Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Pricing of Two Kinds of Power Options under Fractional Brownian Motion, Stochastic Rate, and Jump-Diffusion Models Tue, 21 Oct 2014 11:47:17 +0000 http://www.hindawi.com/journals/aaa/2014/259297/ Option pricing is always one of the critical issues in financial mathematics and economics. Brownian motion is the basic hypothesis of option pricing model, which questions the fractional property of stock price. In this paper, under the assumption that the exchange rate follows the extended Vasicek model, we obtain the closed form of the pricing formulas for two kinds of power options under fractional Brownian Motion (FBM) jump-diffusion models. Kaili Xiang, Yindong Zhang, and Xiaotong Mao Copyright © 2014 Kaili Xiang et al. All rights reserved. Multiple Model ILC for Continuous-Time Nonlinear Systems Tue, 21 Oct 2014 09:55:47 +0000 http://www.hindawi.com/journals/aaa/2014/984742/ Multiple model iterative learning control (MMILC) method is proposed to deal with the continuous-time nonlinear system with uncertain and iteration-varying parameters. In this kind of control strategy, multiple models are established to cover the uncertainty of system; a switching mechanism is used to decide the most appropriate model for system in current iteration. For system operating iteratively in a fixed time interval with uncertain or jumping parameters, this kind of MMILC can improve the transient response and control property greatly. Asymptotical convergence is demonstrated theoretically, and the control effectiveness is illustrated by numerical simulation. Xiaoli Li, Kang Wang, and Yang Li Copyright © 2014 Xiaoli Li et al. All rights reserved. Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces Tue, 21 Oct 2014 07:28:46 +0000 http://www.hindawi.com/journals/aaa/2014/895074/ We prove a quasiconformal analogue of Koebe’s theorem related to the average Jacobian and use a normal family argument here to prove a quasiregular analogue of this result in certain domains in -dimensional space. As an application, we establish that Lipschitz-type properties are inherited by a quasiregular function from its modulo. We also prove some results of Hardy-Littlewood type for Lipschitz-type spaces in several dimensions, give the characterization of Lipschitz-type spaces for quasiregular mappings by the average Jacobian, and give a short review of the subject. Miodrag Mateljević Copyright © 2014 Miodrag Mateljević. All rights reserved. Dynamics of a Predator-Prey System with a Mate-Finding Allee Effect Mon, 20 Oct 2014 13:09:12 +0000 http://www.hindawi.com/journals/aaa/2014/673424/ We consider a ratio-dependent predator-prey system with a mate-finding Allee effect on prey. The stability properties of the equilibria and a complete bifurcation analysis, including the existence of a saddle-node, a Hopf bifurcation, and, a Bogdanov-Takens bifurcations, have been proved theoretically and numerically. The blow-up method has been applied to investigate the structure of a neighborhood of the origin. Our mathematical results show the mate-finding Allee effect can reduce the complexity of system behaviors by making the complicated equilibrium less complicated, and it can be a destabilizing force as well, which makes the system has a high possibility of being threatened with extinction in ecology. Ruiwen Wu and Xiuxiang Liu Copyright © 2014 Ruiwen Wu and Xiuxiang Liu. All rights reserved. A Note on the Minimal Period Problem for Second Order Hamiltonian Systems Mon, 20 Oct 2014 12:25:22 +0000 http://www.hindawi.com/journals/aaa/2014/385381/ We study periodic solutions of second order Hamiltonian systems with even potential. By making use of generalized Nehari manifold, some sufficient conditions are obtained to guarantee the multiplicity and minimality of periodic solutions for second order Hamiltonian systems. Our results generalize the outcome in the literature. Huafeng Xiao Copyright © 2014 Huafeng Xiao. All rights reserved. Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay Mon, 20 Oct 2014 08:50:19 +0000 http://www.hindawi.com/journals/aaa/2014/742385/ We derive a discretized heroin epidemic model with delay by applying a nonstandard finite difference scheme. We obtain positivity of the solution and existence of the unique endemic equilibrium. We show that heroin-using free equilibrium is globally asymptotically stable when the basic reproduction number , and the heroin-using is permanent when the basic reproduction number . Xamxinur Abdurahman, Ling Zhang, and Zhidong Teng Copyright © 2014 Xamxinur Abdurahman et al. All rights reserved. A New Fractional-Order Chaotic Complex System and Its Antisynchronization Mon, 20 Oct 2014 06:43:32 +0000 http://www.hindawi.com/journals/aaa/2014/326354/ We propose a new fractional-order chaotic complex system and study its dynamical properties including symmetry, equilibria and their stability, and chaotic attractors. Chaotic behavior is verified with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme. Cuimei Jiang, Shutang Liu, and Chao Luo Copyright © 2014 Cuimei Jiang et al. All rights reserved. A Survey of Modelling and Identification of Quadrotor Robot Mon, 20 Oct 2014 06:36:49 +0000 http://www.hindawi.com/journals/aaa/2014/320526/ A quadrotor is a rotorcraft capable of hover, forward flight, and VTOL and is emerging as a fundamental research and application platform at present with flexibility, adaptability, and ease of construction. Since a quadrotor is basically considered an unstable system with the characteristics of dynamics such as being intensively nonlinear, multivariable, strongly coupled, and underactuated, a precise and practical model is critical to control the vehicle which seems to be simple to operate. As a rotorcraft, the dynamics of a quadrotor is mainly dominated by the complicated aerodynamic effects of the rotors. This paper gives a tutorial of the platform configuration, methodology of modeling, comprehensive nonlinear model, the aerodynamic effects, and model identification for a quadrotor. Xiaodong Zhang, Xiaoli Li, Kang Wang, and Yanjun Lu Copyright © 2014 Xiaodong Zhang et al. All rights reserved. Erratum to “Resilient Finite-Time Controller Design of a Class of Stochastic Nonlinear Systems” Mon, 20 Oct 2014 06:27:13 +0000 http://www.hindawi.com/journals/aaa/2014/217579/ Zhiguo Yan Copyright © 2014 Zhiguo Yan. All rights reserved. Ground States for the Schrödinger Systems with Harmonic Potential and Combined Power-Type Nonlinearities Sun, 19 Oct 2014 12:15:48 +0000 http://www.hindawi.com/journals/aaa/2014/317571/ We consider a class of coupled nonlinear Schrödinger systems with potential terms and combined power-type nonlinearities. We establish the existence of ground states, by using a variational method. As an application, some symmetry results for ground states of Schrödinger systems with harmonic potential terms are obtained. Baiyu Liu Copyright © 2014 Baiyu Liu. All rights reserved. A Note on Entire Functions That Share Two Small Functions Sun, 19 Oct 2014 11:15:24 +0000 http://www.hindawi.com/journals/aaa/2014/601507/ This note is to show that if is a nonconstant entire function that shares two pairs of small functions ignoring multiplicities with its first derivative , then there exists a close linear relationship between and . This result is a generalization of some results obtained by Rubel and Yang, Mues and Steinmetz, Zheng and Wang, and Qiu. Moreover, examples are provided to show that the conditions in the result are sharp. Jun-Fan Chen Copyright © 2014 Jun-Fan Chen. All rights reserved. Control for a Networked Control Model of Systems with Two Additive Time-Varying Delays Sun, 19 Oct 2014 10:18:27 +0000 http://www.hindawi.com/journals/aaa/2014/923436/ This paper is concerned with control for a networked control model of systems with two additive time-varying delays. A new Lyapunov functional is constructed to make full use of the information of the delays, and for the derivative of the Lyapunov functional a novel technique is employed to compute a tighter upper bound, which is dependent on the two time-varying delays instead of the upper bounds of them. Then the convex polyhedron method is proposed to check the upper bound of the derivative of the Lyapunov functional. The resulting stability criteria have fewer matrix variables but less conservatism than some existing ones. The stability criteria are applied to designing a state feedback controller, which guarantees that the closed-loop system is asymptotically stable with a prescribed disturbance attenuation level. Finally examples are given to show the advantages of the stability criteria and the effectiveness of the proposed control method. Hanyong Shao, Zhengqiang Zhang, Xunlin Zhu, and Guoying Miao Copyright © 2014 Hanyong Shao et al. All rights reserved. Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Self-Adjoint Operators Sun, 19 Oct 2014 09:44:10 +0000 http://www.hindawi.com/journals/aaa/2014/192040/ Let and   be standard real Jordan algebras of self-adjoint operators on complex Hilbert spaces   and  , respectively. For  , let   be a fixed sequence with and assume that at least one of the terms in appears exactly once. Define the generalized Jordan product   on elements in  . Let be a map with the range containing all rank-one projections and trace zero-rank two self-adjoint operators. We show that satisfies that for all , where stands for the peripheral spectrum of , if and only if there exist a scalar and a unitary operator such that for all , or for all , where is the transpose of for an arbitrarily fixed orthonormal basis of . Moreover, whenever is odd. Wen Zhang and Jinchuan Hou Copyright © 2014 Wen Zhang and Jinchuan Hou. All rights reserved. Global Stability Analysis of a Nonautonomous Stage-Structured Competitive System with Toxic Effect and Double Maturation Delays Sun, 19 Oct 2014 06:28:45 +0000 http://www.hindawi.com/journals/aaa/2014/689573/ We investigate a nonautonomous two-species competitive system with stage structure and double time delays due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and the inhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis. Chao Liu and Yuanke Li Copyright © 2014 Chao Liu and Yuanke Li. All rights reserved. Conservation Laws and Self-Consistent Sources for an Integrable Lattice Hierarchy Associated with a Three-by-Three Discrete Matrix Spectral Problem Sun, 19 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/235159/ A lattice hierarchy with self-consistent sources is deduced starting from a three-by-three discrete matrix spectral problem. The Hamiltonian structures are constructed for the resulting hierarchy. Liouville integrability of the resulting equations is demonstrated. Moreover, infinitely many conservation laws of the resulting hierarchy are obtained. Yu-Qing Li and Bao-Shu Yin Copyright © 2014 Yu-Qing Li and Bao-Shu Yin. All rights reserved. Pullback Attractor for Nonautonomous Ginzburg-Landau Equation with Additive Noise Sun, 19 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/921750/ Long time behavior of stochastic Ginzburg-Landau equations with nonautonomous deterministic external forces, dispersion coefficients, and nonautonomous perturbations is studied. The domain is taken as a bounded interval in . By making use of Sobolev embeddings and Gialiardo-Nirenberg inequality we obtain the existence and upper semicontinuity of the pullback attractor in for the equation. The upper semicontinuity shows the stability of attractors under perturbations. Yangrong Li and Hongyong Cui Copyright © 2014 Yangrong Li and Hongyong Cui. All rights reserved. Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function Thu, 16 Oct 2014 14:28:33 +0000 http://www.hindawi.com/journals/aaa/2014/890456/ The family of nth order q-Legendre polynomials are introduced. They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the recursion relations and ODEs satisfied by the nth degree Legendre polynomials. The nth order q-Legendre polynomials are shown to have vanishing kth moments for , as does the nth degree truncated Legendre polynomial. Convergence results are obtained, approximations are given, a reciprocal symmetry is shown, and nearly orthonormal frames are constructed. Conditions are given under which a MADE remains a MADE under inverse Fourier transform. This is used to construct new wavelets as solutions of MADEs. David W. Pravica, Njinasoa Randriampiry, and Michael J. Spurr Copyright © 2014 David W. Pravica et al. All rights reserved. On Eigenvalues of the Generator of a -Semigroup Appearing in Queueing Theory Thu, 16 Oct 2014 14:03:30 +0000 http://www.hindawi.com/journals/aaa/2014/896342/ We describe the point spectrum of the generator of a -semigroup associated with the M/M/1 queueing model that is governed by an infinite system of partial differential equations with integral boundary conditions. Our results imply that the essential growth bound of the -semigroup is 0 and, therefore, that the semigroup is not quasi-compact. Moreover, our result also shows that it is impossible that the time-dependent solution of the M/M/1 queueing model exponentially converges to its steady-state solution. Geni Gupur Copyright © 2014 Geni Gupur. All rights reserved. Adaptive Fault-Tolerant Tracking Control of Nonaffine Nonlinear Systems with Actuator Failure Thu, 16 Oct 2014 13:43:53 +0000 http://www.hindawi.com/journals/aaa/2014/283403/ This paper proposes an adaptive fault-tolerant control scheme for nonaffine nonlinear systems. A model approximation method which is a solution that bridges the gap between affine and nonaffine control systems is developed firstly. A joint estimation approach is based on unscented Kalman filter, in which both failure parameters and states are simultaneously estimated by means of the argument state vector composed of the unknown faults and states. Then, stability analysis is given for the closed-loop system. Finally, the proposed approach is verified using a three-degree-of-freedom simulation of a typical fighter aircraft and the significantly improved system response demonstrates the practical potential of the theoretic results obtained. Hongcheng Zhou, Dezhi Xu, Daobo Wang, and Le Ge Copyright © 2014 Hongcheng Zhou et al. All rights reserved. Further Results on Uniqueness of Meromorphic Functions concerning Fixed Points Thu, 16 Oct 2014 11:25:50 +0000 http://www.hindawi.com/journals/aaa/2014/256032/ We will study the uniqueness problems of meromorphic functions of differential polynomials sharing fixed points. Our results improve or generalize some previous results on meromorphic functions sharing fixed points. Xiao-Bin Zhang Copyright © 2014 Xiao-Bin Zhang. All rights reserved. Integral -Stability in terms of Two Measures for Impulsive Differential Equations with “Supremum” Thu, 16 Oct 2014 11:10:48 +0000 http://www.hindawi.com/journals/aaa/2014/901853/ This paper establishes a criterion on integral -stability in terms of two measures for impulsive differential equations with “supremum” by using the cone-valued piecewise continuous Lyapunov functions, Razumikhin method, and comparative method. Meantime, an example is given to illustrate our result. Peiguang Wang, Xiaojing Liu, and Qing Xu Copyright © 2014 Peiguang Wang et al. All rights reserved. Some Fixed Point Theorems in Generalized Probabilistic Metric Spaces Thu, 16 Oct 2014 09:23:01 +0000 http://www.hindawi.com/journals/aaa/2014/103764/ We introduce the concepts of -contraction and probabilistic -contraction mappings in generalized probabilistic metric spaces and prove some fixed point theorems for such two types of mappings in generalized probabilistic metric spaces. Our results generalize and extend many comparable results in existing literature. Some examples are also given to support our results. Finally, an application to the existence of solutions for a class of integral equations is presented by utilizing one of our main results. Chuanxi Zhu, Wenqing Xu, and Zhaoqi Wu Copyright © 2014 Chuanxi Zhu et al. All rights reserved. Benjamin-Ono-Burgers-MKdV Equation for Algebraic Rossby Solitary Waves in Stratified Fluids and Conservation Laws Thu, 16 Oct 2014 08:40:13 +0000 http://www.hindawi.com/journals/aaa/2014/175841/ In the paper, by using multiple-scale method, the Benjamin-Ono-Burgers-MKdV (BO-B-MKdV) equation is obtained which governs algebraic Rossby solitary waves in stratified fluids. This equation is first derived for Rossby waves. By analysis and calculation, some conservation laws are derived from the BO-B-MKdV equation without dissipation. The results show that the mass, momentum, energy, and velocity of the center of gravity of algebraic Rossby waves are conserved and the presence of a small dissipation destroys these conservations. Hongwei Yang, Shanshan Jin, and Baoshu Yin Copyright © 2014 Hongwei Yang et al. All rights reserved. Strong and -Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT Spaces Thu, 16 Oct 2014 08:24:45 +0000 http://www.hindawi.com/journals/aaa/2014/805168/ Let K be a nonempty closed and convex subset of a complete CAT(0) space. Let , be a family of multivalued demicontractive mappings such that . A Krasnoselskii-type iterative sequence is shown to -converge to a common fixed point of the family . Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT spaces. Furthermore, our method of the proof is of special interest. C. E. Chidume, A. U. Bello, and P. Ndambomve Copyright © 2014 C. E. Chidume et al. All rights reserved. Mathematical Analysis of HIV Models with Switching Nonlinear Incidence Functions and Pulse Control Thu, 16 Oct 2014 08:08:05 +0000 http://www.hindawi.com/journals/aaa/2014/853960/ This paper aims to study the dynamics of new HIV (the human immunodeficiency virus) models with switching nonlinear incidence functions and pulse control. Nonlinear incidence functions are first assumed to be time-varying functions and switching functional forms in time, which have more realistic significance to model infectious disease models. New threshold conditions with the periodic switching term are obtained to guarantee eradication of the disease, by using the novel type of common Lyapunov function. Furthermore, pulse vaccination is applied to the above model, and new sufficient conditions for the eradication of the disease are presented in terms of the pulse effect and the switching effect. Finally, several numerical examples are given to show the effectiveness of the proposed results, and future directions are put forward. Xiying Wang, Wei Xu, Yujun Cui, and Xiaomei Wang Copyright © 2014 Xiying Wang et al. All rights reserved. On Strongly Irregular Points of a Brouwer Homeomorphism Embeddable in a Flow Thu, 16 Oct 2014 07:11:07 +0000 http://www.hindawi.com/journals/aaa/2014/638784/ We study the set of all strongly irregular points of a Brouwer homeomorphism which is embeddable in a flow. We prove that this set is equal to the first prolongational limit set of any flow containing . We also give a sufficient condition for a class of flows of Brouwer homeomorphisms to be topologically conjugate. Zbigniew Leśniak Copyright © 2014 Zbigniew Leśniak. All rights reserved. Global Stability of an Epidemic Model of Computer Virus Wed, 15 Oct 2014 13:22:36 +0000 http://www.hindawi.com/journals/aaa/2014/456320/ With the rapid popularization of the Internet, computers can enter or leave the Internet increasingly frequently. In fact, no antivirus software can detect and remove all sorts of computer viruses. This implies that viruses would persist on the Internet. To better understand the spread of computer viruses in these situations, a new propagation model is established and analyzed. The unique equilibrium of the model is globally asymptotically stable, in accordance with the reality. A parameter analysis of the equilibrium is also conducted. Xiaofan Yang, Bei Liu, and Chenquan Gan Copyright © 2014 Xiaofan Yang et al. All rights reserved. Traveling Wave Solutions of the Benjamin-Bona-Mahony Water Wave Equations Wed, 15 Oct 2014 07:08:50 +0000 http://www.hindawi.com/journals/aaa/2014/926838/ The modeling of unidirectional propagation of long water waves in dispersive media is presented. The Korteweg-de Vries (KdV) and Benjamin-Bona-Mahony (BBM) equations are derived from water waves models. New traveling solutions of the KdV and BBM equations are obtained by implementing the extended direct algebraic and extended sech-tanh methods. The stability of the obtained traveling solutions is analyzed and discussed. A. R. Seadawy and A. Sayed Copyright © 2014 A. R. Seadawy and A. Sayed. All rights reserved. Some Properties of Distances and Best Proximity Points of Cyclic Proximal Contractions in Metric Spaces Wed, 15 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/914915/ This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping , where and , , are nonempty subsets of which satisfy , such that is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed. M. De La Sen and Asier Ibeas Copyright © 2014 M. De La Sen and Asier Ibeas. All rights reserved. A Predictor-Corrector Method for Solving Equilibrium Problems Wed, 15 Oct 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/313217/ We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise to -stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities. Zong-Ke Bao, Ming Huang, and Xi-Qiang Xia Copyright © 2014 Zong-Ke Bao et al. All rights reserved.