Search

• A computational effective discretization scheme for nonlinear dynamical systems is developed in the context of simulations in a digital computer. • It is shown that high-order terms in the fourth order Runge-Kutta method can be neglected with no accuracy loss. • The number of mathematical operations and simulation time have been reduced up to 81.1% and 90.7%, respectively. • Observability of dynamical systems and the largest Lyapunov exponent are preserved under the new schemes. • A novel algorithm for reducing the carbon footprint of computer simulation. Numerical methods are essential to investigate and apply nonlinear continuous-time dynamical systems in many fields of science and engineering and discretization schemes are required to obtain the solutions of such dynamical systems. Although computing power has been speedily growing in recent decades, embedded and large-scale problems have motivated significant research to improve the computational efficiency. Nevertheless, few studies have focused on finite precision limitation on discretization schemes due to round-off effects in floating-point number representation. In this paper, a computational effective discretization scheme for nonlinear dynamical systems is introduced. By means of a theorem, it is shown that high-order terms in the Runge-Kutta method can be neglected with no accuracy loss. The proposed approach is illustrated using three well-known systems, namely the Rössler systems, the Lorenz equations and the Sprott B system. The number of mathematical operations and simulation time have reduced up to 81.1% and 90.7%, respectively. Furthermore, as the step-size decreases, the number of neglected terms increases due to the precision of the computer. Yet, accuracy, observability of dynamical systems and the largest Lyapunov are preserved. The adapted scheme is effective, reliable and suitable for embedded and large-scale applications. [ABSTRACT FROM AUTHOR]

• Sampling-type methods operated at single- and multiple-frequency are proposed for monostatic imaging in two-dimensional limited-aperture scattering problems. • Asymptotic structures of the methods are verified to establish the effect of measurement range on the imaging performance of proposed schemes. • Asymptotic structures of the methods are compared to those of the direct sampling methods in limited-aperture configuration. • Various numerical simulations using synthetic data are presented to validate the theoretical results. We present monostatic sampling methods for limited-aperture scattering problems in two dimensions. The direct sampling method (DSM) is well known to provide a robust, stable, and fast numerical scheme for imaging inhomogeneities from multistatic measurements even with only one or two incident fields. However, in practical applications, monostatic measurements in limited-aperture configuration are frequently encountered. A monostatic sampling method (MSM) was studied in full-aperture configuration in recent literature. In this paper, we develop MSM in limited-aperture configuration and derive an asymptotic formula of the corresponding indicator function. Based on the asymptotic formula, we then analyze the imaging performance of the proposed method depending on the range of measurement directions and the geometric, material properties of inhomogeneities. Furthermore, we propose a modified numerical scheme with multi-frequency measurements that improve imaging performance, especially for small anomalies. Numerical simulations are presented to validate the analytical results. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics of a stochastic SIR epidemic model with saturated incidence is investigated. Firstly, we prove that the system has a unique global positive solution with any positive initial value. Then we verify that random effect may lead the disease to extinction under a simple condition. Thirdly, we establish a sufficient condition for persistence in the mean of the disease. Moreover, we show that there is a stationary distribution to the stochastic system under certain parametric restrictions. Finally, some numerical simulations are carried out to confirm the analytical results. [ABSTRACT FROM AUTHOR]

In this paper we look at the two dimensional stochastic differential equation (SDE) susceptible-infected-susceptible (SIS) epidemic model with demographic stochasticity where births and deaths are regarded as stochastic processes with per capita disease contact rate depending on the population size. First we look at the SDE model for the total population size and show that there exists a unique non-negative solution. Then we look at the two dimensional SDE SIS model and show that there exists a unique non-negative solution which is bounded above given the total population size. Furthermore we show that the number of infecteds and the number of susceptibles become extinct in finite time almost surely. Lastly, we support our analytical results with numerical simulations using theoretical and realistic disease parameter values. [ABSTRACT FROM AUTHOR]

In this paper synchronization of N -coupled chaotic oscillators with multi-scroll attractors is presented. N chaotic oscillators are coupled in regular and irregular topologies. The generalizations of the Genesio & Tesi and Chua’s chaotic oscillators are used as generators of multi-scroll attractors. An alternative scheme for computing the coupling strength is proposed. Synchronization is achieved through the coupling matrix and by using the resulting alternative values. In general, the range of values obtained with the proposed method is smaller than the one given by Wang & Chen method. The effectiveness of this coupling strength is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics of a stochastic SIS model with Lévy jumps are investigated. We first prove that this model has a unique global positive solution starting from the positive initial value. Then, taking the accumulated jump size into account, we find a threshold of the model, denoted by R ˜ 0 , which completely determines the extinction and prevalence of the disease: if R ˜ 0 < 1 , the disease dies out exponentially with probability one; if R ˜ 0 > 1 , the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease. From the view of epidemiology, the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics. Moreover, we find that Lévy noise can suppress disease outbreak. Finally, we introduce some numerical simulations to support the main results obtained. [ABSTRACT FROM AUTHOR]

In this paper we present a one-dimensional model of blood flow in a vessel segment with an elastic wall consisting of several anisotropic layers. The model involves two variables: the radial displacement of the vessel’s wall and the pressure, and consists of two coupled equations of parabolic and hyperbolic type. Numerical simulations on a straight segment of a blood vessel demonstrate that the model can produce realistic flow fields that may appear under normal conditions in healthy blood vessels; as well as flow that could appear during abnormal conditions. In particular we show that weakening of the elastic properties of the wall may provoke a reverse blood flow in the vessel. [ABSTRACT FROM AUTHOR]

This paper considers crow–cuckoo–cat systems in which crows are the host, cuckoos are the parasite, cats are the predator of crow nests, and cuckoo chicks in the nests reveal a mix of caustic and repulsive compounds that repel and deter cats. An over 16-year observation on the crow–cuckoo–cat system shows that the parasite and its host can be mutualistic in the presence of predators (Canestrari et al., 2014). In order to exhibit mechanisms by which the mutualism occurs, a crow–cuckoo–cat model is formed in this work. Global dynamics of the model demonstrate that cats’ predation ability and converting efficiency are crucial to the occurrence of mutualism. When the predation/efficiency is low, cats would be driven into extinction by cuckoos. When the predation/efficiency is intermediate, the three species coexist and interaction outcomes between crows and cuckoos change from parasitism to commensalism and mutualism as the deterrence effect increases. When the predation/efficiency is high, cats would drive cuckoos into extinction if the deterrence is weak. If the deterrence is strong, either cuckoos or cats go extinct, where the species with higher initial density persists. Therefore, results in this work show the empirical observation by Canestrari et al. (2014), and predict situations that have not been observed by Canestrari et al. (2014). Numerical simulations display that the crow–cuckoo–cat model fits the observation well. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical solution of the equations governing two-phase gas–magma mixture in the framework of thermodynamically compatible systems theory. The equations constitute a non-homogeneous system of nonlinear hyperbolic conservation laws. A total variation diminishing (TVD) slope limiter center (SLIC) numerical scheme, based on the Riemann problem, is presented and applied for the solution of the initial boundary value problem for the equations. The model equations and the numerical methods are systematically assessed through a series of numerical test cases. Simulation results are compared and validated with different model equations available in the literature. The computed results compare well with the exact results provided for validation. Strong evidence shows that the model and the methods are accurate, robust and conservative. The model correctly describes the formation of shocks and rarefactions in two-phase gas–magma flow. [ABSTRACT FROM AUTHOR]

The paper deals with an investigation of velocity field in a tank stirred by a standard Rushton impeller located in the middle of the tank height. Time-resolved PIV method was used to measure the angle-resolved velocity field near the impeller blades in horizontal and vertical planes as well. Based on a simplified criterion λ 2 < 0 the location, size and strength of trailing vortices behind the blades were determined. The measurements were carried out in two tanks of diameters T = 0.3 and 0.4 m and at mixing Reynolds numbers in a range 3.3–4.9 × 10 4 . Simultaneously a detached eddy simulation (DES) was performed for the tank diameter T = 0.3 m and rotation speed 200 rpm ( Re M = 3.3 × 10 4 ). The simulation results are compared with the experimental data. [ABSTRACT FROM AUTHOR]

The aim of this paper is to review and classify the different methods that have been developed to enable stable long time simulations of the Vlasov–Maxwell equations and the Maxwell equations with given sources. These methods can be classified in two types: field correction methods and source correction methods. The field correction methods introduce new unknowns in the equations, for which additional boundary conditions are in some cases non trivial to find. The source correction consists in computing the sources so that they satisfy a discrete continuity equation compatible with a discrete Gauss’ law that needs to be defined in accordance with the discretization of the Maxwell propagation operator. [ABSTRACT FROM AUTHOR]

This paper deals with output consensus problem of heterogeneous multi-agent systems. The cases of leaderless and leader-following are considered. For each case, a dynamic consensus protocol is proposed, in which the parameters are dependent on the solution of a regulation equation and a homogeneous system. The homogeneous system can be analyzed by full-developed technique in homogenous multi-agent systems. Furthermore, dynamic regulators based on the state observers also are presented which is suitable for the case that the system states cannot be obtained. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. [ABSTRACT FROM AUTHOR]

This paper concerns the numerical study for the generalized Rosenau–Kawahara-RLW equation obtained by coupling the generalized Rosenau-RLW equation and the generalized Rosenau–Kawahara equation. We first derive the energy conservation law of the equation, and then develop a three-level linearly implicit difference scheme for solving the equation. We prove that the proposed scheme is energy-conserved, unconditionally stable and second-order accurate both in time and space variables. Finally, numerical experiments are carried out to confirm the energy conservation, the convergence rates of the scheme and effectiveness for long-time simulation. [ABSTRACT FROM AUTHOR]

In this paper, by applying a nonstandard finite difference scheme, we formulate a discretized SIRVS epidemic model which takes into account vaccination. Under quite weak assumptions, the threshold value conditions on permanence and extinction of disease are established. Some new threshold values in product forms R 0 * and R 1 * are obtained. We show that the disease is permanent if R 0 * > 1 , and if R 1 * < 1 , then the disease is extinct. When the model degenerates into a periodic model, a sharp threshold value R 0 is obtained for permanence versus extinction of disease. In order to illustrate our analytic analysis, some numerical simulations are also included in the end. [ABSTRACT FROM AUTHOR]

The accurate simulation of compressible multi-phase flows with surface tension effects is currently still one of the most challenging problems in computational fluid dynamics (CFD). The basic difficulties are the capturing of the correct interface dynamics between the two fluids as well as the computation of the interface curvature. In this paper, we present a novel path-conservative finite volume discretization of the continuum surface force method (CSF) of Brackbill et al. to account for the surface tension effect due to curvature of the phase interface. This is achieved in the context of a diffuse interface approach , based on the seven equation Baer–Nunziato model of compressible multi-phase flows. Such diffuse interface methods for compressible multi-phase flows including capillary effects have first been proposed by Perigaud and Saurel. In the CSF method, the surface tension effect is replaced by a volume force, which is usually integrated as a classical volume source term. However, since this source term contains the gradient of a color function that is convected with the flow velocity, we propose to integrate the CSF source term as a non-conservative product and not simply as a source term, following the ideas on path-conservative finite volume schemes put forward by Castro and Parés. For that purpose, we use the new generalized Osher-type Riemann solver (DOT), recently proposed by Dumbser and Toro and compare it with a path-conservative Roe and Rusanov scheme. Via numerical evidence we can show that if the curvature computation is exact, our new scheme is well-balanced for a steady circular bubble in equilibrium according to the Young–Laplace law. This means that the pressure jump term across the interface in the momentum equation is exactly balanced with the surface tension force. We apply our scheme to several one- and two-dimensional test problems, including 1D Riemann problems, an oscillating droplet, as well as a deforming droplet initially attached to a wall and which is subject to gravity and surface tension forces. Finally, we also check the rising of a gas bubble due to buoyancy forces. We compare our numerical results with those published previously in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a two-species stochastic non-autonomous food chain predator-prey system with jumps is proposed and studied. The asymptotic properties of the system are examined. Sufficient conditions for extinction, non-persistence in the mean, weak persistence in the mean and weak persistence of the system are established. Results show that Lévy jumps are disadvantageous for the persistence of the populations. Furthermore, we also show that the solution is stochastically ultimate bounded under certain conditions. Some examples together with numerical simulations are introduced to illustrate our main results. [ABSTRACT FROM AUTHOR]

Class of algorithms referring to the affine projection algorithms (APA) applies updates to the weights in a direction that is orthogonal to the most recent input vectors. This speeds up the convergence of the algorithm over that of the normalized least mean square (NLMS) algorithm, especially for highly colored input processes. In this paper a new statistical analysis model is used to analyze the APA class of algorithms with unity step size. Four assumptions are made, which are based on the direction vector for the APA class. Under these assumptions, deterministic recursive equations for the weight error and for the mean-square error are derived. We also analyze the steady-state behavior of the APA class. The new model is applicable to input processes that are autoregressive as well as autoregressive-moving average, and therefore is useful under more general conditions than previous models for prediction of the mean square error of the APA class. Simulation results are provided to corroborate the analytical results. [ABSTRACT FROM AUTHOR]

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]

This paper investigates robust stability for fractional-order (FO) singular nonlinear systems. The FO system is disturbed by external uncertainty and disturbance. A central analysis technique is enabled by proposing a fundamental boundedness lemma, for the first time. This lemma is used for robust stability analysis of FO systems, especially for Mittag–Leffler stability analysis of FO nonlinear systems. More importantly, how to obtain a more accurate bound is given to reduce conservative. An FO proportional-derivative (PD) controller is proposed to normalize the FO singular system. Furthermore, a criterion for stability of the normalized FO nonlinear systems is provided by linear matrix inequalities (LMIs). Finally, two illustrative simulation examples are presented to illustrate effectiveness of the proposed stability notion. [ABSTRACT FROM AUTHOR]

In this paper, an SEIR epidemiological model with saturation incidence and a time delay describing the latent period of the disease is investigated, where it is assumed that the susceptible population is subject to logistic growth in the absence of the disease. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed. The existence of Hopf bifurcations at the endemic equilibrium is established. By means of Lyapunov functionals and LaSalle’s invariance principle, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable and the disease dies out; if the basic reproduction number is greater than unity, sufficient conditions are obtained for the global stability of the endemic equilibrium. Numerical simulations are carried out to illustrate some theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with establishing some stability and input-to-state stability (ISS) properties in terms of two different measures, h 0 and h , for nonlinear systems of stochastic differential equations of Itô type. To analyze these properties, classical Lyapunov’s method and a comparison principle are used. To justify the proposed theoretical results, applications to state estimating systems of Luenberger type and feedforward (or cascade) systems enhanced with numerical examples and simulations are presented. [ABSTRACT FROM AUTHOR]

This paper studies a three-dimensional multiple chaotic system with three quadratic nonlinear terms. The system is shown to exhibit multiple periodic attractors and multiple chaotic attractors including a four-scroll chaotic attractor. It is shown analytically and numerically that any neighborhood of the four-scroll chaotic attractor contains repelling sets with positive Lebesgue measures. Moreover, in terms of incommensurate fractional order systems, a simple fractional differentiator-based controller is designed to suppress chaos. Some basic dynamical behaviors of the system are investigated through analytical techniques and numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, a delayed ratio-dependent predator–prey model with Holling type III functional response and stage structure for the predator is considered. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established. By utilizing normal form method and center manifold theorem, the explicit formulas which determine the direction of Hopf bifurcation and the stability of bifurcating period solutions are derived. Finally, numerical simulations supporting the theoretical analysis are given. [ABSTRACT FROM AUTHOR]

Dijkstra’s algorithm to solve the shortest path problem (SPP) is a very well-known algorithm. When applied to real situations, although the shortest path can be computed with Dijkstra’s algorithm, it is not always the one that is chosen. In traffic situations, for example, the driver may not know the exact length of the lanes or the shortest path to follow. Even more compelling is the fact that although the driver knows the shortest route, he/she may prefer choosing a different route. In this paper we present the new algorithm PEDA (Probabilistic Extension of Dijkstra’s Algorithm) which introduces probabilistic changes in the weight of the edges and also in the decisions when choosing the shortest path. When PEDA is applied to traffic flow, more realistic simulations, in which the shortest path is not always chosen, are obtained. This more accurately simulates the more normal behavior of drivers. As an example of an application, we introduce the ATISMART + model, an extension of the ATISMART model, where an accelerated-time simulation of car traffic in a smart city was described. In that previous work, all cars in the system used Dijkstra’s algorithm to choose improved ATISMART + model, for accelerated time simulations of traffic flow in smart cities, uses the new PEDA algorithm. The results obtained show that ATISMART + produces more realistic simulations considering different drivers’ behaviors. [ABSTRACT FROM AUTHOR]

Optimization of water distribution is a crucial issue which has been targeted by many modeling tools. Useful models, implemented several decades ago, need to be updated and implemented in more powerful computing environments. This paper presents the distributed and redesigned version of a legacy hydraulic simulation software written in Fortran (IRMA) that has been used for over 30 years by the Société du Canal de Provence in order to design and to maintain water distribution networks. IRMA was developed aiming mainly at the treatment of irrigation networks – by using the Clément demand model and is now used to manage more than 6000 km of piped networks. The complexity and size of networks have been growing since the creation of IRMA and the legacy software could not handle the simulation of very large networks in terms of performance. This limitation has finally imposed to redesign the code by using modern tools and language (Java), and also to run distributed simulations by using the ProActive Parallel Suite. [ABSTRACT FROM AUTHOR]

The paper refers about the development of a fast computational code, which should be able to provide an approximate information about the three-dimensional flow field in a multistage turbine. The code is based upon the solution of circumferentially averaged Euler equations coupled with the thermodynamic, geometry and loss prediction models. The computational domain is the meridional cut of a turbine. The Euler equations are solved by a finite volume solver with the AUSM type flux. Initial tests showed, that developed solver is able to predict well radial distributions of flow parameters upstream and downstream considered blade cascades at a fraction of CPU time compared to fully three-dimensional simulations. [ABSTRACT FROM AUTHOR]

This paper is devoted to analysis of shrinkage and damage of autoclaved aerated concrete. Coupled hydro-thermo-mechanical analysis is used for detailed description of drying which causes the shrinkage and damage consequently. The heat and moisture transfer are fully coupled while the staggered approach is used between transports and mechanics. Material parameters were obtained from laboratory experiments and the results of numerical simulations correspond with measured data. [ABSTRACT FROM AUTHOR]

In this paper, we firstly present the general framework of calculation of normal forms of non-resonance and weak resonance double Hopf bifurcation for the general retarded functional differential equations by using the normal form theory of delay differential equations due to Faria and Magalh a ˜ es. Then, the dynamical behavior of van der Pol–Duffing oscillator with delayed position and velocity feedback is considered. Specifically, the dynamical classification near the double Hopf bifurcation point is investigated by analyzing the obtained normal form. Finally, the numerical simulations support the theoretical results and present some interesting phenomena. [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]

The main aim of this paper is to discuss the neutral predator–prey model with Hassell–Varley type functional response and two time-varying delays. Some new sufficient conditions are obtained for the existence of positive periodic solutions by applying the coincidence degree theorem. Finally, numerical simulations are then carried out as supporting evidences of our analytical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the stochastic disease dynamics of an SIS epidemic model on two patches incorporating media coverage. We give the global existence and positivity of the solutions, and the sufficient conditions for almost surely exponentially stability of the disease-free equilibrium, which means that the disease will be stochastic extinction. Furthermore, we perform some numerical simulations to validate the analytical finding. [ABSTRACT FROM AUTHOR]

In this paper, a special recurrent neural network termed Zhang neural network (ZNN) is proposed and investigated for solving online time-varying linear matrix–vector inequality (LMVI) via equality conversion. That is, by introducing a time-varying vector (of which each element is great than or equal to zero), such a time-varying linear inequality can be converted to a time-varying matrix–vector equation. Then, the ZNN model is developed and investigated for solving online the time-varying matrix–vector equation (as well as the time-varying LMVI) by employing the ZNN design formula. The resultant ZNN model exploits the time-derivative information of time-varying coefficients. Computer-simulation results further demonstrate the efficacy and superiority of the proposed ZNN model for solving online the time-varying LMVI (and the converted time-varying matrix–vector equation). [ABSTRACT FROM AUTHOR]

We study the evacuation model in the framework of game theory and propose a new model in which individuals have preferential directions. In the proposed model, pedestrians are divided into three parts with each part has its own preferred directions. Based on the new model, different positions of a door in rectangle and square rooms were tested to investigate how door positions impact on escape time. In this way, the best location can be found. Simulation results show that no matter how big the room is and how many occupants in it are, the optimal position of a door always locates in the middle of the wall. The optimal door position fits intuitive feeling of human, which also verifies the effectiveness of the proposed model. Therefore, our model simulates the process of pedestrian evacuation naturally. The work in this paper may provide guidance for the reduction of casualties in the event of a real-life escape. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the disease dynamics of a reaction–diffusion Feline Panleukopenia virus model incorporating direct and indirect transmissions as well as spatially environmental heterogeneity. We derive a basic reproduction number and show that the disease-free equilibrium will be locally stable if the basic reproduction number is below one, which means that the disease will be extinct. Furthermore, we perform some numerical simulations to explore the impact of the heterogeneous environment on the disease dynamics. [ABSTRACT FROM AUTHOR]

Tabulation method is usually adopted to describe the mapping relation of the analytic function of the local rules of Cellular Automaton. Although tabulation method is quite suitable to describe the mapping relation among discrete variables, there are numerous if-else sentences for the state decision of independent variables in computer programming. In this paper, we define an analytic function of the local rules of an Elementary Cellular Automaton by constructing the recognition function of the states of the cell and the neighbors. Therefore, a huge number of calculations by if-else sentences are transferred to the function calculation due to the adoption of the function of the local rules during the evolution of the ECA. Finally, the simulation results show that the programming structure is optimized and the programming efficiency is enhanced. In addition, the proposed method can also be extended to other 2-state cellular automata. [ABSTRACT FROM AUTHOR]

In this paper we concern the investment process in a duopoly game played by heterogeneous players. A discrete and dynamic system is built for the case that a boundedly rational player adjusts its investment decision by the locally marginal profit and a naïve player chooses its strategy according to the opponent’s action in the previous period. By stability analysis of the system, we show that the boundary equilibrium is unstable and obtain the stability conditions for the interior equilibrium. Numerical simulations are used to provide evidence for the influence of the model parameters on the system stability and on the complicated behaviors in the system evolution. It is shown that the system with varying model parameters may drive to chaos and the loss of stability may be caused by period doubling bifurcations or Neimark–Sacker bifurcations. It is also shown that the time-delayed feedback control method can be used to keep the system from instability and chaos. All the numerical simulations show that the capital depreciation rate has great influence on the system evolution: a smaller depreciation rate has a stronger stabilization effect on the survival of the system and makes the system easier to control from chaos. [ABSTRACT FROM AUTHOR]

This paper is concerned with a logistic equation with spatio-temporal delay. The local asymptotic behavior of positive constant steady-state solution of the equation is considered. In particular, by using the iterative technique, sufficient conditions are established for the existence of traveling wave front solution connecting the zero and the positive constant steady-state solution. Finally, numerical simulations supporting the theoretical analysis are also included. [ABSTRACT FROM AUTHOR]

Resource matching and recommendation is an important topic in the field of cloud computing. While a lot of cloud resource discovery and negotiation models have been proposed, resource matching and recommendation issues have often been neglected, such as the utilization of attribute weights and the collaborative application of empirical data, price utility and so on. To cope with this challenge, we focus on designing a novel resource recommendation method which can regulate multi-attribute matching between provider solutions and customer demands in this paper. At first, we describe a resource matching algorithm that considers both functional requirements and QoS attributes. Then, we propose a resource recommendation method for cloud computing system that integrates price utility, multi-attribute matching metric and group customer evaluation. Finally, the extensive simulation results demonstrate that our proposed method is effective in various simulated scenarios. Current results are of high significance to design an efficient resource matching and recommendation with guaranteed QoS requirements under the realistic cloud computing circumstances. [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]

The paper deals with the problem of control and synchronization of hyperchaotic systems. The proposed control method is based on the predictive principle which employ an instantaneous control input to guarantee the convergence of the chaotic trajectory towards an unstable equilibrium point. The synchronization is constructed around the drive-response principle. Numerical simulations on some hyperchaotic systems are given to demonstrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, based on the stability theorem of discrete systems and the idea of control theory, the novel three dimensional discrete hyperchaotic Hénon map is analyzed and the feedback and adaptive control methods are presented, respectively to stabilize hyperchaotic Hénon map at different one-periodic orbits. The two methods are compared in different aspects. Numerical simulations show the feasibility and effectiveness of this method. [ABSTRACT FROM AUTHOR]

In this paper, three types of third-order partial differential equations (PDEs) are classified to be third-order PDE of type I, II and III. These classes of third-order PDEs usually occur in many subfields of physics and engineering, for example, PDE of type I occurs in the impulsive motion of a flat plate. An efficient numerical method is proposed for PDE of type I. The PDE of type I is converted to a system of third-order ordinary differential equations (ODEs) using the method of lines. The system of ODEs is then solved using direct Runge–Kutta which we derived purposely for solving special third-order ODEs of the form y ‴ = f ( x , y ) . Simulation results showed that the proposed RKD-based method is more accurate than the existing finite difference method. [ABSTRACT FROM AUTHOR]

In this paper, the effect that produces the Local Linearization of the embedded Runge–Kutta formulas of Dormand and Prince for initial value problems is studied. For this, embedded Locally Linearized Runge–Kutta formulas are defined and their performance is analyzed by means of exhaustive numerical simulations. For a variety of well-known test equations with different dynamics, the simulation results show that the locally linearized formulas exhibit significant higher accuracy than the original ones, which implies a substantial reduction of the number of time steps and, consequently, a sensitive reduction of the overall computational cost of their adaptive implementation. [ABSTRACT FROM AUTHOR]

In this paper, a reduced-order extrapolation algorithm (ROEA) based on proper orthogonal decomposition (POD) technique and classical stabilized finite volume element (SFVE) method for non-stationary Stokes equations is established. The error estimates between the ROEA solutions and the classical SFVE solutions and the implementation for solving ROEA are provided. Some numerical examples are used to verify that the results of numerical computation are consistent with theoretical conclusions. Moreover, it is shown that ROEA based on SFVE formulation and POD method is feasible and efficient for solving non-stationary Stokes equations. [ABSTRACT FROM AUTHOR]

Successful design and operation of hydraulic structures require more effective and reliable tools to be used in a variety of practical problems, including bottom outlets, intakes and/or spillways. Until recently, physical modeling has been the principal approach in studying the flow pattern and behavior of such structures. The main concerns might generally be related to estimating of discharge coefficients, frictional losses, details of local flow patterns, position of the free surface, and air entrainment. The application of a new developed numerical modeling for free surface flow simulation in gated tunnels is presented here. Among various parameters, the free surface profile, pressure distribution and discharge of the flow passing through gated hydraulic structures are considered in the present study. The solution of free surface flow problems is usually carried out through an iterative process due to unknown geometry and nonlinear boundary conditions. Therefore, the solution of these problems using traditional numerical methods presents some difficulties since the computational mesh needs to be modified for each iteration. The application of the smoothed fixed grid finite element method in the solution of free surface flow problems is investigated in this paper. The main advantage of the proposed method is that it is based on non-boundary-fitted meshes which simplify the solution procedure. In this method, the gradient smoothing technique is used to facilitate formulation of boundary intersecting elements. To evaluate the applicability of the proposed method, three representative examples are solved and the results are compared with experimental and numerical results available in the literature. The results of the present study indicated the power of smoothed fixed grid finite element method in solving the free surface potential flows through gated hydraulic structures. [ABSTRACT FROM AUTHOR]

In this paper, we propose one adaptive pinning synchronization scheme in complex networks, whose adaptive law is simple and flexible. Most of all, we find the decreasing law of maximum eigenvalues of the principal submatrices for coupling matrix, and give a method of quickly calculating pinning nodes in complex networks with binary search algorithm. Furthermore, we extend the method to the pinning synchronization scheme with linear feedback control. Numerical simulations give effectiveness of the adaptive pinning synchronization in a scale-free network, and the relations between maximum eigenvalue sequence of the principal submatrices and the number of pinning nodes under the conditions of three pinning strategies in a scale-free network and a small-world network, respectively. [ABSTRACT FROM AUTHOR]

We propose a predator–prey ecoepidemic model with parasitic infection in the prey. We assume infection time delay as the time of transmission of disease from susceptible to infectious prey. We examine the effects of supplying additional food to predator in the proposed model. The essential theoretical properties of the model such as local and global stability and in addition bifurcation analysis is done. The parameter thresholds at which the system admits a Hopf bifurcation are investigated in presence of additional food with non-zero time lag. The conditions for permanence of the system are also determined in this paper. Theoretical analysis results are verified through numerical simulations. By supplying additional food we can control predator population in the model. Most important observation is that we can control parasitic infection of prey species by supplying additional food to predator. Eliminating the most infectious individuals from the prey population, predator quarantine the infected prey and prevent the spreading of disease. [ABSTRACT FROM AUTHOR]

Cognitive processing by intelligent systems involves the deletion of information in favor of higher level abstractions. This process can be addressed through the physics of computation but a formal model that explains this process has not been proposed yet. In this short paper, we propose a model that through physical constraints only generates optimal solution to the collapse of n objects into n sets. A numerical simulation of the model results in a logarithmic function of information loss and condensation that perfectly fits our knowledge of cognitive processes. [ABSTRACT FROM AUTHOR]

In this paper, we propose nonpolynomial and Hermite nonpolynomial interpolation with multiple parameters and present method to determine optimal value of parameters which generate minimum error in approximation. The generalized error analysis results for nonpolynomial and Hermite nonpolynomial interpolations are derived. We establish theoretical relationship among nonpolynomial, polynomial interpolation and the Fourier series, and propose solution to Runge’s phenomenon through nonpolynomial interpolation. The Hermite nonpolynomial cubic spline, nonpolynomial cubic spline interpolation methods and their error analysis are presented. Numerical simulations are carried out for the analysis of error in cubic spline interpolations. Proposed method is applied to the analysis of various time series to show comparison in errors between polynomial and nonpolynomial spline interpolations, and to Empirical Mode Decomposition (EMD) to illustrate practical usefulness of the results. [ABSTRACT FROM AUTHOR]