Discrete Dynamics in Nature and Society http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. Periodic Oscillations in a Chemostat Model with Two Discrete Delays Tue, 03 Mar 2015 12:00:10 +0000 http://www.hindawi.com/journals/ddns/2015/306302/ Periodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the linearized system, a unique positive equilibrium is found and proved to be locally asymptotically stable under some conditions. Meanwhile, a Hopf bifurcation causing periodic solutions is also obtained. Numerical simulations illustrate the theoretical results. Tiansi Zhang, Xuehui Ji, and Bo Li Copyright © 2015 Tiansi Zhang et al. All rights reserved. Hyers-Ulam Stability of a System of First Order Linear Recurrences with Constant Coefficients Mon, 02 Mar 2015 12:28:14 +0000 http://www.hindawi.com/journals/ddns/2015/269356/ We study the Hyers-Ulam stability in a Banach space of the system of first order linear difference equations of the form for (nonnegative integers), where is a given matrix with real or complex coefficients, respectively, and is a fixed sequence in . That is, we investigate the sequences in such that (with the maximum norm in ) and show that, in the case where all the eigenvalues of are not of modulus 1, there is a positive real constant (dependent only on ) such that, for each such a sequence , there is a solution of the system with . Bing Xu and Janusz Brzdęk Copyright © 2015 Bing Xu and Janusz Brzdęk. All rights reserved. Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism Mon, 02 Mar 2015 11:54:42 +0000 http://www.hindawi.com/journals/ddns/2015/206473/ The slider-crank mechanism (SCM) is one of the most important mechanisms in modern technology. It appears in most combustion engines including those of automobiles, trucks, and other small engines. The SCM model considered here is an index-three nonlinear system of differential-algebraic equations (DAEs), and therefore difficult to integrate numerically. In this work, we present the application of the differential transform method (DTM) to obtain an approximate analytical solution of the SCM model in convergent series form. In addition, we propose a posttreatment of the power series solution with the Padé resummation method to extend the domain of convergence of the approximate series solution. The main advantage of the proposed technique is that it does not require an index reduction and does not generate secular terms or depend on a perturbation parameter. Brahim Benhammouda and Hector Vazquez-Leal Copyright © 2015 Brahim Benhammouda and Hector Vazquez-Leal. All rights reserved. Periodic Solutions Generated by Impulses for State-Dependent Impulsive Differential Equation Mon, 02 Mar 2015 11:54:37 +0000 http://www.hindawi.com/journals/ddns/2015/816325/ We study the existence of periodic solutions for a class of state-dependent impulsive differential systems via geometrical analysis methods. Our results show that these periodic solutions are generated by impulses. Moreover, numerical simulations are used to examine the existence of the periodic solutions. Qizhen Xiao and Binxiang Dai Copyright © 2015 Qizhen Xiao and Binxiang Dai. All rights reserved. The -Transform Method and Delta Type Fractional Difference Operators Mon, 02 Mar 2015 10:35:12 +0000 http://www.hindawi.com/journals/ddns/2015/852734/ The Caputo-, Riemann-Liouville-, and Grünwald-Letnikov-type difference initial value problems for linear fractional-order systems are discussed. We take under our consideration the possible solutions via the classical -transform method. We stress the formula for the image of the discrete Mittag-Leffler matrix function in the -transform. We also prove forms of images in the -transform of the expressed fractional difference summation and operators. Additionally, the stability problem of the considered systems is studied. Dorota Mozyrska and Małgorzata Wyrwas Copyright © 2015 Dorota Mozyrska and Małgorzata Wyrwas. All rights reserved. Accuracy, Robustness, and Efficiency of the Linear Boundary Condition for the Black-Scholes Equations Mon, 02 Mar 2015 08:41:04 +0000 http://www.hindawi.com/journals/ddns/2015/359028/ We briefly review and investigate the performance of various boundary conditions such as Dirichlet, Neumann, linear, and partial differential equation boundary conditions for the numerical solutions of the Black-Scholes partial differential equation. We use a finite difference method to numerically solve the equation. To show the efficiency of the given boundary condition, several numerical examples are presented. In numerical test, we investigate the effect of the domain sizes and compare the effect of various boundary conditions with pointwise error and root mean square error. Numerical results show that linear boundary condition is accurate and efficient among the other boundary conditions. Darae Jeong, Seungsuk Seo, Hyeongseok Hwang, Dongsun Lee, Yongho Choi, and Junseok Kim Copyright © 2015 Darae Jeong et al. All rights reserved. Bifurcation in Deterministic Discrete Dynamical Systems: Advances in Theory and Applications Mon, 02 Mar 2015 08:20:11 +0000 http://www.hindawi.com/journals/ddns/2015/960834/ Raghib Abu-Saris, Fathi Allan, Sui Sun Cheng, and Mustafa Kulenović Copyright © 2015 Raghib Abu-Saris et al. All rights reserved. Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise Mon, 02 Mar 2015 07:35:19 +0000 http://www.hindawi.com/journals/ddns/2015/389638/ A competitive system subject to environmental noise is established. By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are established, respectively. An example together with its corresponding numerical simulations is presented to confirm our analytical results. Huili Xiang, Zhuang Fang, Zuxiong Li, and Zhijun Liu Copyright © 2015 Huili Xiang et al. All rights reserved. A Pseudo-Parallel Genetic Algorithm Integrating Simulated Annealing for Stochastic Location-Inventory-Routing Problem with Consideration of Returns in E-Commerce Mon, 02 Mar 2015 07:28:13 +0000 http://www.hindawi.com/journals/ddns/2015/586581/ Facility location, inventory control, and vehicle routes scheduling are three key issues to be settled in the design of logistics system for e-commerce. Due to the online shopping features of e-commerce, customer returns are becoming much more than traditional commerce. This paper studies a three-phase supply chain distribution system consisting of one supplier, a set of retailers, and a single type of product with continuous review (Q, r) inventory policy. We formulate a stochastic location-inventory-routing problem (LIRP) model with no quality defects returns. To solve the NP-hand problem, a pseudo-parallel genetic algorithm integrating simulated annealing (PPGASA) is proposed. The computational results show that PPGASA outperforms GA on optimal solution, computing time, and computing stability. Bailing Liu, Hui Chen, Yanhui Li, and Xiang Liu Copyright © 2015 Bailing Liu et al. All rights reserved. Adaptive Control of MEMS Gyroscope Based on T-S Fuzzy Model Thu, 26 Feb 2015 09:14:50 +0000 http://www.hindawi.com/journals/ddns/2015/419643/ A multi-input multioutput (MIMO) Takagi-Sugeno (T-S) fuzzy model is built on the basis of a nonlinear model of MEMS gyroscope. A reference model is adjusted so that a local linear state feedback controller could be designed for each T-S fuzzy submodel based on a parallel distributed compensation (PDC) method. A parameter estimation scheme for updating the parameters of the T-S fuzzy models is designed and analyzed based on the Lyapunov theory. A new adaptive law can be selected to be the former adaptive law plus a nonnegative in variable to guarantee that the derivative of the Lyapunov function is smaller than zero. The controller output is implemented on the nonlinear model and T-S fuzzy model, respectively, for the purpose of comparison. Numerical simulations are investigated to verify the effectiveness of the proposed control scheme and the correctness of the T-S fuzzy model. Yunmei Fang, Shitao Wang, Juntao Fei, and Mingang Hua Copyright © 2015 Yunmei Fang et al. All rights reserved. Multiple Bifurcations and Chaos in a Discrete Prey-Predator System with Generalized Holling III Functional Response Wed, 25 Feb 2015 07:59:16 +0000 http://www.hindawi.com/journals/ddns/2015/245421/ A prey-predator system with the strong Allee effect and generalized Holling type III functional response is presented and discretized. It is shown that the combined influences of Allee effect and step size have an important effect on the dynamics of the system. The existences of Flip and Neimark-Sacker bifurcations and strange attractors and chaotic bands are investigated by using the center manifold theorem and bifurcation theory and some numerical methods. Xia Liu, Yanwei Liu, and Qiaoping Li Copyright © 2015 Xia Liu et al. All rights reserved. The MLE of the Parameters of a Discrete Competitive System Subject to Environmental Noise Mon, 23 Feb 2015 17:07:37 +0000 http://www.hindawi.com/journals/ddns/2015/305624/ A randomized discrete competitive system is investigated and the maximum likelihood estimation (MLE) of the parameters of the system is obtained. Also, a corresponding numerical simulation is offered to support our theoretical results. Huili Xiang and Zhijun Liu Copyright © 2015 Huili Xiang and Zhijun Liu. All rights reserved. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations Mon, 23 Feb 2015 13:21:55 +0000 http://www.hindawi.com/journals/ddns/2015/752523/ This paper proposes power series method (PSM) in order to find solutions for singular partial differential-algebraic equations (SPDAEs). We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM. U. Filobello-Nino, H. Vazquez-Leal, B. Benhammouda, A. Perez-Sesma, V. M. Jimenez-Fernandez, J. Cervantes-Perez, A. Sarmiento-Reyes, J. Huerta-Chua, L. J. Morales-Mendoza, M. Gonzalez-Lee, A. Diaz-Sanchez, D. Pereyra-Díaz, and R. López-Martínez Copyright © 2015 U. Filobello-Nino et al. All rights reserved. Two Bi-Accelerator Improved with Memory Schemes for Solving Nonlinear Equations Mon, 23 Feb 2015 13:03:38 +0000 http://www.hindawi.com/journals/ddns/2015/938606/ The present paper is devoted to the improvement of the -order convergence of with memory derivative free methods presented by Lotfi et al. (2014) without doing any new evaluation. To achieve this aim one more self-accelerating parameter is inserted, which is calculated with the help of Newton’s interpolatory polynomial. First theoretically it is proved that the -order of convergence of the proposed schemes is increased from 6 to 7 and 12 to 14, respectively, without adding any extra evaluation. Smooth as well as nonsmooth examples are discussed to confirm theoretical result and superiority of the proposed schemes. J. P. Jaiswal Copyright © 2015 J. P. Jaiswal. All rights reserved. Robust Optimization of Fourth Party Logistics Network Design under Disruptions Mon, 23 Feb 2015 07:43:25 +0000 http://www.hindawi.com/journals/ddns/2015/720628/ The Fourth Party Logistics (4PL) network faces disruptions of various sorts under the dynamic and complex environment. In order to explore the robustness of the network, the 4PL network design with consideration of random disruptions is studied. The purpose of the research is to construct a 4PL network that can provide satisfactory service to customers at a lower cost when disruptions strike. Based on the definition of β-robustness, a robust optimization model of 4PL network design under disruptions is established. Based on the NP-hard characteristic of the problem, the artificial fish swarm algorithm (AFSA) and the genetic algorithm (GA) are developed. The effectiveness of the algorithms is tested and compared by simulation examples. By comparing the optimal solutions of the 4PL network for different robustness level, it is indicated that the robust optimization model can evade the market risks effectively and save the cost in the maximum limit when it is applied to 4PL network design. Jia Li, Yanqiu Liu, Ying Zhang, and Zhongjun Hu Copyright © 2015 Jia Li et al. All rights reserved. Periodic and Chaotic Orbits of a Discrete Rational System Mon, 23 Feb 2015 07:26:33 +0000 http://www.hindawi.com/journals/ddns/2015/519598/ We study a rational planar system consisting of one linear-affine and one linear-fractional difference equation. If all of the system’s parameters are positive (so that the positive quadrant is invariant and the system is continuous), then we show that the unique fixed point of the system in the positive quadrant cannot be repelling and the system does not have a snap-back repeller. By folding the system into a second-order equation, we find special cases of the system with some negative parameter values that do exhibit chaos in the sense of Li and Yorke within the positive quadrant of the plane. N. Lazaryan and H. Sedaghat Copyright © 2015 N. Lazaryan and H. Sedaghat. All rights reserved. Analyzing the Influence of Mobile Phone Use of Drivers on Traffic Flow Based on an Improved Cellular Automaton Model Mon, 23 Feb 2015 07:10:50 +0000 http://www.hindawi.com/journals/ddns/2015/573090/ This paper aimed to analyze the influence of drivers’ behavior of phone use while driving on traffic flow, including both traffic efficiency and traffic safety. An improved cellular automaton model was proposed to simulate traffic flow with distracted drivers based on the Nagel-Schreckenberg model. The driving characters of drivers using a phone were first discussed and a value representing the probability to use a phone while driving was put into the CA model. Simulation results showed that traffic flow rate was significantly reduced if some drivers used a phone compared to no phone use. The flow rate and velocity decreased as the proportion of drivers using a phone increased. While, under low density, the risk of traffic decreased first and then increased as the distracted drivers increased, the distracted behavior of drivers, like using a phone, could reduce the flow rate by 5 percent according to the simulation. Yao Xiao and Jing Shi Copyright © 2015 Yao Xiao and Jing Shi. All rights reserved. An Optimization Method for the Remanufacturing Dynamic Facility Layout Problem with Uncertainties Mon, 23 Feb 2015 06:19:04 +0000 http://www.hindawi.com/journals/ddns/2015/685408/ Remanufacturing is a practice of growing importance due to increasing environmental awareness and regulations. Facility layout design, as the cornerstone of effective facility planning, is concerned about resource localization for a well-coordinated workflow that leads to lower material handling costs and reduced lead times. However, due to stochastic returns of used products/components and their uncontrollable quality conditions, the remanufacturing process exhibits a high level of uncertainty challenging the facility layout design for remanufacturing. This paper undertakes this problem and presents an optimization method for remanufacturing dynamic facility layout with variable process capacities, unequal processing cells, and intercell material handling. A dynamic multirow layout model is presented for layout optimization and a modified simulated annealing heuristic is proposed toward the determination of optimal layout schemes. The approach is demonstrated through a machine tool remanufacturing system. Lingling Li, Congbo Li, Huijie Ma, and Ying Tang Copyright © 2015 Lingling Li et al. All rights reserved. New Oscillation Results of Second-Order Damped Dynamic Equations with -Laplacian on Time Scales Sun, 22 Feb 2015 13:42:13 +0000 http://www.hindawi.com/journals/ddns/2015/709242/ By employing a generalized Riccati technique and functions in some function classes for integral averaging, we derive new oscillation criteria of second-order damped dynamic equation with -Laplacian on time scales of the form , where the coefficient function may change sign. Two examples are given to demonstrate the obtained results. Yang-Cong Qiu and Qi-Ru Wang Copyright © 2015 Yang-Cong Qiu and Qi-Ru Wang. All rights reserved. Dynamical Analysis of a Nitrogen-Phosphorus-Phytoplankton Model Sun, 22 Feb 2015 13:19:27 +0000 http://www.hindawi.com/journals/ddns/2015/823026/ This paper presents a nitrogen-phosphorus-phytoplankton model in a water ecosystem. The main aim of this research is to analyze the global system dynamics and to study the existence and stability of equilibria. It is shown that the phytoplankton-eradication equilibrium is globally asymptotically stable if the input nitrogen concentration is less than a certain threshold. However, the coexistence equilibrium is globally asymptotically stable as long as it exists. The system is uniformly persistent within threshold values of certain key parameters. Finally, to verify the results, numerical simulations are provided. Yunli Deng, Min Zhao, Hengguo Yu, and Yi Wang Copyright © 2015 Yunli Deng et al. All rights reserved. Decision-Making Based on Consumers’ Perceived Value in Different Remanufacturing Modes Sun, 22 Feb 2015 11:40:09 +0000 http://www.hindawi.com/journals/ddns/2015/278210/ We investigate how the diversity of consumers’ perceived value in different remanufacturing modes affects remanufacturing decision-making. We establish a two-stage optimal decision-making model of original equipment manufacturer (OEM) remanufacturing and a noncooperative game model of third party remanufacturer (TPR) remanufacturing and then analyze the optimal decisions of OEM and TPR. Comparing the effects of consumers’ perceived value on remanufacturing decision-making in different modes, we find that when OEM remanufactures products, consumers’ perceived value has a negative effect on new products’ price and quantity and has a positive effect on remanufactured products’ quantity and when TPR remanufactures products, consumers’ perceived value has a positive effect on new products price and quantity and has a negative effect on remanufactured products’ quantity. Compared with OEM remanufacturing, TPR remanufacturing can raise the profits of OEM and whole closed-loop supply chain, but it will lower the quantity of remanufacturing products. Wei Li, Hang Wu, and Liurui Deng Copyright © 2015 Wei Li et al. All rights reserved. Fixed Points of Generalized -Suzuki Type Contraction in Complete -Metric Spaces Sun, 22 Feb 2015 10:20:15 +0000 http://www.hindawi.com/journals/ddns/2015/969726/ We introduce the notion of generalized -Suzuki type contraction in -metric spaces and investigate the existence of fixed points of such mappings. The presented results generalize and improve several results of the topics in the literature. Hamed Hamdan Alsulami, Erdal Karapınar, and Hossein Piri Copyright © 2015 Hamed Hamdan Alsulami et al. All rights reserved. Holiday Destination Choice Behavior Analysis Based on AFC Data of Urban Rail Transit Sun, 22 Feb 2015 10:09:00 +0000 http://www.hindawi.com/journals/ddns/2015/136010/ For urban rail transit, the spatial distribution of passenger flow in holiday usually differs from weekdays. Holiday destination choice behavior analysis is the key to analyze passengers’ destination choice preference and then obtain the OD (origin-destination) distribution of passenger flow. This paper aims to propose a holiday destination choice model based on AFC (automatic fare collection) data of urban rail transit system, which is highly expected to provide theoretic support to holiday travel demand analysis for urban rail transit. First, based on Guangzhou Metro AFC data collected on New Year’s day, the characteristics of holiday destination choice behavior for urban rail transit passengers is analyzed. Second, holiday destination choice models based on MNL (Multinomial Logit) structure are established for each New Year’s days respectively, which takes into account some novel explanatory variables (such as attractiveness of destination). Then, the proposed models are calibrated with AFC data from Guangzhou Metro using WESML (weighted exogenous sample maximum likelihood) estimation and compared with the base models in which attractiveness of destination is not considered. The results show that the values are improved by 0.060, 0.045, and 0.040 for January 1, January 2, and January 3, respectively, with the consideration of destination attractiveness. Chang-jun Cai, En-jian Yao, Sha-sha Liu, Yong-sheng Zhang, and Jun Liu Copyright © 2015 Chang-jun Cai et al. All rights reserved. A Novel Representation of the Exact Solution for Differential Algebraic Equations System Using Residual Power-Series Method Sun, 22 Feb 2015 09:34:30 +0000 http://www.hindawi.com/journals/ddns/2015/205207/ We implement a relatively new analytic iterative technique to get approximate solutions of differential algebraic equations system based on generalized Taylor series formula. The solution methodology is based on generating the residual power series expansion solution in the form of a rapidly convergent series with easily computable components. The residual power series method (RPSM) can be used as an alternative scheme to obtain analytical approximate solution of different types of differential algebraic equations system applied in mathematics. Simulations and test problems were analyzed to demonstrate the procedure and confirm the performance of the proposed method, as well as to show its potentiality, generality, viability, and simplicity. The results reveal that the proposed method is very effective, straightforward, and convenient for solving different forms of such systems. Khaled Moaddy, Mohammed AL-Smadi, and Ishak Hashim Copyright © 2015 Khaled Moaddy et al. All rights reserved. Dynamics in Braess Paradox with Nonimpulsive Commuters Sun, 22 Feb 2015 09:24:50 +0000 http://www.hindawi.com/journals/ddns/2015/345795/ In Braess paradox the addiction of an extra resource creates a social dilemma in which the individual rationality leads to collective irrationality. In the literature, the dynamics has been analyzed when considering impulsive commuters, i.e., those who switch choice regardless of the actual difference between costs. We analyze a dynamical version of the paradox with nonimpulsive commuters, who change road proportionally to the cost difference. When only two roads are available, we provide a rigorous proof of the existence of a unique fixed point showing that it is globally attracting even if locally unstable. When a new road is added the system becomes discontinuous and two-dimensional. We prove that still a unique fixed point exists, and its global attractivity is numerically evidenced, also when the fixed point is locally unstable. Our analysis adds a new insight in the understanding of dynamics in social dilemma. Arianna Dal Forno, Ugo Merlone, and Viktor Avrutin Copyright © 2015 Arianna Dal Forno et al. All rights reserved. Dimension Estimation Using Weighted Correlation Dimension Method Sun, 22 Feb 2015 08:52:10 +0000 http://www.hindawi.com/journals/ddns/2015/837185/ Dimension reduction is an important tool for feature extraction and has been widely used in many fields including image processing, discrete-time systems, and fault diagnosis. As a key parameter of the dimension reduction, intrinsic dimension represents the smallest number of variables which is used to describe a complete dataset. Among all the dimension estimation methods, correlation dimension (CD) method is one of the most popular ones, which always assumes that the effect of every point on the intrinsic dimension estimation is identical. However, it is different when the distribution of a dataset is nonuniform. Intrinsic dimension estimated by the high density area is more reliable than the ones estimated by the low density or boundary area. In this paper, a novel weighted correlation dimension (WCD) approach is proposed. The vertex degree of an undirected graph is invoked to measure the contribution of each point to the intrinsic dimension estimation. In order to improve the adaptability of WCD estimation, -means clustering algorithm is adopted to adaptively select the linear portion of the log-log sequence . Various factors that affect the performance of WCD are studied. Experiments on synthetic and real datasets show the validity and the advantages of the development of technique. Yuanhong Liu, Zhiwei Yu, Ming Zeng, and Shun Wang Copyright © 2015 Yuanhong Liu et al. All rights reserved. Coopetition in Intermodal Freight Transport Services Thu, 19 Feb 2015 11:50:14 +0000 http://www.hindawi.com/journals/ddns/2015/680685/ The paper studies the coopetition of the downstream different carriers by providing complementary transport services in intermodal freight transport chain. Considering different information structure, a two-stage dynamic game model with simultaneous actions on investment and price is first formulated. Equilibria show both parties have motivation to select coopetition even if the agreement for cooperation investment is reached in advance. When both firms agree on the specific allocation, the new coopetition with higher efficiency would be emerged. Moreover, we analyze the complexity and evolution of coopetition by repeated pricing game with finitely and infinitely time horizon. In the finitely repeated pricing game, both firms have incentive to reach a tacit understanding to alternate choosing price cooperation and competition after setting suitable allocation scheme; the repeated periods are then going to be an issue. In the infinitely repeated pricing game, the perfect cooperation is realized by designing the suitable trigger strategy. Jian Liu, Yinzhen Li, and Jun Li Copyright © 2015 Jian Liu et al. All rights reserved. Identification of Prior Factors Influencing the Mode Choice of Short Distance Travel Wed, 18 Feb 2015 11:24:57 +0000 http://www.hindawi.com/journals/ddns/2015/795176/ Short distance trips are defined as any trips shorter than or equal to 5 kilometers, which have been found to be a big contributor to the traffic congestion problem. This paper is intended to analyze factors that influence the mode choice of short distance travels in order to help reduce short distance trips by cars. A survey is conducted at two typical kinds of residential areas, one with a high proportion of short distance car trips and another one with a low proportion. Then, by applying the structural equation modeling, it is found that the age, the household income, and the vehicle ownerships have a significant effect on the mode choice of short distance travels. Besides, among residents of the same type (same age, household income, and vehicle ownerships) in surveyed areas, those in the area with a better green-mode travel environment account for a higher proportion choosing the green mode than those in other areas. Based on this result, it is concluded that a better green-mode travel environment leads to a higher proportion of green-mode travels. In the end, the paper shows residents’ stated willingness to change travel modes from cars to the green mode. Ming Li, Guohua Song, Ying Cheng, and Lei Yu Copyright © 2015 Ming Li et al. All rights reserved. Global Stability of Positive Periodic Solutions and Almost Periodic Solutions for a Discrete Competitive System Tue, 17 Feb 2015 13:21:15 +0000 http://www.hindawi.com/journals/ddns/2015/658758/ A discrete two-species competitive model is investigated. By using some preliminary lemmas and constructing a Lyapunov function, the existence and uniformly asymptotic stability of positive almost periodic solutions of the system are derived. In addition, an example and numerical simulations are presented to illustrate and substantiate the results of this paper. Heping Ma, Jianguo Gao, and Lingling Xie Copyright © 2015 Heping Ma et al. All rights reserved. On the Dynamical Behavior of Toxic-Phytoplankton-Zooplankton Model with Delay Tue, 17 Feb 2015 08:19:13 +0000 http://www.hindawi.com/journals/ddns/2015/756315/ A toxin producing phytoplankton-zooplankton model with inhibitory exponential substrate and time delay has been formulated and analyzed. Since the liberation of toxic substances by phytoplankton species is not an instantaneous process but is mediated by some time lag required for maturity of the species and the zooplankton mortality due to the toxic phytoplankton bloom occurs after some time laps of the bloom of toxic phytoplankton, we induced a discrete time delay to both of the consume response function and distribution of toxic substance term. Furthermore, based on the fact that the predation rate decreases at large toxic-phytoplankton density, the system is modelled via a Tissiet type functional response. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models. Mehbuba Rehim, Weixin Wu, and Ahmadjan Muhammadhaji Copyright © 2015 Mehbuba Rehim et al. All rights reserved.