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The effectiveness of this paper lies in presenting a new solution for the singular fractional two-dimensional linear continuous-time systems using the conformable derivative and Sumudu transform. The proposed technique combines the new advantageous features of conformal derivative and double-delta-Kronecker, which efficiently handles singularities and Sumudu transform, and provides an efficient solution for 2D singular Fornasini–Marchesini fractional models. Applying these approaches, we then derive new explicit expressions for the fundamental matrices of the considered model. The applicability and usefulness of our proposed methods are validated and evaluated by numerical simulations in order to show the accuracy of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, based on the nonuniform time meshes, we proposed an efficient difference scheme for solving the time-fractional bi-flux diffusion equation. By the energy method, we then proved that the present scheme is unconditionally stable and convergent in L 2 norm. Several numerical examples are given to verify the theoretical results. In addition, numerical simulations show the order of fractional derivative affects the diffusion rate of the particles. [ABSTRACT FROM AUTHOR]

Two-component reaction–diffusion models in high dimensions involving space-fractional derivatives are used as a powerful modelling approach for understanding several aspects of spatial heterogeneity and nonlocality. In this paper, we propose an accurate, unconditionally stable, and maximum principle preserving fourth-order method both in space and time variables to study the complex dynamical processes of two-component nonlinear space-fractional reaction–diffusion systems posed in high dimensions. To achieve a fast fourth-order accurate method, we adapt the matrix transfer technique with a fast Fourier transform-based implementation in space and an exponential integrator in time. The main advantage of the method is that it avoids storing the large dense matrix resulting from discretizing the fractional operator with the matrix transform approach and significantly reduces the computational costs. Some numerical experiments are carried out in two and three space dimensions to demonstrate the accuracy and computational efficiency of the method. [ABSTRACT FROM AUTHOR]

This paper focuses on the stabilization problem for a class of fractional-order bidirectional associative memory neural networks with mixed time delays (discrete delay and finite-time distributed delay). Based on adaptive control and delay feedback control, two kinds of adaptive control schemes are proposed to realize the global stabilization of systems. Different from those in earlier works, our method mainly depends on two fractional inequalities and a new fractional-order Barbalat lemma. Finally, some numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed adaptive control schemes. [ABSTRACT FROM AUTHOR]

In this paper, we present a split-step Rosenbrock type method for stiff stochastic differential systems. The method is proved to be mean-square (MS) convergent with strong order 1 2 . For one- and two-dimensional Itô test equations with multiplicative noise, we analysis asymptotically MS stability and plot asymptotic MS stability regions. Numerical examples and simulations are given to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed fusion estimation problem for discrete-time multi-sensor stochastic systems with random parameter matrices. It is assumed that the random parameter matrices in the observation equations are one-step autocorrelated and cross-correlated between the different sensors and the additive noises are also correlated. Under these assumptions, a recursive algorithm is proposed to obtain local least squares linear filters based on the measurements of each sensor, and the distributed fusion filter is designed as the matrix-weighted linear combination of these estimators which minimizes the mean squared estimation error. This research is illustrated by two numerical simulation examples where multi-sensor systems with randomly delayed measurements and missing measurements are considered, respectively, and the performance of the proposed estimators is analysed by comparing the estimation error variances of the distributed and centralized fusion filters. [ABSTRACT FROM AUTHOR]

This paper presents a general array model of switched coupled reaction–diffusion neural networks (CRDNNs) with non-delayed and delayed couplings. By utilizing some inequality techniques, we derive several sufficient conditions ensuring the input strict passivity and output strict passivity of the proposed network model. In addition, by constructing an appropriate Lyapunov functional, a sufficient condition is established in the form of linear matrix inequations to guarantee synchronization of CRDNNs with switched topology. Numerical examples with simulation results are provided to demonstrate the effectiveness and correctness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we propose two new kinds of Susceptible, Infective, Removed and Susceptible (SIRS) models with two viruses: continuous SIRS model and discrete-time SIRS model. We obtain sufficient conditions for existence and local stability of the disease-free equilibria and the endemic equilibria in the two models. Moreover, we use numerical simulations to illustrate the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we have formulated an e-epidemic energy efficient susceptible-infected--terminally infected-recovered (SITR) model to analyse the attacking behaviour of worms in wireless sensor network (WSN) using cyrtoid type functional response. In this model, once a sensor node has been attacked by the worms, the terminally infected node spreads the worms to its neighbouring nodes using normal communications, which further spread it to their neighbouring nodes and the process continues. To tackle this issue, we proposed an SITR model by considering the sleep mode concept of WSN in which the operational capabilities and power consumption of the motes decreases. Boundedness, existence of equilibrium points, stability and bifurcation analysis are analysed for the proposed model system. Stability and direction of Hopf-bifurcation are also obtained for endemic equilibrium point using center manifold theorem. Finally, numerical simulations are carried out that supports the analytical findings. The impact of the control parameters like transmission rate (β), inter-nodes interference coefficient (θ1) and intrinsic growth rate (r1) on the dynamics of the model system are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a fractional diffusion equation with degenerate source term. The fractional derivative, acting on the spatial variable, contains left-sided Caputo derivative and right-sided Riemann–Liouville derivative simultaneously. Due to the symmetry property of such fractional derivative pattern, the existence of quenching phenomenon is verified and the quenching time is estimated under certain settings of parameters. An numerical example is carried out by using a finite-difference scheme with uniform and non-unique mesh, which demonstrates the theoretical analysis of this model and presents several significant relation between order of derivatives and size of spatial domain. [ABSTRACT FROM AUTHOR]

In this paper, an approximation of the optimal compressor function using the quadratic spline functions with 2L = 8 segments is described. Since the quadratic spline with 2L = 8 segments provides better approximation of the optimal compression function than quadratic spline with 2L = 4 segments, capitalizing on the benefits of the obtained spline approximation, quantizer designing process is firstly performed for the so assumed number of segments and the Laplacian source of a unit variance. Then, to enhance the usability of the proposed model, the switched quantization technique is applied and a beneficial analysis is derived, providing insight in the robustness of the proposed quantizer performances with respect to the mismatch in designed for and applied to variances. Reached quality has been compared to another model from the literature, and it has been shown that the proposed model outperforms the previous model by almost 1.3 dB. [ABSTRACT FROM PUBLISHER]

In this paper a method based on Sinc approximation is developed for the numerical solution of a nonlinear fractional pantograph equation. In order to use Sinc approximation, the problem needs to have an analytic solution. So we investigated the existence and uniqueness of analytic solutions in the proposed domain. Single and double exponential transformations are used to approximate the solution. Some test problems are given to demonstrate the efficiency and applicability of the methods. The results are compared with some other existing numerical methods to show the performance and good accuracy of the methods. The numerical orders of convergence show that the method has exponential rate of convergence. [ABSTRACT FROM AUTHOR]

Polydisperse sedimentation models can be described by a strongly coupled system of conservation laws for the concentration of each species of solids. Typical solutions for the sedimentation model considered for batch settling in a column include stationary kinematic shocks separating layers of sediment of different composition. This phenomenon, known as segregation of species, is a specially demanding task for numerical simulation due to the need of accurate numerical simulations. Very high-order accurate solutions can be constructed by incorporating characteristic information, available due to the hyperbolicity analysis made in Donat and Mulet [A secular equation for the Jacobian matrix of certain multispecies kinematic flow models, Numer. Methods Partial Differential Equations 26 (2010), pp. 159–175.] But characteristic-based schemes, see Bürgeret al. [On the implementation of WENO schemes for a class of polydisperse sedimentation models, J. Comput. Phys. 230 (2011), pp. 2322–2344], are very expensive in terms of computational time, since characteristic information is not readily available, and they are not really necessary in constant areas, where a less complex method can obtain similar results. With this idea in mind, in this paper we develop a hybrid finite difference WENO scheme that only uses the characteristic information of the Jacobian matrix of the system in those regions where singularities exist or are starting to develop, while it uses a component-wise approximation of the scheme in smooth regions. We perform some experiments showing the computational gains that can be achieved by this strategy. [ABSTRACT FROM PUBLISHER]

The premixed turbulent V-flame is numerically simulated in this paper. The technique used in Chan et al. [Effect of intense turbulence on turbulent premixed V-flame, Int. J. Eng. Sci. 41 (2003), pp. 903-916; Simulation of a premixed turbulent flame with the discrete vortex method, Int. J. Numer. Methods Eng. 48 (2000), pp. 613-627] was based on the random vortex method and the conventional level set method. However, this paper is an improvement of the previous technique by using a conservative level set method. The new algorithm uses a bi-cubic interpolation process together with Newton's method to reconstruct the velocity field to improve the conservation of the level set method. The numerical example in this paper indicates the efficiency of the new method in solving the problem of turbulent premixed V-flame by comparing the results with available data. [ABSTRACT FROM AUTHOR]

In this paper we present some techniques for constructing high-order iterative methods in order to approximate the zeros of a non-linear equation f(x)=0, starting from a well-known family of cubic iterative processes. The first technique is based on an additional functional evaluation that allows us to increase the order of convergence from three to five. With the second technique, we make some changes aimed at minimizing the calculus of inverses. Finally, looking for a better efficiency, we eliminate terms that contribute to the error equation from sixth order onwards. The paper contains a comparative study of the asymptotic error constants of the methods and some theoretical and numerical examples that illustrate the given results. We also analyse the efficiency of the aforementioned methods, by showing some numerical examples with a set of test functions and by using adaptive multi-precision arithmetic in the computation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the modelling and identification in the fed-batch fermentation of glycerol byKlebsiella pneumoniaewith open-loop glycerol input and pH logic control. Taking into account the hybrid characteristic of the fed-batch operation, we present a nonlinear hybrid dynamical system, which is developed by embedding the discrete process of adding glycerol and alkali into the dynamical system of batch culture, to formulate this fermentation process. Some important properties of the solution to the proposed system are then discussed, including the existence, uniqueness, boundedness and regularity. To estimate the unknown parameters in the system, a parameter identification problem subject to continuous state inequality constraints is proposed, and its identifiability is also proved. Subsequently, the parametric sensitivity functions of the system are given and utilized to obtain the requisite gradient information for further numerical computation. Finally, to solve the identification problem, a gradient-based algorithm is constructed in conjunction with constraint transcription and the smoothing approximation technique. Numerical simulations show that the validated hybrid system is fit for describing the fed-batch processes as observed from the experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we construct a numerical method based on cubic splines in tension for solving regularized long wave equation. The truncation error is analysed and the method shows that by choosing suitably parameters we can obtain various accuracy schemes. Numerical stability of the method has been studied by using a linearized stability analysis. Test problems are dealt with. The numerical simulations can validate and demonstrate the advantages of the method. [ABSTRACT FROM AUTHOR]

In this paper, we analyse a delayed Holling-II predator–prey system with stage-structure for the prey. At first, we study the stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays at the positive equilibrium by analysing the distribution of the roots of the associated characteristic equation. Then, the explicit formula that determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions from the Hopf bifurcation are established by using the normal form method and centre manifold argument. Finally, some numerical simulations are carried out to support the main theoretical results. [ABSTRACT FROM AUTHOR]

As a service composition and coordination language, the service choreography gives the global and neutral view on the collaboration among a collection of highly distributed services involving multiple different organizations or heterogeneous independent processes. In this paper, we extend the service choreography by introducing the explicit time activity, which can be used to specify and reason about the timed behaviour of Web service choreography. Then we explore an execution model for the proposed timed service choreography which possesses several novel features, such as timed activity, choreography composition, exception handling and finalization. Furthermore, a set of mapping rules is elaborately designed to translate the timed choreography into communicating sequential programs processes, thus the corresponding simulation and verification of Web services choreographies with timing restrictions can be carried out in the model checker process analysis toolkit. The case study shows that our approach is both effective and practical. [ABSTRACT FROM AUTHOR]

An important direction in the research of P systems is paving the way to modelling real-world biological structures. Clock-free P systems represent an attempt at bringing the P formalism closer to biological origins by eliminating global synchronization, the global clock. The goal of this paper is to provide a formalization of clock-free P systems starting from the formal concept of a network of cells. This approach makes it possible to show that clock-free systems can be simulated with the usual networks of cells. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce ordinary and delay differential equations to describe the interactions between a malignant tumour and the immune systemin vivoin the presence of human immunodeficiency virus (HIV) infection of CD4+T-cells. In the delay model, we take into account the time lags required by the healthy effector cell components to recognize the pathogens and tumour cells. The models consist of four populations: tumour cells, healthy effector cells (CD4+T-cells), effector cells infected by HIVs and free viral particles. The presence of delay term in the model leads to a notable increase in the complexity of the observed behaviour. We investigate the qualitative behaviour of the models and find the conditions that guarantee the asymptotic stability of the steady states. Numerical simulations are provided to illustrate and extend the theoretical results. The obtained results are consistent with the real phenomena and give a better understanding of cancer immunity and viral oncogenesis. [ABSTRACT FROM PUBLISHER]

Our main interest in this paper is the large dicliques in a directed inhomogeneous random graph modelG(n,α, Φ) onnvertices, which has power-law out/in-degree distributions with scaling exponent α>0 and community structures involved in the homophyly matrix Φ. We show that there is a major difference in the size of the largest diclique ωd(G(n,α, Φ)) between the case α<2 and α>2 with an intermediate result for α=2. In addition, we show that a simple algorithm with high probability finds a large diclique of size ωd(G(n,α, Φ)) in a polynomial time. Our simulation results reveal that the connections between different subcommunities are essential for the formation of large clusters in the networks. [ABSTRACT FROM PUBLISHER]

In this work, the approximation of Hilbert-space-valued random variables is combined with the approxi-mation of the expectation by a multilevel Monte Carlo (MLMC) method. The number of samples on the different levels of the multilevel approximation are chosen such that the errors are balanced. The overall work then decreases in the optimal case to 0(h-2) if Ii is the error of the approximation. The MLMC method is applied to functions of solutions of parabolic and hyperbolic stochastic partial differential equations as needed, for example, for option pricing. Simulations complete the paper. [ABSTRACT FROM AUTHOR]

In this paper, we apply a regularized sinc method to compute the eigenvalues of a discontinuous regular Dirac system with transmission conditions at the point of discontinuity. The regularized technique allows us to insert some parameters to the well-known sinc method, strengthening the existing technique, and to avoid the aliasing error. The error analysis is established considering both the truncation and amplitude errors associated with the sampling theorem. Numerical examples together with tables and illustrative figures are given. [ABSTRACT FROM PUBLISHER]

In this paper, a highly demanding computer-assisted classification of four-dimensional finite semifields over the field 𝔽7 is provided. The techniques considered to overcome the difficulties in the management of the large data processed are explained. [ABSTRACT FROM PUBLISHER]

A discrete nonlinear dynamics model has been established based on investment competition for heterogeneous financial institutions in this paper. The cost functions of financial institutions are different in the competitive investment. Theoretical analysis and numerical simulations of the system are investigated in detail. The results show that the dynamic system can undergo chaotic orbits. The stability control is realized by the method combining the feedback control with the parameter variation. The numerical simulation results show that the control method is effective. In practice, by utilizing the sensitivity to disturbance of the model, we can put a tiny perturbation on the chaotic system and induce large influence on investments in order to realize a desirable behaviour. [ABSTRACT FROM PUBLISHER]

Compressive sensing (CS) has inspired significant interests because of its compressive capability and lack of complexity on the sensor side. This paper introduces a novel framework of image fusion based on the CS principle. First, we present a study of three sampling patterns and investigate their performance on CS reconstruction. We then propose a novel image fusion algorithm by using an improved sampling pattern. Finally, the CS-based image fusion approach is applied to various image modalities and evaluated both visually and in terms of fusion quality metrics. The simulations demonstrate that CS-based image fusion has a number of perceived advantages in comparison with image fusion in the multiresolution (MR) domain, providing a truly different and more advanced way for fusing multimodality images. [ABSTRACT FROM AUTHOR]

In this paper, we present new results on multistability and attractivity of second-order networks with unsupervised Hebbian-type learning component and time-varying delays. By using the properties of activation functions, we divide state space into invariant sets and establish new criteria of coexistence of equilibrium points which are exponentially stable. The attained results show that second-order synaptic interactions and learning behaviour have an important effect on the multistable convergence of the networks. Finally, numerical simulations will illustrate multistable learning dynamics of second-order networks. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global asymptotic stability of a class of stochastic bidirectional associative memory neural networks with both multiple discrete and distributed time-varying delays. A new criterion of asymptotic stability is derived in terms of linear matrix inequality, which can be efficiently solved by a standard numerical software. An illustrative numerical example is also given to show the applicability and effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The growing size of the multiprocessor systems increases their vulnerability to component failures. It is crucial to locate and replace the faulty processors to maintain the system's high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. The conditional diagnosis requires that for each processor v in a system, all the processors that are directly connected to v do not fail simultaneously. In this paper, we show that the conditional diagnosability of the crossed cubes CQn under the comparison diagnosis model is 3n-5 when n≥7. Hence, the conditional diagnosability of CQn is three times larger than its classical diagnosability. [ABSTRACT FROM AUTHOR]

In this paper, we construct a group of Saul'yev type asymmetric difference formulas for the dispersive equation. Based on these formulas we derive a new alternating 6-point group algorithm to solve dispersive equations with periodic boundary conditions. The algorithm has a high-order accuracy in space and an unconditional stability. The theoretical results are conformed to the numerical simulation. A comparison of this algorithm with the previous Alternating Group Explicit method is presented. [ABSTRACT FROM AUTHOR]

This paper describes a cubically convergent iteration method for finding the multiple roots of nonlinear equations, f(x)=0, where f:→ is a continuous function. This work is the extension of our earlier work [P.K. Parida, and D.K. Gupta, An improved regula-falsi method for enclosing simple zeros of nonlinear equations, Appl. Math. Comput. 177 (2006), pp. 769-776] where we have developed a cubically convergent improved regula-falsi method for finding simple roots of f(x)=0. First, by using some suitable transformation, the given function f(x) with multiple roots is transformed to F(x) with simple roots. Then, starting with an initial point x0 near the simple root x* of F(x)=0, the sequence of iterates {xn}, n=0, 1, ... and the sequence of intervals {[an, bn]}, with x*∈{[an, bn]} for all n are generated such that the sequences {(xn-x*)} and {(bn-an)} converges cubically to 0 simultaneously. The convergence theorems are established for the described method. The method is tested on a number of numerical examples and the results obtained are compared with those obtained by King [R.F. King, A secant method for multiple roots, BIT 17 (1977), pp. 321-328.]. [ABSTRACT FROM AUTHOR]

In this paper, we present and analyse a new predictor-corrector iterative method for solving non-linear single variable equations. The convergence analysis establishes that the new method is cubically convergent. Numerical tests show that the method is comparable with the well-known existing methods and in many cases gives better results. [ABSTRACT FROM AUTHOR]

In this paper, we present three new schemes for the coupled nonlinear Schrodinger equation. The three new schemes are multi-symplectic schemes that preserve the intrinsic geometry property of the equation. The three new schemes are also semi-explicit in the sense that they need not solve linear algebraic equations every time-step, which is usually the most expensive in numerical simulation of partial differential equations. Many numerical experiments on collisions of solitons are presented to show the efficiency of the new multi-symplectic schemes. [ABSTRACT FROM AUTHOR]

The permeability of a 3D geological fracture network is determined by triangulating the fractures and solving the 2D Darcy's equation in each fracture. Here, the numerical modelling aims to simulate a great number of networks made up of a great number of fractures i.e. from 103 to 106 fractures. Parallel computing allows us to solve very large linear systems improving the realism of simulations. Several algorithms to simulating fluid flow are proposed for the cases of significant matrix permeability. In the case of a weak permeability matrix, the flow is focused in the fractures having a strong permeability and fluids percolate through networks of interconnected fractures. In this paper, we present a complete parallel algorithm for solving flow equations in fracture networks. We consider an imprevious matrix. The different parts of the algorithm are detailed. Numerical examples using the mixed finite element (MFE) method for various fracture networks illustrate the efficiency and robustness of the proposed algorithm. To the best of our knowledge, results for parellel simulation of fluid flow in discrete-fractured media with impervious matrix using the MFE method are the first to appear in the literature. [ABSTRACT FROM AUTHOR]

In this paper, numerical simulations of tornadoes are presented. The problem considered is to first simulate numerically a tornado-like vortex passing through a populated area and then analyse the paths as it impacts structures. This study was invigorated after a tornado, classified F2 on the Fujita scale, striked Embry-Riddle Aeronautical University Daytona Beach Campus in December 2006. The computational domain used in this study is the Florida ERAU Campus and includes accurately all the different buildings. Computations of turbulent flow around several complex shaped buildings are performed using a k-ε turbulence model. The tornado is modelled by means of a vortex which is generated using a pressure gradient. The results obtained are physically reasonable and serve as a first step towards modelling tornadoes. [ABSTRACT FROM AUTHOR]

In this paper, we present a reliable algorithm to study the well-known model of nonlinear dispersive waves proposed by Boussinesq. We solve the Cauchy problem of Boussinesq equation using variational iteration method (VIM). The numerical results of this method are compared with the exact solution of an artificial model to show the efficiency of the method. The approximate solutions show that VIM is a powerful mathematical tool for solving nonlinear problems. [ABSTRACT FROM AUTHOR]

Many mathematical models have the property of developing singularities at a finite time; in particular, the solution u(x, t) of the semi-linear parabolic Equation (1) may blow up at a finite time T. In this paper, we consider the numerical solution with blow-up. We discretize the space variables with a spectral method and the discrete method used to advance in time is an exponential time differencing scheme. This numerical simulation confirms the theoretical results of Herrero and Velzquez [M.A. Herrero and J.J.L. Velzquez, Blow-up behavior of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poincare 10 (1993), pp. 131-189.] in the one-dimensional problem. Later, we use this method as an experimental approach to describe the various possible asymptotic behaviours with two-space variables. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose and validate numerically a set of novel adaptive strategies for synchronization and consensus of complex networks of dynamical systems. We present both centralized and decentralized strategies where the adaptation law is based on, respectively, global and local information at the network nodes. All the proposed adaptive techniques are then validated using computer simulations on ensembles of two types of oscillators: Kuramoto and Rossler. We show that, in both cases, synchronization can be achieved with the adaptive gains reaching asymptotically finite steady-state values. [ABSTRACT FROM AUTHOR]

It is very important to promptly detect the point-of-change of the behavior of a system. In this paper, two algorithms'- the algorithm of cumulative sums and median algorithm - are proposed for detecting the point. Unlike earlier algorithms, the schemes detect the point even when the distribution of the target process shifts before or after the point, and the detection is made in an interval of predefined length. We also develop analytical models predicting the probability of discord omission. The median algorithm allows simpler expression and easier use than the algorithm of cumulative sums. Moreover, it is proved to be applicable for a wide range of parameter values of the distribution. Computer simulation verifies the effectiveness of the proposed algorithms, and it reveals that the points are correctly detected with few false alarms for practical conditions. Also shifted distribution is of great advantage for finding discord. [ABSTRACT FROM AUTHOR]