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The future use of eddy resolving simulations (ERS) such as Large Eddy Simulation (LES), Direct Numerical Simulation (DNS) and related approaches in aerospace is explored. The turbulence modeling requirements with respect to aeroengines and aircraft is contrasted. For the latter, higher Reynolds numbers are more prevalent and this especially gives rise to the need for the hybridization of ERS methods with Reynolds Averaged Navier–Stokes (RANS) approaches. Zones where future use of pure ERS methods is now possible and those where hybridizations with RANS will be needed is outlined. The major focus is the aeroengine for which the component scales are much smaller. This gives rise to generally more benign Reynolds numbers. The use of eddy resolving methods in a wide range of zones in an aeroengine is discussed and the potential benefits and also cost drawbacks with such approaches noted. The tension when using such computationally intensive calculations in an area where the coupling of components and even the airframe and engine is becoming increasingly important is explored. Also, the numerical methods and meshing requirements are considered and the implications of ERS methods for future numerical algorithms. It is postulated that such simulations are ready now for niche uses in industry. However, to perform the scale of simulations that industry requires, to meet pressing environmental needs, challenges remain. For example, there is the need to develop optimal numerical methods that both map to the accuracy requirements for ERS and also future computer architectures. [ABSTRACT FROM AUTHOR]

• kinetic description of a binary game • quasi-invariant limit • numerical simulations This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness. [ABSTRACT FROM AUTHOR]

• For the first time, approximate expressions of periodic solutions of delayed non-smooth dynamical system are obtained. • Approximate expressions of non-impacting and impacting periodic solutions of delayed non-smooth system are obtained. • For the first time, prediction of periodic oscillations of delayed non- smooth TCP-RED system are executed successfully. • Three kinds of bi-stability have been found. • An impacting periodic solution traversing both thresholds has been also obtained. • A route to chaos, i.e., intermittent to chaos, has been also found. • Some solutions seem like periodic solutions are found to be complex oscillations with high frequency and small amplitude. This paper has attended to obtain the approximate analytical expressions of periodic solutions in the delayed non-smooth Internet TCP-RED congestion control system employing the semi-analytical method named as the harmonic balance method with alternating frequency/time (HB-AFT) domain technique. For the first time, the methodology presented herein provides the accurate approximate analytical expressions of periodic solutions, including the non-impacting periodic solutions and impacting periodic solutions, in the non-smooth dynamical system with time-delays. They agree very well with the results of numerical simulations by MATLAB. It implies that the proposed method in this paper is accurate and effective. Furthermore, rich dynamics of this delayed non-smooth system is discovered in the present paper. Three kinds of bi-stability, i.e. coexistence of asymptotically stable equilibrium and equilibrium, equilibrium and periodic solution, periodic solution and periodic solution, have been found in the system with the variation of the delay. And the grazing solution, the impacting solution traversing both the lower threshold T min and the larger threshold T max , and a route to chaos, i.e., intermittent to chaos, have been also obtained by varying the delay employing numerical method. [ABSTRACT FROM AUTHOR]

• Unlike [7,8] and [31] , which designs the controller under the assumption that the system states are available and the Lipschitz condition is needed for the nonlinear term. This paper designs the NNs-based observer to estimate unknown states and approximate nonlinear terms simultaneously, which guarantees the robustness and stability of the MASs can be improved. • Compared to Yang et al. [20] , He et al. [21] , Ma et al. [22] , Liu et al. [23] , Fu et al. [24] , Zhao and Yang [25] dealing with deception attacks by using the global topology information, the fully distributed intrusion-tolerance control scheme is designed in this paper to achieve the consensus control for multi-agent systems that suffer from deception attacks, which only uses adjacent agent information in the design process of controller. In addition, the impact of the error signal injected by the attacker on the adaptive parameters are considered. This paper proposes a novel resilient intrusion-tolerance control scheme to solve the consensus control problem of multi-agent systems (MASs) under deception attacks. Consider the state unavailability of MASs with unknown nonlinear terms, the unmeasurable state is estimated by designing the neural-networks(NNs)-based observer. Then, a fully distributed intrusion-tolerant adaptive protocol is developed to implement the consensus control task. The designed control strategy only involves the agent states that interact with the neighboring agent and does not relate to the whole communication topology information. The designed controller can ensure that the consensus error of the nonlinear MASs is eventually ultimately bounded under deception attacks. Finally, a numerical simulation is provided to verify the feasibility of the designed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we explore complete synchronization for the delayed discrete-time fractional-order competitive neural networks (DDFCNNs). Firstly, several definitions with respect to Caputo fractional-order difference are given. Next, a novel method for proving Caputo fractional difference inequality of 2 k -norm function is given, then by making use of the inequality we prove and Hanalay inequality, some sufficient criteria on complete synchronization of DDFCNNs are obtained under the linear feedback controller. In the end, some numerical simulations are given to verify effectiveness of the theoretical consequences. • A novel approach is put forward to prove discrete-time Caputo fractional inequality on 2 k -norm function based on some definitions and lemmas of fractional difference. • To achieve complete synchronization of DDFCNNs, we design a brief linear feedback controller, which is easier than adaptive controller designed in [34]. • Several sufficient conditions on complete synchronization of DDFCNNs are attained by our established lemma. [ABSTRACT FROM AUTHOR]

The motivation of this paper is inspired by the research of Zanette et al. (2011) [4] , which reveals that the perception of predation risk can reduce the number of juvenile prey. To investigate how fear affects the behavior of prey population, we formulate a predator-prey model with a stage structure for prey in which adult prey is undergoing the interference of fear. First, the dynamic properties of the model are analyzed, including the existence and stability of equilibria, bifurcations dynamics, such as transcritical, saddle-node, and Hopf bifurcations. Our results reveal that fear can promote the formation of the stability of the model by transforming it from an unstable state to a stable state. Numerical simulations and theoretical analysis indicated that when the level of fear reaches 25.4, the number of juvenile prey affected by fear decreases by 40% compared to those not affected by fear. Terrifyingly, the predators are on the brink of extinction in high levels of fear. Moreover, we examine the impact of time delay on fear in the previous model as prey needs some time to assess the predation risk. Some dynamic characteristics of this delayed model are also analyzed. Results indicate that the fear effect is conducive to generating a stable state, while delay is detrimental to generating a stable state, leading to limit cycles or even chaos. • A stage-structure predator-prey model with fear and delay is proposed. • The feasibility equilibria and bifurcation dynamics of the model are studied. • Fear can transform a model from an unstable state to a stable state. • Delay is detrimental to generating a stable state, leading to limit cycles or chaos. [ABSTRACT FROM AUTHOR]

This paper investigates practical stabilization of multi-links highly nonlinear Takagi-Sugeno fuzzy complex networks with Lévy noise (MHFNLs) via aperiodically intermittent discrete-time observation control (AIDOC). It is worth pointing out that AIDOC is considered into MHFNLs for the first time. Due to the difficulty of satisfying linear conditions in real life, polynomial growth conditions are used instead of linear growth conditions. Meanwhile, a global Lyapunov function is constructed and sufficient conditions which can remain MHFNLs practically stable are gained. Finally, an application and its numerical simulations are presented to verify the effectiveness and availability of the theoretical results. • Polynomial growth conditions are used instead of linear growth conditions. • We consider Lévy noise and construct a global Lyapunov function. • Aperiodically intermittent discrete-time observation control is designed. • The theoretical result is applied to Van der Pol-Duffing oscillator. [ABSTRACT FROM AUTHOR]

Abstract The paper is concerned with a qualitative analysis for a nonlinear second-order parabolic problem, subject to non-homogeneous Cauchy–Neumann boundary conditions, extending the types already studied. Under some certain assumptions, we prove the existence, estimate, regularity and uniqueness of a classical solution. The considered nonlinear second-order anisotropic diffusion model is then particularized for an image restoration task. The resulted PDE-based model is solved numerically by constructing a finite-difference based approximation algorithm that is consistent to the model and converges fast to its solution. An effective detail-preserving image filtering scheme that removes successfully the white additive Gaussian noise while overcoming the unintended effects is thus obtained. Our successful image restoration and method comparison results are also discussed in this paper. [ABSTRACT FROM AUTHOR]

Abstract In this paper, for the first time, fractional Taylor–Jumarie series expansion is used to solve a glass of time-fractional delay partial differential equation by piecewise interpolation reproducing kernel method (RKM), this class of equations describe sand motion model in beach formation. The aim of this work is to obtain more accurate numerical solution by fractional Taylor–Jumarie series expansion and piecewise interpolation technique. Three numerical experiments are provided to show the advantage of this method, the results show the characteristics of sand motion. The research in this paper is the theoretical basis for further sand motion study. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the direct meshless local Petrov–Galerkin (DMLPG) method is applied to find the numerical solution of coupled damped nonlinear Schrödinger system in one, two and three-dimensional spaces. The propagation properties of single soliton, double and triple solitons of coupled damped nonlinear Schrödinger system are simulated and the interactions between these solitons are studied numerically. The efficient time differencing Runge–Kutta method is utilized for the time discretization. DMLPG shifts the numerical integrations over low-degree polynomials rather than over complicated shape functions and this significantly increases the computational efficiency of DMLPG in comparison with the other meshless local weak form methods especially in two and three dimensions. The main aim of this paper is to show that the DMLPG method can be simply used for solving high-dimensional system of non-linear partial differential equations especially coupled damped nonlinear Schrödinger system. The numerical results confirm the good efficiency of the proposed method for solving our model. [ABSTRACT FROM AUTHOR]

• Different from the state estimation and the controller design, this paper uses the method of system identification to study the security problem of FIR system in the quantized framework. • This paper considers the problem of the attacker, and gives the optimal attack strategy with attack energy limitation. • An encryption-type defense algorithm is presented to ensure the consistency of the identification algorithm when the system is under DoS attack. DoS (Denial-of-Service) attack is a very common network attack, under which it is of great practical significance to study the system performance. This paper addresses the security problem in the identification of FIR (Finite Impulse Response) systems with binary-valued observations when the data is under DoS attacks in the process of transmission. From the attacker's point of view, the optimal attack strategy to maximize the estimation error is given, where the attack is constrained by the average and the maximum energies. From the defender's point of view, the encryption-type defense scheme is proposed, and the sufficient and necessary conditions are given to make the algorithm consistent. The effectiveness of the conclusion is verified by numerical simulation. Finally, the correctness of the obtained conclusion is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

In the recent paper entitled “Hopf bifurcation analysis and ultimate bound estimation of a new 4-D quadratic autonomous hyper-chaotic system” in [Appl. Math. Comput. 291 (2016) 323–339] by Amin Zarei and Saeed Tavakoli, they proposed the following new four-dimensional (4-D) quadratic autonomous hyper-chaotic system: x 1 ˙ = a ( x 2 − x 1 ) , x 2 ˙ = b x 1 − x 2 + e x 4 − x 1 x 3 , x 3 ˙ = − c x 3 + x 1 x 2 + x 1 2 , x 4 ˙ = − d x 2 , which generates double-wing chaotic and hyper-chaotic attractors with only one equilibrium point. Combining theoretical analysis and numerical simulations, they investigated some dynamical properties of that system like Lyapunov exponent spectrum, bifurcation diagram, phase portrait, Hopf bifurcation, etc. In particular, they formulated a conclusion that the system has the ellipsoidal ultimate bound by employing the method presented in the paper entitled “Ultimate bound estimation of a class of high dimensional quadratic autonomous dynamical systems” [Int. J. Bifurc. Chaos, 21(09) (2011), 2679–2694] by P. Wang et al. However, by means of detailed theoretical analysis, we show that both the conclusion itself and the derivation of its proof in [Appl. Math. Comput. 291 (2016) 323–339] are erroneous. Furthermore, we point out that the method adopted for studying the ultimate bound of that system is not applicable at all. Therefore, the ultimate bound estimation of that system needs further studying in future work. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the cooperative robust consensus tracking problem of uncertain networked Euler-Lagrange systems (NELSs) with time-varying delays and output constraints. By systematically integrating the neural network (NN) adaptive technique and the logarithmic type Barrier Lyapunov Function (BLF) in combination with the additional robust control law, two distributed robust consensus schemes for uncertain NELSs are proposed for two cases of time-varying communication and input delays respectively, which can fully guarantee to constrain the output consensus error within a safety region simultaneously. Furthermore, numerical simulation examples are provided to demonstrate the comparable potential advantages of the proposed robust control law over some existing algorithms, including adaptability, stability, and robustness, as well as delay effects. • An NN-based robust controller is designed to effectively handle the uncertainty of NELSs. • Combining NN with BLF ensures the adaptability, stability, and robustness of the consensus tracking scheme for NELSs. • A unified analytical framework is developed by deriving upper bounds on the allowed values of communication and input delays. [ABSTRACT FROM AUTHOR]

This paper research downhole temperature distribution in oil production and water injection using reproducing kernel Hilbert space method (RKHSM) for the first time. The aim of this paper is that using the highly accurate RKHSM can solve downhole temperature problems effectively. According to 2-D mathematical models of downhole temperature distribution, the analytical solution was given in a series expansion form and the approximate solution was expressed by n -term summation of reproducing kernel functions which initial and boundary conditions were selected properly. Numerical results of downhole temperature distribution with multiple pay zones, in which different radial distance and different injection–production conditions (such as injection rate, injection temperature, injection time, oil layer thickness), were carried out by mathematical 7.0, and numerical results correspond to general knowledge and show that use RKHSM to research downhole temperature distribution is feasible and effective. [ABSTRACT FROM AUTHOR]

• This paper considers the finite-time contractive stabilization for impulsive systems with time-varying parametric uncertainties. • A class of aperiodic intermittent controller involving uncertain impulsive disturbance is designed. • In the framework of finite-time, relationships between impulsive disturbance, aperiodic control periods, and widths are established. This paper ensures finite-time stabilization (FTS) and finite-time contractive stabilization (FTCS) for impulsive systems with time-varying parametric uncertainties by investigating the design of an aperiodic intermittent controller, where uncertain impulsive disturbance is generated at the instants caused by the control action to the plant. Based on the Lyapunov methods, several sufficient conditions are proposed to guarantee the FTS and FTCS. In the framework of finite-time, two relationships between impulsive disturbance, aperiodic control periods, and aperiodic control widths are established to guarantee the FTS and FTCS for the system, respectively. Moreover, such two relationships can potentially increase the freedom of the designed control periods and control widths. Finally, two numerical simulations and a practical application are given to show the validity of the aperiodic intermittent controller. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of feedback fuzzy control design for networked systems involving both random measurement and actuation delays and subject to quantization and random packet dropout. It is assumed that system state or output signal is quantized before being communicated. The paper focuses initially on an observer-based output feedback fuzzy controller design and then derives a state feedback controller as special case. Sufficient conditions for the existence of an admissible fuzzy controller are established to ensure the exponential stability of the resulting closed-loop fuzzy system. Simulation experiments on a lab-scale four-tank system to demonstrate the applicability of the designed fuzzy control algorithm. [ABSTRACT FROM AUTHOR]

The backward substitution method is a newly developed meshless method that has been used for the simulation of many problems in science and engineering with high accuracy and efficiency. In this paper, we explore the feasibility of employing the backward substitution method for simulating two-dimensional incompressible flows. Two non-increment pressure correction projection methods are considered to decompose the original velocity and pressure coupling system into two boundary value problems of intermediate velocity and pressure. Then, two boundary value problems are solved by the backward substitution method in each time iteration step. Five numerical examples are provided to demonstrate the accuracy, computational efficiency and convergence of the method. Comparisons with some existing meshless methods verify the method's advantages and potential applications to engineering. • The backward substitution method is first raised for the simulation of incompressible flows. • Investigated effects of the time step and the number of collocation points on the accuracy. • Verification benchmark comprising several fluid flows problems. • Two projection methods are considered to verify the algorithm. • The algorithm is easily extended to three-dimensional incompressible flows. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the consensus problem of leaderless multi-agent systems with external disturbance under denial-of-service (DoS) attacks. First, the state predictor is constructed to reproduce the state information blocked during the active periods of DoS attacks. Then, a robust non-smooth consensus protocol is designed using the predictor states, which mitigates the open-loop phenomenon caused by the DoS attacks. Besides, we obtain the sufficient condition for agents to achieve consensus within a region, and demonstrate that the protocol can enhance the anti-disturbance and anti-attack capabilities of the systems. Finally, the theoretical results are verified through numerical simulations. • We introduce a non-smooth consensus protocol based on predictive data to enhance the resilience of multi-agent systems against attacks. The incorporation of distributed predictors prevents the system from entering an open-loop mode due to data unavailability during active periods of DoS attacks. This ensures the avoidance of severe uncontrolled divergence behaviors of multi-agent systems during active periods of attack, thus ensuring rapid consensus recovery as the dormant periods of DoS attack start. • As observed in the current research on multi-agent system control under DoS attacks, linear or sliding mode consensus algorithms are commonly employed. In this study, by incorporating non-smooth functions, the multi-agent system is endowed with faster convergence speed and stronger disturbance resistance capacity. • We incorporate the multiple inertially stabilized platforms system. The effectiveness and superiority of the proposed consensus protocol are demonstrated through comparison with traditional consensus protocols. This not only offers empirical substantiation for future investigations but also emphasizes the practical applicability of studying the consensus of first-order multi-agent systems with external disturbance under DoS attacks. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical simulation of the interaction of compressible viscous flow with a nonlinear elastic structure. The flow is described by the compressible Navier–Stokes equations written in the arbitrary Lagrangian–Eulerian (ALE) form. For the elastic deformation the St. Venant–Kirchhoff model is used. In the space discretization the discontinuous Galerkin finite element method (DGM) is applied both for the flow problem in a time-dependent domain and for the dynamic nonlinear elasticity system. We show that the DGM is applicable to the discretization of both problems. As a new result we particularly present the application of the DGM to the discretization of the dynamic nonlinear elasticity problem and the DGM solution of the fluid–structure interaction (FSI). The applicability of the developed technique is demonstrated by several numerical experiments. The main novelty of the paper is the application of the DGM to the FSI problem using the model of compressible flow coupled with nonlinear elasto-dynamic system. [ABSTRACT FROM AUTHOR]

This paper is interested in numerical simulations of the interaction of the fluid flow with an airfoil, particularly the problem of the aeroelastic response of the airfoil to a sudden gust is considered. The main attention is paid to the finite element approximations of the incompressible viscous flow over a flexibly supported airfoil. The gust is modelled using the time dependent boundary condition. The structure vibration is governed by the nonlinear system of ordinary differential equations. The flow is described using the Reynolds averaged Navier–Stokes equations, the system is enclosed by the two equation k – ω turbulence model together with the transition model based on the intermittency equation. Modelling of this laminar – turbulence transition of the flow on the airfoil surface is the main novelty of the paper. The motion of the computational domain is treated with the aid of the arbitrary Lagrangian–Eulerian method. The solution of the nonlinear coupled problem is discussed and numerically tested using a stabilized finite element method. [ABSTRACT FROM AUTHOR]

In this paper, a new split-step θ (SS θ ) method for stochastic age-dependent population equations with Poisson jumps is constructed. The main aim of this paper is to investigate the convergence of the SS θ method for stochastic age-dependent population equations with Poisson jumps. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory, the results show that the SS θ method has better accuracy compared to the Euler method. [ABSTRACT FROM AUTHOR]

In this paper, we deal with numerical analysis of a transport fragmentation coagulation equation with power fragmentation rates and separable coagulation kernels. For numerical simulations, the model is rewritten in a conservative form and semi-discretized in space using a Laguerre pseudo-spectral method. Some error estimates are derived and efficiency of the numerical scheme is considered. The paper is concluded with several computational examples. [ABSTRACT FROM AUTHOR]

Two numerical simulation methods, asynchronous updating and synchronous updating, are applied to mimic epidemic spreading and identify epidemic threshold. As a continuous time Markov process, asynchronous updating makes only one node be selected to change its state in each time step, and thus reflects the fact that nodes are updated independently, which is more reasonable to describe the real dynamic process of disease spreading. Unlike previous studies based on prevalent synchronous updating, in this paper, we mainly apply asynchronous updating to precisely identify epidemic thresholds of SIR spreading dynamics in real networks. Meanwhile, we also use four benchmark theoretical methods, i.e., the heterogeneous mean-field (HMF), the quenched mean-field (QMF), the dynamical message passing (DMP) and the connectivity matrix (CM), to verify the identification accuracy based on asynchronous updating. The extensive numerical experiments in 41 real networks show that the identification accuracy approaches more closely to the theoretical results obtained from the CM because the CM incorporates network topology with dynamic correlations. In addition, because asynchronous updating is high time complexity comparing with synchronous updating, we further investigate the approximation of synchronous updating to asynchronous updating by modulating very small time step. When the time step of synchronous updating is set with 0.2, it can approach closely to the identification accuracy based asynchronous updating, and guarantee a lower time complexity. [ABSTRACT FROM AUTHOR]

• Compared with design methods in related results, the novel piecewise constant virtual control signals are designed and the requirement of designing a differentiator is avoided. Thus, the backstepping method in this paper is more suitable for networked control systems. • A semi-synchronous event-triggered scheme is designed. Compared with some conventional event-triggered schemes, the triggering instants among the channels are largely staggered to reduce network congestion; A self-triggered scheme is further proposed to avoid the continuous monitoring of the event-triggered conditions. • Compared with some switching methods, the constraints of ADT are canceled to allow more frequent switchings. • A class of nonlinear systems with Hölder condition and linear growth condition is introduced, such that the robustness of the proposed backstepping method is extended. The paper investigates the backstepping robust control problem for a class of nonlinear networked systems. The non-Lipschitz conditions of linear growth condition and Hölder condition are considered in the time-varying disturbance and uncertainty. An important innovation is that the virtual controller is designed to be piecewise constant such that the usage of the command filter is avoided. In the process of designing the robust controller, a semi-synchronous event-triggered scheme is proposed to relieve the communication pressure in high-order systems. Thus, a switched controller without using average dwell time (ADT) is considered. The finite-time practical stability with the form of fast terminal sliding mode (TSM) is also obtained. Then, the Zeno behavior is excluded and a self-triggered scheme is further proposed to avoid the continuous monitoring of the event-triggered conditions. Compared with some existing command-filtered results, the design process is simplified and more suitable for networked systems. The effectiveness of the proposed theory is validated by the numerical simulation of a hypersonic vehicle. [ABSTRACT FROM AUTHOR]

In this paper, an I2S2R rumor spreading model in complex networks is established and analyzed. Firstly, the threshold value is acquired to identify the existence and stability of rumor-free equilibria state and rumor equilibria state by using the next generation matrix method. Secondly, based on Routh–Hurwitz judgment, Lyapunov stability theory and LaSalle's invariance principle, the local and global stability of rumor-free/rumor equilibrium points are discussed. Thirdly, the sensitivity analysis about the threshold value is given to analyze the impact of model parameters on rumor propagation. Finally, some numerical simulations are presented to illustrate the validity and feasibility of corresponding results. [ABSTRACT FROM AUTHOR]

More complex data are generated with a response on vector and matrix predictors in statistics and machine learning. Recently, Zhou and Li (2014) proposed matrix regression based on least squares (LS) method but they mainly considered the regularized matrix regression with nuclear norm penalty when the distribution of noise is with mean 0 and covariance being fixed. In practice, noises may be heavy-tailed or the distribution is unknown. In this case, it is well known that least absolute deviation (LAD) method yields better performances than LS method. Considering structures of predictors, we propose the double fused Lasso penalized LAD for matrix regression in this paper. The new penalty term combines fused Lasso and matrix-type fused Lasso. We achieve the strong duality theorem between the double fused Lasso penalized LAD and its dual. Based on it, we design a highly scalable symmetric Gauss–Seidel based Alternating Direction Method of Multipliers (sGS-ADMM) algorithm to solve the dual problem. Moreover, we give the global convergence and Q-linear rate of convergence. Finally, effectiveness of our method is demonstrated by numerical experiments on simulation and real datasets. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the coexistence and local stability of multiple equilibrium points for competitive neural networks, where the Gaussian-wavelet-type activation functions are employed and the unbounded time-varying delays are considered. Based on geometric formulation, the fixed point theorem, contraction mapping theorem and rigorous mathematical analysis, a series of sufficient conditions are derived to ascertain that the addressed neural networks have exactly 5 n equilibrium points, among which 3 n equilibrium points are locally stable. On this basis, some criteria are also obtained on the multiple exponential stability, multiple power stability and multiple log-stability of Hopfield neural networks with Gaussian-wavelet-type activation functions. The obtained results generalize and improve the existing multistability results of Hopfield neural networks and competitive neural networks without time delays and with Gaussian-wavelet-type activation functions. Moreover, it is highlighted that the competitive neural networks with Gaussian-wavelet-type activation functions can have both more total equilibrium points and more locally stable equilibrium points than the ones with Mexican-hat-type activation function. Finally, two numerical examples with computer simulations are provided to illustrate and validate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, an avian influenza epidemic model with half saturated incidence is investigated. Firstly we study the local asymptotical stability of equilibria of the deterministic model. Then for the stochastic model, the existence of the global positive solution is proved and different thresholds are obtained. In addition, we get sufficient conditions for the existence of an ergodic stationary distribution by using Has'minskii theory and Lyapunov function. Finally, some numerical simulations illustrate the analytical results. [ABSTRACT FROM AUTHOR]

Abstract We study the three-point boundary value problems for the fractional differential coupled systems with both left and right fractional derivatives in the paper. Firstly, the upper-lower solutions method for the systems is presented and some existence results to the systems solutions are also obtained. Secondly, we also give out an iterative approach for finding approximate solutions of the systems. Finally, we consider a concrete example where we obtain the existence result of the solution and also give out its numerical solution and the graphical simulation. [ABSTRACT FROM AUTHOR]

Abstract Pressure retarded osmosis (PRO) power plants generate power from mixing of saltwater and freshwater by means of membrane systems. In this paper we present a model which describes the complete power station, suitable to optimize the power station both with respect to system parameters and in operating conditions. Special attention is dedicated to the flow model of the "core" membrane unit. It considers the relevant water and salt flows in the system. It also accounts for irreversible losses in the flow across the membrane as well as through the membrane unit, and in the surrounding pump-turbine system. The model represents a compromise between needed complexity (including the most relevant chemo-physics) and simplicity to allow rapid simulations which is an important prerequisit for optimisation. Finally, we optimise numerically, i.e., the net power output (per membrane area) with respect to geometric parameters, membrane parameters as well as operational parameters such as the applied pressure settings during operation. [ABSTRACT FROM AUTHOR]

Highlights • A hybrid stochastic double delayed system with impulse and Lévy jumps is proposed. • Combined dynamic effects of impulse, time delays and Lévy jumps are investigated. • Sufficient conditions for persistence in the mean and extinction are investigated. • The asymptotical stability in distribution of the proposed hybrid system is studied. • Optimal price control and maximum of expectation of sustainable yield are discussed. Abstract In this paper, a hybrid stochastic double delayed prey predator bioeconomic system with impulses and Lévy jumps is established, where commercial harvesting on each population and impulsive contaminants emission from surrounding environment on each population growth are taken into account. Sufficient conditions for persistence in the mean and extinction of interacting population are investigated. The asymptotical stability in distribution of the proposed system is studied. Furthermore, optimal price control strategy and maximum of expectation of sustainable yield are discussed. Numerical simulations are carried out to illustrate theoretical analysis. [ABSTRACT FROM AUTHOR]

Abstract In this paper, based on a chain Hindmarsh–Rose (HR) neural network under the action of electromagnetic field, the effects of connection strength between adjacent neurons on the wave propagation are investigated by utilizing numerical simulations. When the connection strength is increased via the decreasing of distance from central neuron, it is found that the firing rates of neurons in chain HR neural network are increased, and the velocity of wave propagation also becomes fast with the increasing of connection strength maximum. The chemical autapse imposed on the central neuron has a great influence on the firing rates of neurons and the wave propagation with different autaptic intensities. The firing rates of neurons are high, and many neurons can stand the excited state by increasing the field coupling strength. However, when the connection strength is decreased via the decreasing of distance from central neuron, the influences of connection strength maximum on the wave propagation are very small. The synchronization factor of the chain HR neural network is investigated by changing the maximum of connection strength, the autaptic intensity, and the field coupling intensity, respectively. It is found that the larger the field coupling strength is, the better the synchronization of neurons in the chain neural network will be, and the firing rates of neurons are high. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a new stochastic diffusion process, in which the mean function is proportional to the density function of the Weibull distribution. This is considered a useful model for survival populations, reliability studies and life-testing experiments. The main features of the process are analysed, including the transition probability density function and conditional and non-conditional mean functions. The parameters of the process are estimated by maximum likelihood using discrete sampling. Newton-Raphson and simulated annealing numerical methods are proposed to solve the likelihood equations, and are compared using a simulation example. [ABSTRACT FROM AUTHOR]

Abstract This paper presents, a novel semi-analytical algorithm, based on the Chebyshev collocation method, for the solution of space-fractional diffusion equations. The original fractional equation is transformed into a system of ordinary differential equations (ODEs) by the Chebyshev collocation method. A new semi-analytical method is then used to approximate the solution of the resulting system. To emphasize the reliability of the new scheme, a convergence analysis is presented. It is shown that highly accurate solutions can be achieved with relatively few approximating terms and absolute errors are rapidly decrease as the number of approximating terms is increased. By presenting some numerical examples, we show that the proposed method is a powerful and reliable algorithm for solving space-fractional diffusion equations and can be extended to solve another space-fractional partial differential equations. Comparison with other methods in the literature, demonstrates that the proposed method is both efficient and accurate. [ABSTRACT FROM AUTHOR]

Abstract The importance of coupling between neurons is confirmed that signal propagation and exchange between neurons depend on the biological function of synapse connection. There is a high demand for models to simulate this phenomenon comprehensively. In this paper, we introduce four models to describe different types of coupling, based on the type of synapses. These models are derived from a model of electrical activity under magnetic flow effect which is based on Hindmarsh–Rose (HR) model. Then it is developed by extrapolating this model from a single neuron, to two neurons and adding coupling factor. Changes in the behavior of these models are examined by changing external current. These models show different dynamics such as regular firing, burst, periodic and asynchronous burst. The simulations show that only one of those four models is sensitive to initial conditions. The other three models don't have such sensitivity. [ABSTRACT FROM AUTHOR]

Highlights • A new compartmental model for the co-dynamics of measles and dysentery diarrhea is proposed. • The system exhibits a backward bifurcation. • Optimal control and cost-effectiveness analysis are addressed. • Numerical simulations illustrate theoretical results and indicate suggestions for disease elimination. • The most cost-effective strategy for the control of the diseases is recommended. Abstract In this paper we propose a co-dynamics deterministic system for measles and dysentery diarrhea diseases in a single host population. Using center manifold theory, we show that the co-dynamics model may exhibit a backward bifurcation for some parameter values. Numerical simulations of the system show that the two diseases always coexist if R 0 > 1. The system is extended to include time-dependent control-variables: vaccination, treatment and sanitation of the environment, to minimize the number of infected humans and the cost of implementation of the controls. The Pontryagin Maximum Principle was employed to find the necessary conditions for the existence of the optimal controls. The numerical simulations show that the effective controls could reduce the diseases in the community. The incremental cost-effectiveness ratio was used to quantify the cost-effectiveness analysis. It is found that the control strategy which implements vaccination, treatment of dysentery diarrhea and sanitation of the environment is the most cost-effective. [ABSTRACT FROM AUTHOR]

Abstract Since donation list contains a lot of information, the way of dealing with it certainly affects the evolution of cooperation. This paper considers gossip and individuals' tolerance towards their own self-assessment of face into public goods game and then explore the necessity of publishing the donation list. Subsequently, we try to find a convenient and effective way to set up an optimal threshold for publishing the donation list. Through numerical simulations, results show that publishing the list incompletely can foster cooperation. Moreover, a reasonable threshold can make results better. By contract, we observe that let threshold vary with the mean of the last contributions is the ideal strategy. It is convenient and efficient. Under these circumstances, more money can be raised and the difference between individuals' donation is also small. What is more, the gossipmongers is not accepted by others when the evolution reaches a steady state. They either cluster together or be isolated. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a class of hybrid stochastic functional differential equations is investigated. Under some suitable assumptions, the p th moment stability, asymptotic stability and exponential stability are discussed by means of constructing an auxiliary functional differential equation and using the comparison principle. The proposed criteria removes some conditions in some earlier publications. Moreover, two examples and simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Abstract This paper considers Hopf bifurcation of complex network with two independent delays. By analyzing the eigenvalue equations, the local stability of the system is studied. Taking delay as parameter, the change of system stability with time is studied and the emergence of inherent bifurcation is given. By changing the value of the delay, the bifurcation of a given system can be controlled. Numerical simulation results confirm the validity of the results found. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we develop a mixed Jacobi–Fourier pseudospectral method for solving the Fisher equation in a disc. Fisher's equation always plays a large role in many fields, such as logistic population growth models, tissue engineering, nuclear reactions, and neurophysiology, etc.. It is very important to study how to solve these equations numerically. In this work, we employ the generalized Jacobi approximation to simulate the singularity of solutions at the regional center. Some mixed Jacobi–Fourier interpolation approximation results are established, which play important roles in numerical simulation of various problems defined in a disc. As an application, the mixed Jacobi–Fourier pseudospectral scheme is provided for the Fisher equation in a disk. The generalized stability and convergence of the proposed scheme are proved. Some numerical results are presented to demonstrate the efficiency of this new algorithm. [ABSTRACT FROM AUTHOR]

Abstract Many numerical methods are based in mesh files to represent the computational domain. Also, an efficient storage and retrieval of mesh information can be achieved by data structures. Moreover, the development of topological operators is one of the important goals of the geometric modeling research field. While it loads mesh files more efficiently, it also allocates less main memory, provides persistence and allows consistent query operations. This paper proposes an improving of the computational scheme of high-order WENO schemes by coupling a standard cell centered, unstructured mesh, finite volume method with an topological data structure. The solver module uses the finite volume technique with a formulation that sets the property values to the control volume centroids. The two dimensional Euler equations are considered to represent the flow of interest. Beyond experiments using the improved approach, the computational cost of the data structure was measured by comparing with the traditional representation, and the results showed that our approach provides scalable loading and managing of meshes, having less memory occupation rate when comparing meshes with an increasing number of elements. [ABSTRACT FROM AUTHOR]

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]

Abstract In this paper, a dynamical two-stage Cournot duopoly game with R&D spillover effect and product differentiation is established. The stability of all the equilibrium points is studied using Jury criterion, and then the stability condition is given. The direction of flip bifurcation is given by using central manifold theorem and norm form theory. By numerical simulation, two routes to chaos are studied through 2-D bifurcation diagram, one of which is flip bifurcation and the other is Neimark-Sacker bifurcation at period-2 point. The system will lose its stability as the speed of adjustment increases. In addition, a common nonlinear phenomenon named intermittent chaos is observed in the built model. Two types of intermittent chaos are displayed in time series plots and phase diagrams, one of which is PM-III intermittent chaos and the other is induced by crisis. And then four types of coexistence of attractors are illustrated through basin of attraction, which are coexistence of periodic attractor and chaotic attractor, coexistence of multiple chaotic attractors, coexistence of periodic attractor, quasi-periodic attractor and chaotic attractor, and coexistence of multiple periodic attractors, respectively. [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]

Abstract In this paper, a new stochastic eco-epidemiological model is proposed and investigated, and the high dimensional model includes time delay and a general incidence rate which make the study more complex. First, the existence and uniqueness of the global positive solution with any positive initial value are verified. Second, using stochastic analysis methods and some differential inequality techniques, we explore the long-time asymptotic properties of the stochastic delayed system. Furthermore, we prove that the solution of the stochastic delayed system has a unique stationary distribution and it has ergodic property. Third, the sufficient conditions of permanence in mean or extinction for the ecological populations are obtained. Finally, we introduce a series of computer simulations to show the performance of the theoretical results. [ABSTRACT FROM AUTHOR]

A general model and computational code for transient gas-liquid two-phase flow in wellbore are developed in this paper. The model consists of mass conservation equation for each phase and mixture momentum conservation equation. The interactions of each phase are taken into account by invoking the Shi slip relation in the proposed model. The model is numerically solved by the second order AUSMV scheme, which is obtained by using classical MUSCL technique. The computational code is validated by the classical numerical cases, Zuber–Findlay tube and complex mass transport problem. The simulation results show good agreement with the references which are obtained by using first-order flux-limited Roe scheme with refined grids. The computational code also succeeds in obtaining the transient behavior of each phase for a normal gas-kick occurrence in wellbore. The simulation results illustrate the degree of pressure variation in the upper wellbore is greater than that in the lower wellbore. The pressures of wellbore increase before the corresponding gas mass flow rate reach max inlet gas mass flow rate, then decrease. [ABSTRACT FROM AUTHOR]

• Existence of T-periodic solution for a stochastic Crowley-Martin model with impulse is investigated. • Asymptotical stability in probability for the Crowley-Martin model is discussed. • Existence and ergodicity of stationary distribution for the Markov switching case are studied. • Our conclusion improves and generalizes the corresponding existing ones. This paper systematically investigates a stochastic Crowley-Martin predator-prey model. Firstly, we derive sufficient conditions for the existence of positive T -periodic solution for the impulsive case. Secondly, distinguished from the previous papers, asymptotical stability in probability is investigated by combining Khasminskii theory of stability with Lyapunov method. Our conclusion also improves and extends the corresponding existing ones. Thirdly, we establish the sufficient criteria for the existence of a unique ergodic stationary distribution for the Markovian switching case. Finally, two numerical examples are presented to demonstrate the effectiveness and feasibility of our analytical results and reveal the respective effect of white noises and Markovian switching. [ABSTRACT FROM AUTHOR]

• This paper is devoted to study the general depletion model. • A better understanding of the existence and asymptotic stability of constant solutions is obtained. • The difficulty lies in how to clarify the number and the region of constant solutions. • The steady-state bifurcation from constant solutions is given. • Numerical simulations are done to suggest that steady spike solutions may occur. In this paper, we deal with a depletion model which is constructed by an activator and a substrate in a bounded domain. A better understanding of the asymptotic stability of constant solutions is obtained for such a general depletion model. The difficulty lies in how to clarify the number and the region of constant solutions. Next, we analyze the steady-state bifurcation from constant solutions. Finally, some numerical simulations are done to complement analytical results, and steady spike solutions are observed for proper parameters. [ABSTRACT FROM AUTHOR]

• In this paper, the problem of multiple ψ -type stability of fractional-order quaternion-valued neural networks was investigated. To the best of our knowledge, this is the first time to discuss the multiple ψ -type stability problem for quaternion networks. • A quaternion-valued matrix is uniquely decomposed into four real valued matrices and mapped into two similarly sized systems this method will help to avoid many redundant computations. • Compared with the complex-valued neural networks quaternion valued neural networks have 3 4 n equilibrium points. Among them 2 4 n equilibrium points are exponentially stable. The multiple ψ − type stability of fractional-order quaternion-valued neural networks (FQVNNs) was investigated in this paper. Some new conditions ensuring the existence of multiple equilibrium points of the considered FQVNNs are provided. Meanwhile, the ψ − type stability for the proposed neural networks is studied by employing the fractional calculus theory and fractional derivative techniques into the system dynamics. Finally, an numerical simulation is given to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

• In this paper, we study the dynamics of a delay differential model for three species preypredator system (of two preys and one predator), with Monod-Haldane and Holling type IIfunctional responses, and cooperation between the two-teams of prays against predation. • Two discrete time-delays are incorporated to justify the reaction time of predator with each prey. • The permanence of such system is proved. Local and global stabilities of interior steady states are discussed. • Hopf bifurcation analysis in terms of time-delay parameters is investigated, and threshold parameters τ 1 * and τ 2 * are obtained. • Sensitivity analysis, which estimates how the model predictions can vary to small changes in the parameters of the model, is also studied. Some numerical simulations are provided to show the effectiveness of the theoretical results. In this paper, we study the dynamics of a delay differential model of predator-prey system involving teams of two-prey and one-predator, with Monod-Haldane and Holling type II functional responses, and a cooperation between the two-teams of preys against predation. We assume that the preys grow logistically and the rate of change of the predator relies on the growth, death and intra-species competition for the predators. Two discrete time-delays are incorporated to justify the reaction time of predator with each prey. The permanence of such system is proved. Local and global stabilities of interior steady states are discussed. Hopf bifurcation analysis in terms of time-delay parameters is investigated, and threshold parameters τ 1 * and τ 2 * are obtained. Sensitivity analysis that measures the impact of small changes in the model parameters into the model predictions is also investigated. Some numerical simulations are provided to show the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]