Journal of Applied Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals Mon, 22 Dec 2014 00:10:31 +0000 http://www.hindawi.com/journals/jam/2014/832015/ We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. We compare the classical notion of stability of the causal differential systems to the notion of initial time difference stability of causal differential systems and present a comparison result in terms of Lyapunov functions. We have utilized Lyapunov functions and Lyapunov functional in the study of stability theory of causal differential systems when establishing initial time difference stability of the perturbed causal differential system with respect to the unperturbed causal differential system. Coşkun Yakar and Mustafa Bayram Gücen Copyright © 2014 Coşkun Yakar and Mustafa Bayram Gücen. All rights reserved. Bifurcation of Safe Basins and Chaos in Nonlinear Vibroimpact Oscillator under Harmonic and Bounded Noise Excitations Sun, 21 Dec 2014 11:27:24 +0000 http://www.hindawi.com/journals/jam/2014/967395/ The erosion of the safe basins and chaotic motions of a nonlinear vibroimpact oscillator under both harmonic and bounded random noise is studied. Using the Melnikov method, the system’s Melnikov integral is computed and the parametric threshold for chaotic motions is obtained. Using the Monte-Carlo and Runge-Kutta methods, the erosion of the safe basins is also discussed. The sudden change in the character of the stochastic safe basins when the bifurcation parameter of the system passes through a critical value may be defined as an alternative stochastic bifurcation. It is founded that random noise may destroy the integrity of the safe basins, bring forward the occurrence of the stochastic bifurcation, and make the parametric threshold for motions vary in a larger region, hence making the system become more unsafely and chaotic motions may occur more easily. Rong Haiwu, Wang Xiangdong, Luo Qizhi, Xu Wei, and Fang Tong Copyright © 2014 Rong Haiwu et al. All rights reserved. A General Setting and Solution of Bellman Equation in Monetary Theory Sun, 21 Dec 2014 10:08:45 +0000 http://www.hindawi.com/journals/jam/2014/495089/ As an important tool in theoretical economics, Bellman equation is very powerful in solving optimization problems of discrete time and is frequently used in monetary theory. Because there is not a general method to solve this problem in monetary theory, it is hard to grasp the setting and solution of Bellman equation and easy to reach wrong conclusions. In this paper, we discuss the rules and problems that should be paid attention to when incorporating money into general equilibrium models. A general setting and solution of Bellman equation in monetary theory are provided. The proposed method is clear, is easy to grasp, is generalized, and always leads to the correct results. Xiaoli Gan and Wanbo Lu Copyright © 2014 Xiaoli Gan and Wanbo Lu. All rights reserved. Variational Inequalities and Vector Optimization 2014 Sun, 21 Dec 2014 08:59:23 +0000 http://www.hindawi.com/journals/jam/2014/214957/ Xian-Jun Long, Jian-Wen Peng, Nan-Jing Huang, and Jen-Chih Yao Copyright © 2014 Xian-Jun Long et al. All rights reserved. 1 : 3 Resonance and Chaos in a Discrete Hindmarsh-Rose Model Wed, 17 Dec 2014 09:01:08 +0000 http://www.hindawi.com/journals/jam/2014/896478/ 1 : 3 resonance of a two-dimensional discrete Hindmarsh-Rose model is discussed by normal form method and bifurcation theory. Numerical simulations are presented to illustrate the theoretical analysis, which predict the occurrence of a closed invariant circle, period-three saddle cycle, and homoclinic structure. Furthermore, it also displays the complex dynamical behaviors, especially the transitions between three main dynamical behaviors, namely, quiescence, spiking, and bursting. Bo Li and Zhimin He Copyright © 2014 Bo Li and Zhimin He. All rights reserved. Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions Wed, 10 Dec 2014 00:11:09 +0000 http://www.hindawi.com/journals/jam/2014/710437/ We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations. Zakieh Avazzadeh, Mohammad Heydari, Wen Chen, and G. B. Loghmani Copyright © 2014 Zakieh Avazzadeh et al. All rights reserved. Working with Missing Data: Imputation of Nonresponse Items in Categorical Survey Data with a Non-Monotone Missing Pattern Sun, 07 Dec 2014 10:23:31 +0000 http://www.hindawi.com/journals/jam/2014/368791/ The imputation of missing data is often a crucial step in the analysis of survey data. This study reviews typical problems with missing data and discusses a method for the imputation of missing survey data with a large number of categorical variables which do not have a monotone missing pattern. We develop a method for constructing a monotone missing pattern that allows for imputation of categorical data in data sets with a large number of variables using a model-based MCMC approach. We report the results of imputing the missing data from a case study, using educational, sociopsychological, and socioeconomic data from the National Latino and Asian American Study (NLAAS). We report the results of multiply imputed data on a substantive logistic regression analysis predicting socioeconomic success from several educational, sociopsychological, and familial variables. We compare the results of conducting inference using a single imputed data set to those using a combined test over several imputations. Findings indicate that, for all variables in the model, all of the single tests were consistent with the combined test. Machelle D. Wilson and Kerstin Lueck Copyright © 2014 Machelle D. Wilson and Kerstin Lueck. All rights reserved. An Improved Central Force Optimization Algorithm for Multimodal Optimization Sun, 07 Dec 2014 08:00:51 +0000 http://www.hindawi.com/journals/jam/2014/895629/ This paper proposes the hybrid CSM-CFO algorithm based on the simplex method (SM), clustering technique, and central force optimization (CFO) for unconstrained optimization. CSM-CFO is still a deterministic swarm intelligent algorithm, such that the complex statistical analysis of the numerical results can be omitted, and the convergence intends to produce faster and more accurate by clustering technique and good points set. When tested against benchmark functions, in low and high dimensions, the CSM-CFO algorithm has competitive performance in terms of accuracy and convergence speed compared to other evolutionary algorithms: particle swarm optimization, evolutionary program, and simulated annealing. The comparison results demonstrate that the proposed algorithm is effective and efficient. Jie Liu and Yu-ping Wang Copyright © 2014 Jie Liu and Yu-ping Wang. All rights reserved. A QFD-Based Mathematical Model for New Product Development Considering the Target Market Segment Mon, 01 Dec 2014 06:58:43 +0000 http://www.hindawi.com/journals/jam/2014/594150/ Responding to customer needs is important for business success. Quality function deployment provides systematic procedures for converting customer needs into technical requirements to ensure maximum customer satisfaction. The existing literature mainly focuses on the achievement of maximum customer satisfaction under a budgetary limit via mathematical models. The market goal of the new product for the target market segment is usually ignored. In this study, the proposed approach thus considers the target customer satisfaction degree for the target market segment in the model by formulating the overall customer satisfaction as a function of the quality level. In addition, the proposed approach emphasizes the cost-effectiveness concept in the design stage via the achievement of the target customer satisfaction degree using the minimal total cost. A numerical example is used to demonstrate the applicability of the proposed approach and its characteristics are discussed. Liang-Hsuan Chen and Cheng-Nien Chen Copyright © 2014 Liang-Hsuan Chen and Cheng-Nien Chen. All rights reserved. Refinements of Generalized Hölder’s Inequalities Thu, 27 Nov 2014 13:13:51 +0000 http://www.hindawi.com/journals/jam/2014/274310/ We present some new versions of generalized Hölder’s inequalities. The results are used to improve Minkowski’s inequality and a Beckenbach-type inequality. Jingfeng Tian, Wen-Li Wang, and Donal O’Regan Copyright © 2014 Jingfeng Tian et al. All rights reserved. New Results on Robust Model Predictive Control for Time-Delay Systems with Input Constraints Thu, 27 Nov 2014 09:50:08 +0000 http://www.hindawi.com/journals/jam/2014/528926/ This paper investigates the problem of model predictive control for a class of nonlinear systems subject to state delays and input constraints. The time-varying delay is considered with both upper and lower bounds. A new model is proposed to approximate the delay. And the uncertainty is polytopic type. For the state-feedback MPC design objective, we formulate an optimization problem. Under model transformation, a new model predictive controller is designed such that the robust asymptotical stability of the closed-loop system can be guaranteed. Finally, the applicability of the presented results are demonstrated by a practical example. Qing Lu, Yiyong Sun, Qi Zhou, and Zhiguang Feng Copyright © 2014 Qing Lu et al. All rights reserved. Recent Advances on Mathematical Modeling and Control Methods for Complex Vehicle Systems Thu, 27 Nov 2014 09:47:52 +0000 http://www.hindawi.com/journals/jam/2014/872860/ Hamid Reza Karimi, Zheping Yan, Yuxin Zhao, Weichao Sun, and Mohammed Chadli Copyright © 2014 Hamid Reza Karimi et al. All rights reserved. Modified Homotopy Perturbation Method for Solving Fractional Differential Equations Wed, 26 Nov 2014 11:24:03 +0000 http://www.hindawi.com/journals/jam/2014/594245/ The modified homotopy perturbation method is extended to derive the exact solutions for linear (nonlinear) ordinary (partial) differential equations of fractional order in fluid mechanics. The fractional derivatives are taken in the Caputo sense. This work will present a numerical comparison between the considered method and some other methods through solving various fractional differential equations in applied fields. The obtained results reveal that this method is very effective and simple, accelerates the rapid convergence of the series solution, and reduces the size of work to only one iteration. A. A. Hemeda Copyright © 2014 A. A. Hemeda. All rights reserved. The Nonpermutation Flowshop Scheduling Problem: Adjustment and Bounding Procedures Wed, 26 Nov 2014 07:17:11 +0000 http://www.hindawi.com/journals/jam/2014/273567/ We consider the makespan minimization in a flowshop environment where the job sequence does not have to be the same for all the machines. Contrarily to the classical permutation flowshop scheduling problem, this strongly NP-hard problem received very scant attention in the literature. In this paper, some improved single-machine-based adjustment procedures are proposed, and a new two-machine-based one is introduced. Based on these adjustments, new lower and upper bounding schemes are derived. Our experimental analysis shows that the proposed procedures provide promising results. Anis Gharbi, Mohamed Labidi, and Mohamed Aly Louly Copyright © 2014 Anis Gharbi et al. All rights reserved. Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems Tue, 25 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/983643/ One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms. W. A. Oliveira, A. Beato-Moreno, A. C. Moretti, and L. L. Salles Neto Copyright © 2014 W. A. Oliveira et al. All rights reserved. Dynamical Analysis of the Lorenz-84 Atmospheric Circulation Model Sun, 23 Nov 2014 12:26:22 +0000 http://www.hindawi.com/journals/jam/2014/296279/ The dynamical behaviors of the Lorenz-84 atmospheric circulation model are investigated based on qualitative theory and numerical simulations. The stability and local bifurcation conditions of the Lorenz-84 atmospheric circulation model are obtained. It is also shown that when the bifurcation parameter exceeds a critical value, the Hopf bifurcation occurs in this model. Then, the conditions of the supercritical and subcritical bifurcation are derived through the normal form theory. Finally, the chaotic behavior of the model is also discussed, the bifurcation diagrams and Lyapunov exponents spectrum for the corresponding parameter are obtained, and the parameter interval ranges of limit cycle and chaotic attractor are calculated in further. Especially, a computer-assisted proof of the chaoticity of the model is presented by a topological horseshoe theory. Hu Wang, Yongguang Yu, and Guoguang Wen Copyright © 2014 Hu Wang et al. All rights reserved. A Class of Approximate Damped Oscillatory Solutions to Compound KdV-Burgers-Type Equation with Nonlinear Terms of Any Order: Preliminary Results Sun, 23 Nov 2014 06:51:16 +0000 http://www.hindawi.com/journals/jam/2014/935915/ This paper is focused on studying approximate damped oscillatory solutions of the compound KdV-Burgers-type equation with nonlinear terms of any order. By the theory and method of planar dynamical systems, existence conditions and number of bounded traveling wave solutions including damped oscillatory solutions are obtained. Utilizing the undetermined coefficients method, the approximate solutions of damped oscillatory solutions traveling to the left are presented. Error estimates of these approximate solutions are given by the thought of homogeneous principle. The results indicate that errors between implicit exact damped oscillatory solutions and approximate damped oscillatory solutions are infinitesimal decreasing in the exponential form. Yan Zhao and Weiguo Zhang Copyright © 2014 Yan Zhao and Weiguo Zhang. All rights reserved. Localizing Brain Activity from Multiple Distinct Sources via EEG Sun, 23 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/232747/ An important question arousing in the framework of electroencephalography (EEG) is the possibility to recognize, by means of a recorded surface potential, the number of activated areas in the brain. In the present paper, employing a homogeneous spherical conductor serving as an approximation of the brain, we provide a criterion which determines whether the measured surface potential is evoked by a single or multiple localized neuronal excitations. We show that the uniqueness of the inverse problem for a single dipole is closely connected with attaining certain relations connecting the measured data. Further, we present the necessary and sufficient conditions which decide whether the collected data originates from a single dipole or from numerous dipoles. In the case where the EEG data arouses from multiple parallel dipoles, an isolation of the source is, in general, not possible. George Dassios, Michael Doschoris, and Konstantia Satrazemi Copyright © 2014 George Dassios et al. All rights reserved. Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations Sun, 23 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/813474/ A new scheme, deduced from Khan’s homotopy perturbation transform method (HPTM) (Khan, 2014; Khan and Wu, 2011) via optimal parameter, is presented for solving nonlinear differential difference equations. Simple but typical examples are given to illustrate the validity and great potential of Khan’s homotopy perturbation transform method (HPTM) via optimal parameter in solving nonlinear differential difference equation. The numerical solutions show that the proposed method is very efficient and computationally attractive. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems. The results reveal that the method is very effective and simple. This method gives more reliable results as compared to other existing methods available in the literature. The numerical results demonstrate the validity and applicability of the method. Mohamed S. Mohamed, Khaled A. Gepreel, Faisal A. Al-Malki, and Nouf Altalhi Copyright © 2014 Mohamed S. Mohamed et al. All rights reserved. Invariant Surfaces under Hyperbolic Translations in Hyperbolic Space Thu, 20 Nov 2014 12:27:04 +0000 http://www.hindawi.com/journals/jam/2014/838564/ We consider hyperbolic rotation (), hyperbolic translation (), and horocyclic rotation () groups in , which is called Minkowski model of hyperbolic space. Then, we investigate extrinsic differential geometry of invariant surfaces under subgroups of in . Also, we give explicit parametrization of these invariant surfaces with respect to constant hyperbolic curvature of profile curves. Finally, we obtain some corollaries for flat and minimal invariant surfaces which are associated with de Sitter and hyperbolic shape operator in . Mahmut Mak and Baki Karlığa Copyright © 2014 Mahmut Mak and Baki Karlığa. All rights reserved. Design Mode Analysis of Pareto Solution Set for Decision-Making Support Thu, 20 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/520209/ Decision making in engineering design problems is challenging because they have multiple and conflicting criteria and complex correlation between design parameters. This study proposes a decision-making support methodology named design mode analysis, which consists of data clustering and principal component analysis (PCA). A design mode is indicated by the eigenvector obtained by PCA and reveals the dominant design parameters in a given dataset. The proposed method is a general framework to obtain the design modes from high-dimensional and large datasets. The effectiveness of the proposed method is verified on the conceptual design problem of the hybrid rocket engine. Satoru Hiwa, Tomoyuki Hiroyasu, and Mitsunori Miki Copyright © 2014 Satoru Hiwa et al. All rights reserved. Pricing Parisian Option under a Stochastic Volatility Model Wed, 19 Nov 2014 10:12:32 +0000 http://www.hindawi.com/journals/jam/2014/956454/ We study the pricing of a Parisian option under a stochastic volatility model. Based on the manipulation problem that barrier options might create near barriers, the Parisian option has been designed as an extended barrier option. A stochastic volatility correction to the Black-Scholes price of the Parisian option is obtained in a partial differential equation form and the solution is characterized numerically. Min-Ku Lee and Kyu-Hwan Jang Copyright © 2014 Min-Ku Lee and Kyu-Hwan Jang. All rights reserved. Linearization from Complex Lie Point Transformations Wed, 19 Nov 2014 08:54:59 +0000 http://www.hindawi.com/journals/jam/2014/793247/ Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension , with . We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. Furthermore we provide a geometrical construction of the procedure adopted that provides an analogue in of the linearizability criteria in . Sajid Ali, M. Safdar, and Asghar Qadir Copyright © 2014 Sajid Ali et al. All rights reserved. Performance Modeling of Proposed GUISET Middleware for Mobile Healthcare Services in E-Marketplaces Tue, 18 Nov 2014 13:48:05 +0000 http://www.hindawi.com/journals/jam/2014/248293/ GUISET is a proposed middleware engine currently under study in South Africa. The goal is to provide utility services for small, medium, and macroenterprises in the context of mobile e-services. Three things are important to make this engine effective and efficient: the implementation, performance, and the pricing strategy. The literature has delved richly into implementation issue of similar projects. Both the performance and the pricing strategy issues have not been fully discussed especially in the context of mobile healthcare services. Some literature has addressed the performance issue using the exogenous nonpriority and the preemptive model. However, with providers offering different services using that approach may prove to be difficult to implement. This work extends existing and widely adopted theories to non-preemptive model by using the queuing theory and the simulation model in the context of mobile healthcare services. Our evaluation is based on non-preemptive priority and nonpriority discipline. Our results reveal that the unconditional average waiting time remains the same with reduction in waiting time over the non-preemptive priority model in four out of the five classes observed. This is envisaged to be beneficial in mobile healthcare services where events are prioritized and urgent attention is needed to be given to urgent events. Alaba Olu Akingbesote, Mathew Olusegun Adigun, Sibisuso Xulu, and Edgar Jembere Copyright © 2014 Alaba Olu Akingbesote et al. All rights reserved. Existence Results for a Coupled System of Nonlinear Fractional Differential Equations in Banach Spaces Tue, 18 Nov 2014 08:51:46 +0000 http://www.hindawi.com/journals/jam/2014/463148/ We investigate boundary value problems for a coupled system of nonlinear fractional differential equations involving Caputo derivative in Banach spaces. A generalized singular type coupled Gronwall inequality system is given to obtain an important a priori bound. Existence results are obtained by using fixed point theorems and an example is given to illustrate the results. Yuping Cao and Chuanzhi Bai Copyright © 2014 Yuping Cao and Chuanzhi Bai. All rights reserved. The Exact Endoscopic Effect on the Peristaltic Flow of a Nanofluid Tue, 18 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/367526/ The problem of the peristaltic flow of a nanofluid under the effect of an endoscope is reinvestigated. The mathematical model is governed by a system of linear and nonlinear partial differential equations with prescribed boundary conditions. Really, the exact solution for any physical problem, if available, is of great importance which inevitably leads to a better understanding of the behaviour of the involved physical phenomena. An attempt for doing so has been done in the present paper, where the temperature equation is solved exactly by the help of Laplace transform and, accordingly, the exact expressions for the nanoparticle concentration, the axial velocity, the pressure gradient, and the pressure rise are established. Furthermore, it is showed in this paper that the physical interpretations of some involved phenomena are found totally different than those previously obtained by the approximate solutions using the homotopy perturbation method. In addition, several comparisons between the current results and the approximate ones have been displayed. Finally, the effect of various parameters on the temperature distribution, the nanoparticle concentration, the pressure gradient, and the pressure rise has been also discussed through graphs. S. M. Khaled, Abdelhalim Ebaid, and Fahd Al Mutairi Copyright © 2014 S. M. Khaled et al. All rights reserved. Modelling Shallow Water Wakes Using a Hybrid Turbulence Model Mon, 17 Nov 2014 11:52:38 +0000 http://www.hindawi.com/journals/jam/2014/714031/ A numerical research with different turbulence models for shallow water equations was carried out. This was done in order to investigate which model has the ability to reproduce more accurately the wakes produced by the shock of the water hitting a submerged island inside a canal. The study of this phenomenon is important for the numerical methods application advancement in the simulation of free surface flows since these models involve a number of simplifications and assumptions that can have a significant impact on the numerical solutions quality and thus can not reproduce correctly the physical phenomenon. The numerical experiments were carried out on an experimental case under controlled conditions, consisting of a channel with a submerged conical island. The numerical scheme is based on the Eulerian-Lagrangian finite volume method with four turbulence models, three mixing lengths (ml), and one joining on the horizontal axis with a mixing-length model (ml) on the vertical axis. The experimental results show that a with ml turbulence model makes it possible to approach the experimental results in a more qualitative manner. We found that when using only a model in the vertical and horizontal direction, the numerical results overestimate the experimental data. Additionally the computing time is reduced by simplifying the turbulence model. Clemente Rodriguez-Cuevas, Carlos Couder-Castañeda, Esteban Flores-Mendez, Israel Enrique Herrera-Díaz, and Rodolfo Cisneros-Almazan Copyright © 2014 Clemente Rodriguez-Cuevas et al. All rights reserved. A Joint Doppler Frequency Shift and DOA Estimation Algorithm Based on Sparse Representations for Colocated TDM-MIMO Radar Sun, 16 Nov 2014 11:11:34 +0000 http://www.hindawi.com/journals/jam/2014/421391/ We address the problem of a new joint Doppler frequency shift (DFS) and direction of arrival (DOA) estimation for colocated TDM-MIMO radar that is a novel technology applied to autocruise and safety driving system in recent years. The signal model of colocated TDM-MIMO radar with few transmitter or receiver channels is depicted and “time varying steering vector” model is proved. Inspired by sparse representations theory, we present a new processing scheme for joint DFS and DOA estimation based on the new input signal model of colocated TDM-MIMO radar. An ultracomplete redundancy dictionary for angle-frequency space is founded in order to complete sparse representations of the input signal. The SVD-SR algorithm which stands for joint estimation based on sparse representations using SVD decomposition with OMP algorithm and the improved M-FOCUSS algorithm which combines the classical M-FOCUSS with joint sparse recovery spectrum are applied to the new signal model’s calculation to solve the multiple measurement vectors (MMV) problem. The improved M-FOCUSS algorithm can work more robust than SVD-SR and JS-SR algorithms in the aspects of coherent signals resolution and estimation accuracy. Finally, simulation experiments have shown that the proposed algorithms and schemes are feasible and can be further applied to practical application. Tao Chen, Huanxin Wu, and Lutao Liu Copyright © 2014 Tao Chen et al. All rights reserved. Horseshoe Chaos in a Simple Memristive Circuit Sun, 16 Nov 2014 00:00:00 +0000 http://www.hindawi.com/journals/jam/2014/546091/ A simple memristive circuit model is revisited and the stability analysis is to be given. Furthermore, we resort to Poincaré section and Poincaré map technique and present rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoe theory. Lei Wang, XiaoSong Yang, WenJie Hu, and Quan Yuan Copyright © 2014 Lei Wang et al. All rights reserved. HSV-2 and Substance Abuse amongst Adolescents: Insights through Mathematical Modelling Thu, 13 Nov 2014 13:24:45 +0000 http://www.hindawi.com/journals/jam/2014/104819/ Herpes simplex virus infection is mostly spread and occurs more commonly among substance abusing adolescents as compared to the nonsubstance abusing. In this paper, a mathematical model for the spread of HSV-2 within a community with substance abusing adolescents is developed and analysed. The impacts of condom use and educational campaigns are examined. The study suggests that condom use is highly effective among adolescents, when we have more of them quitting than becoming substance abusers. Measures such as educational campaigns can be put in place to try and reduce adolescents from becoming substance abusers. Further, we applied optimal control theory to the proposed model. The controls represent condom use and educational campaigns. The objective is based on maximising the susceptible nonsubstance abusing adolescents, while minimising the susceptible substance abusing adolescents, the infectious nonsubstance abusing adolescents, and the infectious substance abusing adolescents. We used Pontrygin’s maximum principle to characterise the optimal levels of the two controls. The resulting optimality system is solved numerically. Overall, the application of the optimal control theory suggests that more effort should be devoted to condom use as compared to educational campaigns. A. Mhlanga, C. P. Bhunu, and S. Mushayabasa Copyright © 2014 A. Mhlanga et al. All rights reserved.