equilibrium Constraints Thu, 17 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/792984/ The purpose of this paper is introduce several types of Levitin-Polyak well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Base on criterion and characterizations for these types of Levitin-Polyak well-posedness we argue on diameters and Kuratowski’s, Hausdorff’s, or Istrǎtescus measures of noncompactness of approximate solution sets under suitable conditions, and we prove the Levitin-Polyak well-posedness for bilevel vector equilibrium and optimization problems with equilibrium constraints. Obtain a gap function for bilevel vector equilibrium problems with equilibrium constraints using the nonlinear scalarization function and consider relations between these types of LP well-posedness for bilevel vector optimization problems with equilibrium constraints and these types of Levitin-Polyak well-posedness for bilevel vector equilibrium problems with equilibrium constraints under suitable conditions; we prove the Levitin-Polyak well-posedness for bilevel equilibrium and optimization problems with equilibrium constraints. Phan Quoc Khanh, Somyot Plubtieng, and Kamonrat Sombut Copyright © 2014 Phan Quoc Khanh et al. All rights reserved. Bifurcations of Tumor-Immune Competition Systems with Delay Wed, 16 Apr 2014 17:26:31 +0000 http://www.hindawi.com/journals/aaa/2014/723159/ A tumor-immune competition model with delay is considered, which consists of two-dimensional nonlinear differential equation. The conditions for the linear stability of the equilibria are obtained by analyzing the distribution of eigenvalues. General formulas for the direction, period, and stability of the bifurcated periodic solutions are given for codimension one and codimension two bifurcations, including Hopf bifurcation, steady-state bifurcation, and B-T bifurcation. Numerical examples and simulations are given to illustrate the bifurcations analysis and obtained results. Ping Bi and Heying Xiao Copyright © 2014 Ping Bi and Heying Xiao. All rights reserved. Representation of the Solutions of Linear Discrete Systems with Constant Coefficients and Two Delays Wed, 16 Apr 2014 14:28:41 +0000 http://www.hindawi.com/journals/aaa/2014/320476/ The purpose of this paper is to develop a method for the construction of solutions to initial problems of linear discrete systems with constant coefficients and with two delays where , are fixed, , , are constant matrices, is a given vector, and is an unknown vector. Solutions are expressed with the aid of a special function called the discrete matrix delayed exponential for two delays. Such approach results in a possibility to express an initial Cauchy problem in a closed form. Examples are shown illustrating the results obtained. Josef Diblík and Blanka Morávková Copyright © 2014 Josef Diblík and Blanka Morávková. All rights reserved. On Hölder and Minkowski Type Inequalities Wed, 16 Apr 2014 14:25:07 +0000 http://www.hindawi.com/journals/aaa/2014/915635/ We obtain inequalities of Hölder and Minkowski type with weights generalizing both the case of weights with alternating signs and the classical case of nonnegative weights. Petr Chunaev, Ljiljanka Kvesić, and Josip Pečarić Copyright © 2014 Petr Chunaev et al. All rights reserved. Modelling the Influence of Awareness Programs by Media on the Drinking Dynamics Wed, 16 Apr 2014 14:14:25 +0000 http://www.hindawi.com/journals/aaa/2014/938080/ We develop a nonlinear mathematical model with the effect of awareness programs on the binge drinking. Due to the fact that awareness programs are capable of inducing behavioral changes in nondrinkers, we introduce a separate class by avoiding contacts with the heavy drinkers. Furthermore we assume that cumulative density of awareness programs increases at a rate proportional to the number of heavy drinkers. We establish some sufficient conditions for the stability of the alcohol free and the alcohol present equilibria and give some numerical simulations to explain our main result. Our results show that awareness programs is an effective measure in reducing alcohol problems. Hai-Feng Huo and Qian Wang Copyright © 2014 Hai-Feng Huo and Qian Wang. All rights reserved. Focusing Modeling of OPFC Linear Array Transducer by Using Distributed Point Source Method Wed, 16 Apr 2014 14:14:00 +0000 http://www.hindawi.com/journals/aaa/2014/840748/ The improvement of ultrasonic phased array detection technology is a major concern of engineering community. Orthotropic piezoelectric fiber composite (OPFC) can be constructed to multielement linear array which may be applied conveniently to actuators and sensors. The phased array transducers can generate special directional strong actuator power and high sensitivity for its orthotropic performance. Focusing beam of the linear phased array transducer is obtained simply only by adjusting a parabolic time delay. In this work, the distributed point source method (DPSM) is used to model the ultrasonic field. DPSM is a newly developed mesh-free numerical technique that has been developed for solving a variety of engineering problems. This work gives the basic theory of this method and solves the problems from the application of new OPFC phased array transducer. Compared with traditional transducer, the interaction effect of two OPFC linear phased array transducers is also modeled in the same medium, which shows that the pressure beam produced by the new transducer is narrower or more collimated than that produced by the conventional transducer at different angles. DPSM can be used to analyze and optimally design the OPFC linear phased array transducer. Ziping Wang and Ying Luo Copyright © 2014 Ziping Wang and Ying Luo. All rights reserved. Stability of a Class of Coupled Systems Wed, 16 Apr 2014 14:13:35 +0000 http://www.hindawi.com/journals/aaa/2014/835765/ We consider a class of coupled systems with damping terms. By using multiplier method and the estimation techniques of the energy, we show that even if the kernel function is nonincreasing and integrable without additional conditions, the energy of the system decays also to zero in a good rate. Kun-Peng Jin Copyright © 2014 Kun-Peng Jin. All rights reserved. On the Analyticity for the Generalized Quadratic Derivative Complex Ginzburg-Landau Equation Wed, 16 Apr 2014 14:11:09 +0000 http://www.hindawi.com/journals/aaa/2014/607028/ We study the analytic property of the (generalized) quadratic derivative Ginzburg-Landau equation in any spatial dimension with rough initial data. For , we prove the analyticity of local solutions to the (generalized) quadratic derivative Ginzburg-Landau equation with large rough initial data in modulation spaces . For , we obtain the analytic regularity of global solutions to the fractional quadratic derivative Ginzburg-Landau equation with small initial data in . The strategy is to develop uniform and dyadic exponential decay estimates for the generalized Ginzburg-Landau semigroup to overcome the derivative in the nonlinear term. Chunyan Huang Copyright © 2014 Chunyan Huang. All rights reserved. New Rational Homoclinic and Rogue Waves for Davey-Stewartson Equation Wed, 16 Apr 2014 14:09:56 +0000 http://www.hindawi.com/journals/aaa/2014/572863/ A new method, homoclinic breather limit method (HBLM), for seeking rogue wave solution of nonlinear evolution equation is proposed. A new family of homoclinic breather wave solution, and rational homoclinic solution (homoclinic rogue wave) for DSI and DSII equations are obtained using the extended homoclinic test method and homoclinic breather limit method (HBLM), respectively. Moreover, rogue wave solution is exhibited as period of periodic wave in homoclinic breather wave approaches to infinite. This result shows that rogue wave can be generated by extreme behavior of homoclinic breather wave for higher dimensional nonlinear wave fields. Changfu Liu, Chuanjian Wang, Zhengde Dai, and Jun Liu Copyright © 2014 Changfu Liu et al. All rights reserved. Nontrivial Solutions for Asymmetric Kirchhoff Type Problems Wed, 16 Apr 2014 14:05:18 +0000 http://www.hindawi.com/journals/aaa/2014/163645/ We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at and in . Namely, it is 4-linear at and 4-superlinear at . However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by combining Mountain Pass Theorem and a variant version of Mountain Pass Theorem with Moser-Trudinger inequality. Ruichang Pei and Jihui Zhang Copyright © 2014 Ruichang Pei and Jihui Zhang. All rights reserved. A New System of Multivalued Mixed Variational Inequality Problem Wed, 16 Apr 2014 13:45:15 +0000 http://www.hindawi.com/journals/aaa/2014/982606/ We consider a new system of multivalued mixed variational inequality problem, which includes some known systems of variational inequalities as special cases. Under suitable conditions, the existence of solutions for the system of multivalued mixed variational inequality problem and the convergence of iterative sequences generated by the generalized -projection algorithm are proved. A perturbational algorithm for solving a special case of multivalued mixed variational inequality problem is formally constructed. The results concerned with the existence of solutions and the convergence of iterative sequences generated by the perturbational algorithm are also given. Some known results are improved and generalized. Xi Li and Xue-song Li Copyright © 2014 Xi Li and Xue-song Li. All rights reserved. Stability Analysis of a Population Model with Maturation Delay and Ricker Birth Function Wed, 16 Apr 2014 10:59:08 +0000 http://www.hindawi.com/journals/aaa/2014/136707/ A single species population model is investigated, where the discrete maturation delay and the Ricker birth function are incorporated. The threshold determining the global stability of the trivial equilibrium and the existence of the positive equilibrium is obtained. The necessary and sufficient conditions ensuring the local asymptotical stability of the positive equilibrium are given by applying the Pontryagin's method. The effect of all the parameter values on the local stability of the positive equilibrium is analyzed. The obtained results show the existence of stability switch and provide a method of computing maturation times at which the stability switch occurs. Numerical simulations illustrate that chaos may occur for the model, and the associated parameter bifurcation diagrams are given for certain values of the parameters. Chongwu Zheng, Fengqin Zhang, and Jianquan Li Copyright © 2014 Chongwu Zheng et al. All rights reserved. Infinitely Many Periodic Solutions of Duffing Equations with Singularities via Time Map Wed, 16 Apr 2014 09:33:46 +0000 http://www.hindawi.com/journals/aaa/2014/398512/ We study the periodic solutions of Duffing equations with singularities . By using Poincaré-Birkhoff twist theorem, we prove that the given equation possesses infinitely many positive periodic solutions provided that satisfies the singular condition and the time map related to autonomous system tends to zero. Tiantian Ma and Zaihong Wang Copyright © 2014 Tiantian Ma and Zaihong Wang. All rights reserved. Delay-Dependent Robust Filtering for a Class of Fuzzy Stochastic Systems Wed, 16 Apr 2014 09:09:51 +0000 http://www.hindawi.com/journals/aaa/2014/673956/ This paper is concerned with the filtering problem for a kind of Takagi-Sugeno (T-S) fuzzy stochastic system with time-varying delay and parameter uncertainties. Parameter uncertainties in the system are assumed to satisfy global Lipschitz conditions. And the attention of this paper is focused on the stochastically mean-square stability of the filtering error system, and the performance level of the output error with the disturbance input. The method designed for the delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed method is substantiated with an illustrative example. Ze Li and Xinhao Yang Copyright © 2014 Ze Li and Xinhao Yang. All rights reserved. The Stability of Solutions for a Fractional Predator-Prey System Wed, 16 Apr 2014 08:45:58 +0000 http://www.hindawi.com/journals/aaa/2014/124145/ We study a class of fractional predator-prey systems with Holling II functional response. A unique positive solution of this system is obtained. In order to prove the asymptotical stability of positive equilibrium for this system, we study the Lyapunov stability theory of a fractional system. Yingjia Guo Copyright © 2014 Yingjia Guo. All rights reserved. Global Bifurcation of a Novel Computer Virus Propagation Model Wed, 16 Apr 2014 06:25:27 +0000 http://www.hindawi.com/journals/aaa/2014/731856/ In a recent paper by J. Ren et al. (2012), a novel computer virus propagation model under the effect of the antivirus ability in a real network is established. The analysis there only partially uncovers the dynamics behaviors of virus spread over the network in the case where around bifurcation is local. In the present paper, by mathematical analysis, it is further shown that, under appropriate parameter values, the model may undergo a global B-T bifurcation, and the curves of saddle-node bifurcation, Hopf bifurcation, and homoclinic bifurcation are obtained to illustrate the qualitative behaviors of virus propagation. On this basis, a collection of policies is recommended to prohibit the virus prevalence. To our knowledge, this is the first time the global bifurcation has been explored for the computer virus propagation. Theoretical results and corresponding suggestions may help us suppress or eliminate virus propagation in the network. Jianguo Ren, Yonghong Xu, and Jiming Liu Copyright © 2014 Jianguo Ren et al. All rights reserved. Learning Theory Wed, 16 Apr 2014 06:14:28 +0000 http://www.hindawi.com/journals/aaa/2014/138960/ Ding-Xuan Zhou, Qiang Wu, and Yiming Ying Copyright © 2014 Ding-Xuan Zhou et al. All rights reserved. Stochastic Maximum Principle for Partial Information Optimal Control Problem of Forward-Backward Systems Involving Classical and Impulse Controls Tue, 15 Apr 2014 16:26:28 +0000 http://www.hindawi.com/journals/aaa/2014/452124/ We study the partial information classical and impulse controls problem of forward-backward systems driven by Lévy processes, where the control variable consists of two components: the classical stochastic control and the impulse control; the information available to the controller is possibly less than the full information, that is, partial information. We derive a maximum principle to give the sufficient and necessary optimality conditions for the local critical points of the classical and impulse controls problem. As an application, we apply the maximum principle to a portfolio optimization problem with piecewise consumption processes and give its explicit solutions. Yan Wang, Aimin Song, and Enmin Feng Copyright © 2014 Yan Wang et al. All rights reserved. Multiple Results to Some Biharmonic Problems Tue, 15 Apr 2014 16:24:05 +0000 http://www.hindawi.com/journals/aaa/2014/267052/ We study a nonlinear elliptic problem defined in a bounded domain involving biharmonic operator together with an asymptotically linear term. We establish at least three nontrivial solutions using the topological degree theory and the critical groups. Xingdong Tang and Jihui Zhang Copyright © 2014 Xingdong Tang and Jihui Zhang. All rights reserved. Oscillation Results for Second-Order Nonlinear Damped Dynamic Equations on Time Scales Tue, 15 Apr 2014 13:25:31 +0000 http://www.hindawi.com/journals/aaa/2014/351256/ This paper is concerned with second-order nonlinear damped dynamic equations on time scales of the following more general form . New oscillation results are given to handle some cases not covered by known criteria. An illustrative example is also presented. Yang-Cong Qiu and Qi-Ru Wang Copyright © 2014 Yang-Cong Qiu and Qi-Ru Wang. All rights reserved. A Suzuki Type Coupled Fixed Point Theorem for Generalized Multivalued Mapping Tue, 15 Apr 2014 12:29:38 +0000 http://www.hindawi.com/journals/aaa/2014/820482/ We obtain a new Suzuki type coupled fixed point theorem for a multivalued mapping from into , satisfying a generalized contraction condition in a complete metric space. Our result unifies and generalizes various known comparable results in the literature. We also give an application to certain functional equations arising in dynamic programming. Pushpendra Semwal and Ramesh Chandra Dimri Copyright © 2014 Pushpendra Semwal and Ramesh Chandra Dimri. All rights reserved. Strong Convergence of the Split-Step -Method for Stochastic Age-Dependent Capital System with Random Jump Magnitudes Tue, 15 Apr 2014 12:29:06 +0000 http://www.hindawi.com/journals/aaa/2014/791048/ We develop a new split-step (SS) method for stochastic age-dependent capital system with random jump magnitudes. The main aim of this paper is to investigate the convergence of the SS method for a class of stochastic age-dependent capital system with random jump magnitudes. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory. Jianguo Tan, A. Rathinasamy, Hongli Wang, and Yongfeng Guo Copyright © 2014 Jianguo Tan et al. All rights reserved. Error Bound for Conic Inequality in Hilbert Spaces Tue, 15 Apr 2014 11:47:22 +0000 http://www.hindawi.com/journals/aaa/2014/785213/ We consider error bound issue for conic inequalities in Hilbert spaces. In terms of proximal subdifferentials of vector-valued functions, we provide sufficient conditions for the existence of a local error bound for a conic inequality. In the Hilbert space case, our result improves and extends some existing results on local error bounds. Jiangxing Zhu, Qinghai He, and Jinchuan Lin Copyright © 2014 Jiangxing Zhu et al. All rights reserved. Positive Solutions for the Eigenvalue Problem of Semipositone Fractional Order Differential Equation with Multipoint Boundary Conditions Tue, 15 Apr 2014 11:30:17 +0000 http://www.hindawi.com/journals/aaa/2014/925010/ We study the existence of positive solution for the eigenvalue problem of semipositone fractional order differential equation with multipoint boundary conditions by using known Krasnosel'skii's fixed point theorem. Some sufficient conditions that guarantee the existence of at least one positive solution for eigenvalues   sufficiently small and sufficiently large are established. Ge Dong Copyright © 2014 Ge Dong. All rights reserved. A New Approach to Fixed Point Results in Triangular Intuitionistic Fuzzy Metric Spaces Tue, 15 Apr 2014 11:28:45 +0000 http://www.hindawi.com/journals/aaa/2014/690139/ The aim of this paper is to propose some fixed point theorems in complete parametric metric spaces. Using these theorems, we deduce as corollaries the recent results of Ionescu et al. Moreover, we suggest some new contractions and prove certain fixed point theorems in triangular intuitionistic fuzzy metric spaces. We also discuss some illustrative examples to highlight the realized improvements. N. Hussain, S. Khaleghizadeh, P. Salimi, and Afrah A. N. Abdou Copyright © 2014 N. Hussain et al. All rights reserved.