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Abstract Let G be a connected graph. The edge k -partiteness of G is the minimum number of edges whose deletion from G yields a k -partite graph. The Kirchhoff index Kf (G) of G is the sum of the resistance distance between all unordered pairs of vertices. In this paper, we study the problem to determine the minimum Kirchhoff index of graphs with a given edge k -partiteness. First, we theoretically characterize the graphs with minimum Kirchhoff index in this graph family when the edge k -partiteness is not big compared to the number of vertices of G. Then we propose an exhaustive search algorithm to find the optimal graphs. At last, three strategies are used to reduce the computation complexity of our algorithm and several performance comparisons of these strategies are given. [ABSTRACT FROM AUTHOR]

Highlights • A time delay model of the complex interaction between Tumor, CD8+T cells and T - helper cells. • The model undergoes Hopf bifurcation in which time delay plays an important role to destabilize the system. • Extensive numerical simulations are performed to validate our analytical findings. Abstract In this paper, we consider a three-dimensional nonlinear delay differential system (tumor cells, cytotoxic-T lymphocytes, T-helper cells) with single interaction delay. We perform linear stability of the equilibria and the existence of Hopf bifurcation in which the discrete time delay is used as a bifurcation parameter. We estimate the length of delay to preserve the stability of period-1 limit cycle. We also investigate the direction, period, and the stability of bifurcated periodic solutions by applying normal form method and center manifold theory. We observe that the discrete time delay plays an important role in stability switching. Numerical simulations are presented to illustrate the rich dynamical behavior of the model with different values for the time delay τ including the existence of periodic oscillations, which demonstrate the phenomena of long-term tumor relapse. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes. [ABSTRACT FROM AUTHOR]

This paper systematically investigates the optimal harvesting of a stochastic delay competitive Lotka–Volterra model with Lévy jumps. Under some simple assumptions, the sufficient conditions for extinction and stable in the time average of each species are established. The stability in distribution of this model is proved under our assumptions. Finally, the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained. And some numerical simulations are introduced to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with a parabolic equation with variable coefficient modeling MEMS technology, and we will prove the solution of the problem quenches in finite time in the case without stationary solutions. Numerical simulations are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Based on biological meaning, a kind of diffusive intraguild predation (IGP: resource, IG prey and IG predator) model with delay effect is investigated in this paper. The model has Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type II functional response between IG prey and IG predator. We first give sufficient conditions on the stability of possible nonnegative constant steady-state solutions for the proposed model, which give us a complete picture of the global dynamics. Then we investigate Hopf bifurcation near the unique positive constant steady-state solution by taking delay as bifurcation parameter and derive the Hopf bifurcation threshold. It is shown that the delay can induce three types of bistability (node-node bistability, node-cycle bistability and cycle-cycle bistability), periodic oscillations and irregular oscillations triggering spatiotemporal chaos in the diffusive IGP model. Numerical simulations are performed to illustrate our theoretical results and suggest that delay can even trigger the emergence of self-organised spatiotemporal patterns, which evolve from spiral patterns to irregular spatial patterns via spatiotemporal Hopf bifurcation. In addition, the impact of diffusion on the model’s dynamics under certain time delay are also explored. [ABSTRACT FROM AUTHOR]

In this paper, Cournot oligopoly model is examined with an uncertain quadratic cost function. A random quadratic cost function is introduced in this model. The model consists of three competed firms on which each firm in the model wants to maximize its expected profit and also wants to minimize its uncertainty by minimizing the cost. To handle this multi-objective optimization problem, the expectation and worst-case approaches are adopted used to study uncertainty. The existence and uniqueness of the equilibrium are obtained. The asymptotic behavior of the equilibrium point is also investigated. Complete stability and bifurcation analysis are provided. The obtained theoretical results are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a variable-territory predator–prey model with Dirichlet boundary condition. We establish a necessary and sufficient condition for the existence of positive solutions to steady state. Furthermore, we also prove that the local bifurcation positive solutions are unconditional stable. By regular perturbation theorem, we investigate the convergence and stability of positive solutions when handling time m is large enough. At the end of this paper, there are some numerical simulations and biological significance to check and complement our theoretical analysis results. [Copyright &y& Elsevier]

Abstract: The research in this paper presents a new approach for the modeling of epidemic spread by using a set of connected social networks. The purpose of this work is to simulate the spreading of the well know A/H1N1 pandemic virus. The case study analyzed in this paper refers to the spreading of A/H1N1 in Romania. The epidemic is followed from its beginning throughout its evolution in Romania, i.e. between May 2009 and February 2010. The evolution is performed in a hierarchical way, taking into account the state divisions, the influences among them, national level as well as influences from abroad (from other infected countries). Numerical experiments performed analyze the monthly evolution of the infection in each county and at the country level and compare the results with the real ones (collected during and at the end of the epidemic spread). The simulations results are closer to the reality than the ones provided by the Health Ministry in Romania. [Copyright &y& Elsevier]

Abstract: This paper introduces a saturated treatment function into an SIS model with saturated incidence rate. The treatment function is a continuous and differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large. Sufficient conditions for the existence and global asymptotical stability of the disease-free and endemic equilibria are given in this paper, and the nonexistence of limit cycles is also demonstrated. A backward bifurcation is found when the capacity of the treatment is low. It indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of diseases. By mathematical analysis and numerical simulations, it is shown that the system undergoes Hopf bifurcation and Bogdanov–Takens bifurcation. [Copyright &y& Elsevier]

The nonlinear incidence rate can explain the complicated infectious process of disease. And time delay describing the latent period widely exists in the process of disease contagion. In this paper, a spatiotemporal epidemic model with nonlinear incidence rate is investigated. In particular, we considered that the time delay is relatively small. In this case, the characteristic equation are derived, we obtain two mechanisms of instability of the positive constant stationary state, that is, One is the diffusion induced instability, and the other one is delay induced instability. Moreover, the results of numerical simulation validate our theoretical analyses. The obtained results may well catch some major features for epidemic models. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we proposed and analyzed a prey predator system with stage-structured for the predator population. A time delay is incorporated due to the gestation for the matured predator. All the possible non-negative equilibria are obtained and their local as well as global behavior are studied. Choosing delay as a bifurcation parameter, the existence of the Hopf bifurcation of the system has been investigated. Moreover, we use the normal form method and the center manifold theorem to examine the direction of the Hopf bifurcation and the nature of the bifurcating periodic solution. Some numerical simulations are given to support the analytical results. Some interesting conclusions are obtained from our analysis and it is given at the end of the paper. [Copyright &y& Elsevier]

In this paper, we propose a delayed mathematical model for the transmission of Ebola in humans. We consider the transmission of infection between the living humans and from infectious corpses to the living individuals in which the latent period of Ebola is incorporated. We identify the basic reproduction number R 0 for the model, prove that the disease-free equilibrium is always globally asymptotically stable when R 0 < 1, the disease is persistence and a unique endemic equilibrium exists when R 0 > 1. We show that the endemic steady state is locally asymptotically stable under certain condition and globally asymptotically stable in a special case of the model. Numerical simulations are provided to demonstrate and complement the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we pay attention to the problem of particle evacuation from a high-pressure region. This research was inspired by the known problem of the explosion suppression by a cloud of inert and solid particles. This issue has been so far investigated experimentally where the most important tasks have been to find the proper suppressant, estimate its quantity, as well as design the quenching device. Also some attention has been paid to numerical investigation where by use of computer simulation the same questions have been asked. In this paper, we focus on the numerical study, where the first moment of the suppressing process is analysed: the exact behaviour of the particle cloud as it interacts with the gas. A mathematical model is presented that bases on the Eulerian–Lagrangian approach for the description of the gas and solid phases. Finally, some results are shown: both snapshots of particle location as well as some statistics, such as particle cloud area and particle distribution within the cloud. According to the observations, we obtain different behaviour especially if the particle diameter varies. For some values the particles do not seem to be well-distributed and an example are smaller particles that tend to gather along the edges of the eddies formed in the gas phase. [Copyright &y& Elsevier]

Abstract: A three degree of freedom (3 DOF) nanomanipulator with revolute revolute prismatic (RRP) actuator structure, named here MM3A, can be utilized for a variety of nanomanipulation tasks. This first paper in the series presents the mathematical modeling and development of a memory-based robust adaptive controller for the nanomanipulator driving principle. Unlike widely used Cartesian-structure nanomanipulators, the MM3A is equipped with revolute-piezoelectric actuators which result in outstanding performance in controlling the nanomanipulator’s tip alignment during the nanomanipulation. However, the RRP structure of the nanomanipulator introduces complexity in kinematic and dynamic equations of the system which needs to be addressed in order to control the nanomanipulation process. Dissimilar to the ordinary piezoelectric actuators which provide only a couple of micrometers working range, the piezoelectric actuators utilized in MM3A, namely Nanomotors®, provide wide range of action (120° in revolute actuators and 12mm in prismatic actuator) with nanoscale precision (0.1μrad in revolute actuators and 0.25nm in prismatic actuator). This wide range of action combined with nanoscale precision is achieved using a special stick/slip moving principle of the Nanomotors®. However, such stick/slip motion results in stepping movement of the MM3A. Hence, due to the RRP structure and stepping movement principle of the MM3A nanomanipulator, development and implementation of an appropriate controller for such nanomanipulation process is not a trivial task. In this paper, a novel memory-based robust adaptive controller is proposed to overcome such shortfalls. Following the development the controller, numerical simulations are preformed to demonstrate the positioning performance capability of the controller in a variety of nanomanipulation tasks. [Copyright &y& Elsevier]

Abstract: Due to lack of position and velocity feedbacks in MM3A nanomanipulator, a fused vision/force feedback robust controller has been recently designed by the authors. This second paper in the series presents the optimal utilization of the visual servoing and force sensor feedbacks for use in the nanomanipulation tasks discussed in the first paper (Part A). More specifically, the visual servoing and force feedback structures are investigated through extensive simulations in order to reveal issues in practical implementation. For this, a set of numerical simulations is performed to demonstrate the effectiveness of utilizing just vision feedback as well as force feedback only, at both macro and microscale. It is shown that although each feedback module could provide reasonably accurate results at either macro or microscale, precise positioning of such nanomanipulator requires employment of both modules with a proper (optimal) switching strategy. This paper extends our previously introduced robust controller for nanomanipulator positioning and offers a novel switching framework to be used between vision feedback and force feedback modules. Utilizing a soft switching function, the problem of jump in the actuator force during fused vision/force control of the nanomanipulation can be overcome. Following the development of the soft switching approach, numerical simulations are used to verify the positioning performance and effectiveness of each switching strategy. [Copyright &y& Elsevier]

In this paper, we derive a nonlocal delayed and diffusive dengue transmission model with a spatial domain being bounded as well as unbounded. We first address the well-posedness to the initial-value problem for the model. In the case of a bounded spatial domain, we establish the threshold dynamics for the spatially heterogeneous system in terms of the basic reproduction number R 0 . Also, a set of sufficient conditions is further obtained for the global attractivity of the endemic steady state where all the parameters are spatially independent. In the case of an unbounded spatial domain, and when the coefficients are all constants, we show that there exist traveling wave solutions of the model. Numerical simulations are performed to illustrate our main analytic results. [ABSTRACT FROM AUTHOR]

HIV-1 infection and treatment may occur in the non-constant environment due to the time-varying drug susceptibility and growth of target cells. In this paper, we propose a within-host virus model with multiple stages for infected cells under time-varying environments, to study how the multiple infected stages affect on the counts of viral load and CD4 + -T cells. We establish the sufficient conditions for both persistent HIV infection and clearance of HIV infection based on two positive constants R * , R * . When the system is under persistent infection, we further obtained detailed estimates of both the lower and upper bounds of the viral load and the counts of CD4 + -T cells. Furthermore, numerical simulations are carried out to verify our analytical results and demonstrate the combined effects of multiple infected stages and non-constant environments, and reflect that both persistence and clearance of infection are possible when R * < 1 < R * holds. In particular, the numerical results exhibit the viral load of system with multiple infected stages may be less than that with single infected stage, and simulate the effect of time-varying environment of the autonomous system with multiple infected stages. We expect that our theoretical and simulation results can provide guidance for clinical therapy for HIV infections. [ABSTRACT FROM AUTHOR]

Evolution problem is always a hot topic in the mathematical biology field. In this paper, we investigate the evolutionary effects of selective disturbance on an evolving trait (e.g. body size and maturation age) of the predator individuals in one-predator two-prey community. By using methods of adaptive dynamics and population dynamics we construct an invasion fitness function and obtain the conditions for evolutionary branching and evolutionary stability under selective disturbance in both monomorphic and dimorphic populations. We further conduct a size-selective disturbance function founded on chi-square distribution to study evolutionary stable coexistence, and considering the evolutionary branching and evolutionary stability by using theoretic analysis and numerical simulations. The evolutionary results from a biological point of view show that (1) two strategies could gradually evolve to form a single ancestral strategy, moreover, higher levels of polymorphism cannot build up during evolution, that is, following first evolutionary branching two species will eventually evolve into two generalist species and reach an evolutionary stable coexistence; (2) smaller disturbance could touch off higher levels of dimorphism during evolution, while large disturbance can go against evolutionary branching and advance evolutionary stability. [ABSTRACT FROM AUTHOR]

In this paper, a new modified Chua oscillator is introduced. The original Chua oscillator is well known for its simple implementation and mathematical modeling. A modification of the oscillator is proposed in order to facilitate the synchronization and the encryption and decryption scheme. The modification consists in changing the nonlinear term of the original oscillator to a smooth and bounded nonlinear function. A bifurcation diagram, a Poincaré map and the Lyapunov exponents are presented as proofs of chaoticity of the newly modified oscillator. An application to secure communications is proposed in which two channels are used. Numerical simulations are performed in order to analyze the communication system. [ABSTRACT FROM AUTHOR]

In this paper, we consider the effect of distributed time delays on dynamics of a mathematical model of gene expression. Both the weak and strong delay kernels are discussed. Sufficient conditions for the local stability of the unique equilibrium are obtained. Taking the average delay as a bifurcation parameter, we investigate the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions by using the method of multiple time scales. Finally, numerical simulation is carried out to illustrate our theoretical results. It shows both subcritical and supercritical Hopf bifurcations can happen. [ABSTRACT FROM AUTHOR]

This paper deals with a three-dimensional plant-herbivore-predator model that incorporates explicitly the plant toxicity in plant-herbivore interactions. The existence and stability conditions of all the feasible equilibria are established. Our results indicate that plant toxicity may play a key role in the dynamical behavior of the system. By adding another plant species with a different toxicity level to this system, we derive threshold conditions on the invasion of the second plant species. The analysis indicates that several parameters may be critical to determine successful invasion. Numerical simulations are also provided to reinforce the theoretical conclusions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider a non-autonomous ratio-dependent predator–prey system driven by Lévy noise. Firstly, we show the existence of global positive solution and stochastic boundedness. Secondly, the conditions of persistent in mean and extinction are established and we also give the asymptotic properties of the solution. Finally, we simulate the model to illustrate our main analytical results. [Copyright &y& Elsevier]

Abstract: This paper characterizes the qualitative dynamics of a stochastic SIRS epidemic model. The study shows that the dynamics of the model are determined by a certain threshold quantity expressed in terms of the model parameters and the intensity of the noise. If , the disease will be eliminated from the community; whereas an epidemic occurs if . Our results recover the known results in the earlier literature as special cases. The presented results are illustrated by numerical simulations. [Copyright &y& Elsevier]

Abstract: In this paper we investigate a three species ecosystem consisting of a prey, a predator and a top predator. The predator survives on the prey and the top predator survives on both the prey and the predator. The mathematical model consists of non-linear simultaneous differential equations. All the eight equilibrium points of the model are identified and by using Routh–Hurwitz criteria as well as Lyapunov function, we derive the criteria for local and global stabilities. Also the population intensities of fluctuations (variances) around the positive equilibrium due to noise are computed; their stability is also analyzed with computer simulation using Matlab. Some Numerical simulations for justifying the theoretical analysis are also provided. The main conclusions are supplied in conclusion. [Copyright &y& Elsevier]

Abstract: A biological population mechanism with a protection zone under random environments is described as a stochastic system in this paper. The long time dynamical properties, several methods to strengthen the effect of protection zone and a method of dividing the protection zone are given for this stochastic system. Results show that environmental influences on different parameters have different effects. Conclusions also illustrate the positive effect of protection zone. That is protection zone can potentially strengthen protective effects in random environments. At last, some examples and several numerical simulations are introduced to explain the theoretical conclusions. [Copyright &y& Elsevier]

In the paper, we consider a prey-dependent model with integrated pest management strategies, that is, when the pest population reaches the economic injury level, we use a combination tactics such as biological, cultural, and chemical control tactics such that pests reduce to a tolerable level. The sufficient conditions for the existence and stability of semi-trivial and positive periodic solutions are obtained by using the Poincaré map and the analogue of the Poincaré criterion. The qualitative analysis shows that the positive periodic solution bifurcates from the semi-trivial solution through a fold bifurcation. Finally, we give an example and numerical simulations to explain the mathematical conclusions. [ABSTRACT FROM AUTHOR]

Abstract: This is a continuation of the paper Liu and Wang (2012) [14]. Firstly, we consider a general non-autonomous logistic model with delays and stochastic perturbation. Then sufficient conditions for extinction are established as well as nonpersistence in the mean, weak persistence and stochastic permanence. The threshold between weak persistence and extinction is obtained. Finally, numerical simulations are introduced to support the theoretical analysis results. [Copyright &y& Elsevier]

Abstract: In this paper, a nonlinear mathematical model for cleaning an infected computer network by using antivirus software is proposed and analyzed. In the modeling process, the total number of nodes in the network are divided in three subclasses, namely, the number of susceptible nodes, number of infected nodes and the number of protected nodes. A variable representing the number of antivirus softwares, assumed to be proportional to number of infected nodes, is also considered in the model which interacts with other nodes bilinearly to conduct the cleaning process. The model is analyzed by using stability theory of differential equations and computer simulation. The analysis shows that it is possible to clean the computer network under certain condition which depend upon the inflow rate of infected nodes in the computer network, the rate of interaction of infected nodes with susceptible nodes and their interactions with antivirus software, etc. It is found that the entire network can be cleaned eventually if the antivirus software is applied on the network, where a separate class of protected nodes is formed. The computer simulation confirms the analytical results. [Copyright &y& Elsevier]

Abstract: Vaccination is important for the elimination of infectious diseases. In this paper, a basic SVIR epidemic model with age of vaccination is considered. The model allows the vaccinated individuals to become susceptible again when vaccine loses its protective properties with time. The vaccination classes satisfy partial differential equations for the vaccination age. By means of LaSalle’s invariance principle and constructing suitable Lyapunov function(al)s, the dynamical property of the model is established. It is shown that the global stability results of the infection-free equilibrium and the endemic equilibrium depend only on the basic reproductive number . Finally, some numerical simulations are carried out to illustrate the main results. The combined effects of the vaccination rate and the age factor on the dynamics of the disease are displayed. [Copyright &y& Elsevier]

Abstract: In this work, we investigate the spatiotemporal dynamics of reaction–diffusion equations subject to cross-diffusion in the frame of a two-dimensional ratio-dependent predator–prey model. The conditions for diffusion-driven instability are obtained and the Turing space in the parameters space is achieved. Moreover, the criteria for local and global asymptotic stability of the unique positive homogeneous steady state without diffusion are discussed. Numerical simulations are carried out in order to validate the feasibility of the obtained analytical findings. Different types of spatial patterns through diffusion-driven instability of the proposed model are portrayed and analysed. Lastly, the paper finishes with an external discussion of biological relevance of the analysis regarding cross-diffusion and pattern issues. [Copyright &y& Elsevier]

Abstract: The paper deals with numerical solution of laminar and turbulent flows of Newtonian and non-Newtonian fluids in branched channels with two outlets. Mathematical model of the flow is based on the Reynolds averaged Navier–Stokes equations for the incompressible fluid. In the turbulent case, the closure of the system of equations is achieved by the explicit algebraic Reynolds stress (EARSM) turbulence model. Generalized non-Newtonian fluids are described by the power-law model. The governing equations are solved by cell-centered finite volume schemes with the artificial compressibility method; dual time scheme is applied for unsteady simulations. Channels considered in presented calculations are of constant square or circular cross-sections. Numerical results for laminar flow of non-Newtonian fluid are presented. Further, turbulent flow through channels with perpendicular branch is simulated. Possible methods for setting the flow rate are discussed and numerical results presented for two flow rates in the branch. [Copyright &y& Elsevier]

Abstract: Edge covering problem (ECP) is to find an edge cover with the minimum weight in a graph. By quantifying costs, time or opponent’s payoffs as weights on edges, ECP is employed to model many real-life problems in engineering and management. Since various types of uncertainty always exist in real world, this paper considers ECP under hybrid uncertain environments where randomness and fuzziness coexist. We propose three decision models and present a hybrid intelligent algorithm to solve the proposed models where genetic algorithm and random fuzzy simulation are embedded. Numerical experiments are performed to show the robustness of the proposed algorithm. [Copyright &y& Elsevier]

Abstract: This paper discusses a nonlinear single species discrete with feedback control. First, for the periodic system, it is proved that under certain conditions there exists a unique positive periodic solution which is globally attractive. Moreover, we discuss almost periodic phenomena, and obtain some sufficient conditions which assure the unique existence and global attractivity of almost positive periodic solution. An example together with numerical simulation indicates the feasibility of the main result. Our results improve and complement some in the literature. [Copyright &y& Elsevier]

Abstract: A nonlinear dynamic triopoly game model is studied based on the theory of nonlinear dynamics and previous researches in this paper. A lagged structure is introduced to the model to study stability conditions of the Nash equilibrium under a local adjustment process when players price their products with delayed bounded rationality. Numerical simulations are provided to demonstrate the complexity of system evolvement and influence of the strategy of delayed bounded rationality on system stability. We find that besides the lagged structure, suitable delayed parameters are also important factors to eliminate chaos or expand the stable region of the system, and various players’ adjustment parameters have different effect on stability of the system. [Copyright &y& Elsevier]

Abstract: Synchronization in large ensembles of coupled interacting units is a fundamental phenomenon, which is helpful for the understanding of working mechanisms in neuronal networks, social network, etc. In this paper, we will investigate the synchronization phenomenon in a network model. A feedback control scheme is proposed for the synchronization of the given complex networks. The obtained result indicates that synchronization can be achieved for growing chaotic network model. Method enhance the synchronizability of the given model are given at the same time. Finally, numerical simulations are given to show the effectiveness of obtained results. [Copyright &y& Elsevier]

Abstract: In this paper, a new complex-valued recurrent neural network (CVRNN) called complex-valued Zhang neural network (CVZNN) is proposed and simulated to solve the complex-valued time-varying matrix-inversion problems. Such a CVZNN model is designed based on a matrix-valued error function in the complex domain, and utilizes the complex-valued first-order time-derivative information of the complex-valued time-varying matrix for online inversion. Superior to the conventional complex-valued gradient-based neural network (CVGNN) and its related methods, the state matrix of the resultant CVZNN model can globally exponentially converge to the theoretical inverse of the complex-valued time-varying matrix in an error-free manner. Moreover, by exploiting the design parameter , superior convergence can be achieved for the CVZNN model to solve such complex-valued time-varying matrix inversion problems, as compared with the situation without design parameter involved (i.e., the situation with ). Computer-simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a CVZNN model for online complex-valued time-varying matrix inversion. [Copyright &y& Elsevier]

Abstract: The paper presents the mathematical results for a double-walled carbon nanotube model with nonconservative boundary conditions, given in the form of two Timoshenko beams coupled through a distributed Van Der Waals force. The system is clamped at the left end and subject to a four-parameter family of dynamical boundary conditions at the right end. We also present the four-branch vibrational spectrum of the system. All the results are purely analytical; they will be complemented by numerical simulations in a forthcoming work. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a mathematical model for the lactic acid fermentation in membrane bioreactor is investigated. Firstly, continuous input substrate is taken. The existence and local stability of two equilibria are studied. According to Poincare–Bendixson theorem, we obtain the condition for the globally asymptotical stability of the equilibria. Secondly, using the Floquet’s theorem and small-amplitude perturbation method, we obtain the biomass-free periodic solution is locally stable if R 2 <1. The permanent conditions of the system are also given. Finally, our findings are confirmed by means of numerical simulations. [ABSTRACT FROM AUTHOR]

Abstract: In most models of population dynamics in a polluted environment, the emission of toxicant is generally considered to be continuous, but it is often the case that toxicant is emitted in regular pulses. This paper deals with the effects of pulse toxicant input with constant rate on two-species Lotka–Volterra competition system in a polluted environment. The thresholds between persistence and extinction of each population are obtained. Moreover, our results indicate that the release amount of toxicant and the pulse period will affect the fate of each population. Finally, the results are verified through computer simulations. [Copyright &y& Elsevier]

Abstract: For a connected graph G, the super edge-connectivity is the minimum cardinality of an edge-cut F in G such that contains no isolated vertices. It is a more refined index than the edge-connectivity for the fault-tolerance of the network modeled by G. This paper deals with the super edge-connectivity of product graphs , which is one important model in the design of large reliable networks. Let be a connected graph with order and edge-connectivity for . We show that for and deduce the super edge-connectedness of when and are maximally edge-connected with . Furthermore we state sufficient conditions for to be -optimal, that is, . As a consequence, we obtain the -optimality of some important interconnection networks. [Copyright &y& Elsevier]

Abstract: The region growing pulse coupled neural network (PCNN) algorithm is an efficient method for multi-value image segmentation. However, as a kind of PCNN models, choosing appropriate parameters are usually difficult. This paper brings forward a new approach which improves the region growing PCNN model by modifying the linking channel function and decreases the complexity of adjusting parameters. The region growing PCNN is not effective when processing the edge pixels between different regions because the edge pixels and central pixels are dealt with unfairly. In order to overcome this disadvantage, the proposed method processes the edge pixels by setting the edge pixels and central pixels to receive same linking input if they are in similar condition. Computer simulations prove it can process the edge pixels efficiently and obtain clear boundaries between different regions. [Copyright &y& Elsevier]

Abstract: In this paper, we present an interference-cancelled wireless personal area network (WPAN) system based on ultra wideband (UWB) wireless communication system using binary zero-correlation-duration (ZCD) spreading sequences. The proposed interference-cancelled WPAN system is based on the direct sequence-ultra wideband (DS-UWB) scheme using special binary spreading sequences with zero-correlation-duration (ZCD) characteristics. After presenting a mathematical model for interference-cancelled WPAN system, we present theoretical bit error rate (BER) performance. Through computer simulation, we verify high system capacity of the proposed system and superior performance over the conventional Walsh-based DS-UWB systems in multi-path and in multiple access environments. Furthermore, outstanding performance of the proposed system is provided under multiple access interference (MAI) and multi-path interference (MPI). Finally, we show that perfect interference cancellation and high system capacity can be achieved without adopting expensive multi-user detection (MUD) scheme or other interference cancellation schemes. [Copyright &y& Elsevier]