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This paper presents the qualitative analysis of a predator–prey model with nonmonotonic functional response and impulsive effects. Different from previous work, by considering two factors of nonmonotonic functional response and impulsive effects, this paper studies the existence and stability of the periodic semi-trivial solution y = 0 first. Then, by constructing an appropriate Poincare map and introducing geometric theory, it is shown that the predator–prey model can exhibit a variety of dynamic phenomena, including orbitally asymptotically stable order-1 periodic solution (O1PS), order-2 periodic solution (O2PS) and globally stable equilibrium point under certain conditions. When there exists an O2PS, its appearance and disappearance as well as the appearance of bifurcation phenomenon are discussed in detail with different selections of the initial value of predator. Finally, numerical simulations illustrate the correctness of the results of the theoretical analysis. The theoretical results presented in this paper can be seen as an advancement to the previous related works. [ABSTRACT FROM AUTHOR]

One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations is to render their hyperbolic character to elliptic form. This paper is devoted to the study of a stabilized linear, domain decomposition, finite element method for the time harmonic Maxwell's equations, in a dual form, obtained through the Laplace transformation in time. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. The discrete problem is coercive in a symmetrized norm, equivalent to the discrete norm of the model problem. This yields discrete stability, which together with continuity guarantees the well-posedness of the discrete problem, cf Arnold et al. (2002) [3] , Di Pietro and Ern (2012) [45]. The convergence is addressed both in a priori and a posteriori settings. In the a priori error estimates we confirm the theoretical convergence of the scheme in a L 2 -based, gradient dependent, triple norm. The order of convergence is O (h) in weighted Sobolev space H w 2 (Ω) , and hence optimal. Here, the weight w ≔ w (ɛ , s) where ɛ is the dielectric permittivity function and s is the Laplace transformation variable. We also derive, similar, optimal a posteriori error estimates controlled by a certain, weighted, norm of the residuals of the computed solution over the domain and at the boundary (involving the relevant jump terns) and hence independent of the unknown exact solution. The a posteriori approach is used, e.g. in constructing adaptive algorithms for the computational purposes, which is the subject of a forthcoming paper. Finally, through implementing several numerical examples, we validate the robustness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Chaotic systems are widely used in designing encryption algorithms for their ideal dynamical performances. One-dimensional (1D) chaotic maps have the highest efficiency in implementation and have achieved great attention. However, 1D chaotic maps have a common security weakness, which is that their key space is relatively small. Therefore, in this paper, a cluster of 1D quadratic chaotic maps is proposed according to the topological conjugate theory. The 1D chaotic map has three tunable parameters which have a significant expansion in parameter space than the traditional 1D chaotic maps. The 1D map is proved to be chaotic theoretically since it is topologically conjugated with a logistic chaotic map. An example of a 1D quadratic chaotic map is provided in this paper, and several numerical simulation results indicate that this 1D quadratic map has ideal chaotic characteristics, which are consistent with the theoretical analysis. To verify the effectiveness of this 1D quadratic map, a novel image encryption algorithm is proposed. The security of this image encryption algorithm is completely dependent on the properties of the 1D quadratic map. Security experimental test results show that this image encryption algorithm has a high-security level, and is quite competitive with other chaos-based image encryption algorithms. [ABSTRACT FROM AUTHOR]

A Stein-type characterization of the Lindley distribution is derived. It is shown that if using the generalized derivative in the sense of distributions, one can choose all indicator functions as the characterization functions class. This extends some known recent results about characterizations of the Lindley distribution. In addition, a new characterization based on another independent exponential random variable is also provided. As an application of the novel results, some moment formulas related to the Lindley distribution are obtained. Furthermore, generalized method-of-moments estimators for both the discrete and continuous Lindley distribution are proposed, which lead to a notably lower bias at the cost of an only modest increase in mean squared error compared to existing estimators. It is also demonstrated how the Stein characterization might be used to construct a goodness-of-fit test with respect to the null hypothesis of the Lindley distribution. The paper concludes with an illustrative real-data example. [ABSTRACT FROM AUTHOR]

This article presents a numerical study of the initial boundary value problem for a singularly perturbed system of two equations of convection–diffusion type. The perturbation parameter in both equations leads to the boundary layer in both solution components. The sign of the convection coefficient decides the position of the boundary layer at the right end of the spatial domain. We suggest a numerical method composed of a spline-based scheme with a Shishkin mesh for solving the proposed system. Convergence analysis shows that the numerical technique is nearly second-order uniformly convergent concerning the perturbation parameter. The numerical illustration is delivered to support the theoretical results. • The systems of singularly perturbed problems are challenging to solve numerically. • To effectively resolve the boundary layers, this paper offers a novel concept. • The cubic spline basis functions are used to solve problems with wild behavior. • The boundary layer is resolved using Shishkin mesh. • The convergence of the numerical approach is proved theoretically. [ABSTRACT FROM AUTHOR]

This paper investigates the new model order reduction (MOR) methods via bivariate discrete orthogonal polynomials for two-dimensional (2-D) discrete systems. The 2-D discrete system is described by the Kurek model. First, we deduce algebraically the shift-transformation matrix of the classical discrete orthogonal polynomials of one variable. By means of the shift-transformation matrices, 2-D discrete systems are expanded in the spaces spanned by bivariate discrete orthogonal polynomials. The coefficient matrices are calculated from matrix equations. Then the reduced-order systems are produced by the orthogonal projection matrices defined by the coefficient matrices. Theoretical analysis shows that the reduced-order systems can match a certain number of coefficient vectors of the original outputs. Finally, one numerical example is simulated to demonstrate the feasibility and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Time-delay is a universal phenomenon in control systems, which usually leads to instability and poor performance of systems. In this paper, the p th moment asymptotic stability of trivial solutions to uncertain dynamical systems with time-delays is investigated. The concept of the generalized expected value is introduced with its properties based on uncertainty theory. Sufficient conditions for ensuring the stability of uncertain delay systems are derived by Lyapunov direct method. Several illustrative examples with numerical simulations are arranged to demonstrate the effectiveness of the stability results. [ABSTRACT FROM AUTHOR]

In this paper, a stage-structured predator–prey model is considered in a toxic environment, emphasizing on the affect of the toxic substances on growth of the species in presence of time delays. The positivity and boundedness of solutions have been discussed. The analytical and numerical simulations of the proposed model show that the coexistence equilibrium point is stable for low and moderate values of the delay parameter associated with the predator's maturity. Even though there is an interval of the maturation time in which the system exhibits oscillatory behaviour, a longer maturity duration may lead to the extinction of the predator species. The impact of toxicity on the proposed system is also investigated. The stability of the system repeatedly switches as the time delay, related to the changes of toxicity incurred in the adult predator, varies, and finally becomes unstable for a significant value of it. Besides that, the delay related to the prey's toxicity has also led some exciting results. [ABSTRACT FROM AUTHOR]

Selection of an appropriate therapy threshold to restrain the virus load is still challenging on structured treatment interruptions (STIs) for HIV. In this paper, we ponder that how the sliding control and multistability to regulate the treatment effect through comprehensive dynamics of a virus-immune model. Firstly, based on piecewise therapy, we propose a delayed reaction–diffusion virus-immune model under the homogeneous Neumann boundary condition. Secondly, the existence and stabilities of five kinds of equilibria as well as the direction and stability of spatial Hopf bifurcation at regular equilibrium are investigated. Thirdly, the sliding domain and the boundary node bifurcations are addressed by theoretical analysis. Finally, we appraise the effects of therapy threshold, sliding domain and multistability on HIV therapy by simulations, and further seek out the appropriate therapy threshold for infected patients with given physiological parameters and present the corresponding principles. Our explorations will provide evidence for HIV and other disease therapies. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-dimensional time-fractional inverse heat conduction problem, which is severely ill-posed. A quasi-reversibility method is proposed to solve this problem with disturbed boundary value. We give the selection of regularization parameters of quasi-reversibility method both under a priori and a posteriori rules, and give the proof of error estimates between the exact solution and its regularization approximation. Further more, numerical results are included to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we apply the Bernstein collocation method to construct the solution set of the Sylvester matrix differential equation (Sy-MDE) which involves the Lyapunov matrix differential equation. The method depends on the collocation method and Bernstein polynomials. The main advantage of the proposed method is that by using this method Sy-MDE reduces to a linear system of algebraic equations which can be solved by using an appropriate iterative method. We analyze the error and give a theorem that bounds the error. We also give the residual correction procedure to estimate the error. By using the procedure, we obtain a new approximate solution, namely a corrected Bernstein collocation solution. To illustrate how the proposed method is applied, several examples are given. Numerical experiments show the effectiveness and accuracy of the method for solving such types of Sy-MDE. [ABSTRACT FROM AUTHOR]

This paper presents a new compact finite difference scheme for solving linear high-dimensional time-dependent partial differential equations (PDEs). Despite the different spatial and time conditions in time-dependent problems, we propose a new compact finite difference scheme simultaneously both in time and space with arbitrary order accuracy. The merit of the proposed method is that the approximation of partial derivatives are derived simultaneously at all grid points. Also, by substituting the partial derivatives in the linear time-dependent PDEs a linear system of equations is derived. To show the efficiency and applicability of the proposed method, the fourth, sixth, and eighth-order simultaneously compact finite difference schemes are used for solving parabolic and convection–diffusion equations which have both time and spatial partial derivatives. The numerical results show the accuracy of the proposed method. • A new simultaneously compact finite difference scheme both in time and space. • The partial derivatives of high-dimensional functions are obtained simultaneously. • The approximate partial derivatives have arbitrary order both in time and space. [ABSTRACT FROM AUTHOR]

The flow direction algorithm (FDA) is a new physics-based meta-heuristic optimization algorithm that is being used successfully in a variety of applications. However, FDA lacks theoretically rigorous convergency analysis and suffers from several drawbacks, such as premature convergence, lack of population diversity, and imbalance between exploitation and exploration. In this paper, the supermartingale convergence theorem is used to analyse the global convergence of FDA in a continuous search space. We first demonstrate that FDA's global convergence is determined by the accumulation of the minimum probability (P t ∗) that the flow swarm fall into the global optimal region in each iteration. Then, an improved flow direction algorithm, namely, guided flow direction algorithm (GFDA), is proposed to increase the minimum probability by making full use of the neighbourhood information. Comprehensive experimental studies were conducted to test and validate the proposed GFDA. Twenty competitive meta-heuristic optimization algorithms, twenty-three classical benchmark functions, ten recently single objective bound constrained numerical optimization problems(CEC2020), and four constrained engineering problems were used. Finally, the experimental results and statistical tests (Friedman test and Wilcoxon test) demonstrate the superiority of GFDA compared to other algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann–Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus. [ABSTRACT FROM AUTHOR]

Recently, the long time numerical simulation of PDEs with weak nonlinearity (or small potentials) becomes an interesting topic. In this paper, for the Klein–Gordon–Schrödinger equation (KGSE) with a small coupling constant ɛ ∈ (0 , 1 ] , we proposed a time-splitting Fourier pseudo-spectral (TSFP) scheme by reformulating the KGSE into a coupled nonlinear Schrödinger system (CNLSS). Through rigorous error analysis, we establish improved error bounds for the scheme at O (h m + ɛ τ 2) up to the long time at O (1 / ɛ) where h is the mesh size and τ is the time step, respectively, and m depends on the regularity conditions. Compared with the results of existing numerical analysis, our analysis has the advantage of showing the long time numerical errors for the KGSE with the small coupling constant. The tools for error analysis mainly include the mathematical induction and the standard energy method as well as the regularity compensation oscillation (RCO) technique which has been developed recently. The numerical experiments support our theoretical analysis. Our scheme is novel because that to the best of our knowledge there has not been any TSFP scheme and any relevant long time analysis for the KGSE. [ABSTRACT FROM AUTHOR]

This paper addresses an H ∞ control approach on neural networks with hybrid-triggered mechanism (HTM) under deception attacks. With the aim of mitigating the burden of the transmission network, an HTM is introduced to handle unforeseen non-ideal environment influence, which is characterized by Bernoulli distribution. The weight combination coefficients ϵ j related to historical information are conducted to develop an improved HTM. By taking into account network-induced delay, and the randomly happened deception attacks in transmission network, a Lyapunov–Krasovskii functional (LKF) is constructed. Using linear matrix inequality (LMI), sufficient conditions are formed to render the system asymptotically stable and the H ∞ hybrid-triggered controller is designed. Finally, simulation examples are executed to validate the feasibility of the developed method. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with Trefftz discretizations of the time-dependent Maxwell equations in anisotropic media in three-dimensional domains. We propose a class of space–time Trefftz DG methods, which include the Trefftz variational formulation from Egger et al. (2015). We prove the error estimates of the approximate solutions with respect to the meshwidth and the condition number of the coefficient matrices. Furthermore, we propose the global Trefftz DG method combined with local DG methods to solve the time-dependent linear nonhomogeneous Maxwell equations in anisotropic media. The numerical results verify the validity of the theoretical results, and show that the resulting approximate solutions possess high accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a new system of nonlinear ordinary differential equations to study the unemployment problem in a context of financial crisis. We first prove the existence of a unique positive equilibrium. Then, using an appropriate Lyapunov function under some specified conditions, we prove the global stability of the unique positive equilibrium. We also propose and compare two control strategies with the objective to improve, at the lowest cost, the employment rate. Our results suggest that, in order to reduce the unemployment rate, it is better for a government to assist unemployed people in building their own business which will allow them to further create new vacancies than to assist self-employed individuals to create new vacancies. Numerical simulations are presented to substantiate the theoretical results. • We propose a new model to study the unemployment problem in financial crisis context. • We prove the global asymptotic stability of the unique equilibrium. • We propose two control strategies to improve, at lowest cost, the employment rate. • We perform numerical simulations to illustrate the theoretical results obtained. [ABSTRACT FROM AUTHOR]

The subject of this paper is the numerical investigation of a singularly perturbed parabolic problem with a simple interior turning point on a rectangular domain in the x − t plane with Dirichlet boundary conditions. At the location of the turning point, the solution to this class of problems has an internal layer. By decomposing the solution into a regular and singular component, we may first establish stronger bounds for the regular and singular components, as well as their derivatives. The fitted mesh finite difference scheme, which consists of a hybrid finite difference operator on a non-uniform Shishkin mesh in the space direction and a backward implicit Euler scheme on a uniform mesh in the time variable, is used to identify the approximate numerical solution. The accuracy of the resulting scheme is then improved in the temporal direction using the Richardson extrapolation scheme, which reveals that the extrapolated scheme is almost second-order uniformly convergent in both space and time variables when ɛ ≤ C N − 1 . Two numerical examples are used to demonstrate the efficacy and accuracy of the finite difference approaches mentioned. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a class of nonconvex optimization problems with fuzzy objective functions under granular differentiability concept. In order to get it, we give the definition of granular preinvex fuzzy functions and discuss its fascinating characteristics. In particular, two necessary and sufficient conditions for granular differentiable fuzzy functions to be granular preinvex are proved. As an application of granular preinvex fuzzy functions, we study a class of nonconvex fuzzy optimization problems with constraints, and obtain the existence of the optimal solution by solving the fuzzy variational inequalities. In addition, the developed theory is illustrated by some numerical examples. [ABSTRACT FROM AUTHOR]

This paper suggests a new and efficient variance reduction technique based on the Monte-Carlo simulation method for pricing the reinsurance contract in a regime-switching environment. The proposed approach extends the standard antithetic variables method to K > 2 antithetic variables per replication of the Monte-Carlo simulation. Since the model under the regime-switching framework describes a market with arbitrage opportunities, a risk-neutral measure by Esscher transform is provided. Under this probability measure, the proposed estimator is unbiased for pricing the reinsurance contract and increasing K which leads to more variance reduction. Finally, the success of the introduced method is confirmed numerically, and the efficacy of contract parameters is evaluated on its price. [ABSTRACT FROM AUTHOR]

Numerical simulation is more and more used during the design stage of a manufactured product in order to optimize its performances. However, it is often too time consuming, particularly when it is used to solve optimization problems, preventing an intensive usage. A-posteriori Model Order Reduction methods can be very effective to shorten the computational time. An approximated solution is then sought in a space of small dimension defined by a reduced basis. The accuracy of such methods is highly dependent on the choice of the reduced basis, extracted from preliminary numerical simulation. The method usually applied to construct such reduced basis is based on the Singular Value Decomposition (SVD), which can be time consuming, and is not adapted when a large collection of preliminary numerical simulations must be used to construct the basis. An alternative to this approach has been proposed recently with the Maximum Entropy Snapshot Sampling (MESS) method. In this paper, we propose to compare these methods with other approaches usually used for clustering or data classification based on vectors distance calculation, like the Centroidal Voronoi Tessellation (CVT), Density Based Spatial Clustering of Applications with Noise (DBSCAN), and Clustering Using Representatives (CURE). The methods are compared on a complex and realistic nonlinear problem in low frequency electromagnetics. The quality of the reduced bases obtained by the different methods are compared. Then, field distributions and global quantities, like eddy current losses and magnetic energy, are computed from the reconstructed results, to further analyze the quality of the reduced bases. • Description of a posteriori model order reduction methods using projection in a reduced basis. • Singular Value Decomposition, Centroidal Voronoi Tessellation, and 3 other methods. • Application on results from a non-linear low frequency electromagnetic simulation. • Calculation of fields and global values from reconstructed results. • Comparison of studied approaches in terms of projection error. [ABSTRACT FROM AUTHOR]

In this paper, the globally exponential lag quasi-synchronization problem of stochastic complex dynamical networks with impulsive control is studied. Sufficient conditions ensuring the exponential lag quasi-synchronization in mean square for the systems with and without communication delay are obtained by using some important inequalities, Lyapunov function and Itô formula respectively. The results show that the lag quasi-synchronization of stochastic complex dynamical networks can be realized by using the impulsive control method. Two numerical examples are also given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The fractional advection–diffusion equation can describe the anomalous diffusion associated with complicated diffusion medium and pollution source in application problems. The variable-order fractional advection–diffusion equation can change the order of fractional operator by controlling the power of order function. In this paper, 1D and 2D time–space variable-order fractional advection–diffusion equations are studied on a bounded domain, in which the order of time fractional derivatives are time dependent while the order of space fractional derivatives depend on either time or space. The time fractional derivatives are approximated by full-implicit difference scheme and the space fractional derivatives are discretized via Kansa's method combined with Wendland's C 6 compactly supported radial basis function. The Gauss–Jacobi quadrature is utilized to evaluate the weakly singular integration during the computation of the space fractional derivative of radial basis function. Finally, some numerical experiments are provided to verify the accuracy and efficiency of the proposed methods in 1D and 2D cases. [ABSTRACT FROM AUTHOR]

In overset grid assembly (OGA), the efficiency of assembly has been a major concern. In this paper, we propose an OGA strategy focuses on the re-assembly process in dynamic grid systems. Based on the recognition and expansion process of the hole boundary, we define a new set of cells for continuing OGA step. In this method, the number of cells participating in the new OGA process constitutes only a small portion of the primary grid system, leading to an acceleration in assembly and wall distance calculation. Not limited to the dynamic grid system, the static OGA is also improved based on the proposed method, without the need for additional mesh and only need minor changes to the program. We investigate cases including static and dynamic grid systems to verify the efficacy of the proposed method. The results confirm that the new method reduces the time consumption by 50% compared to the original method, particularly in the improvement of wall distance calculation. • An improved dynamic overset grid assembly (OGA) strategy is proposed. • The cells participate in the new OGA process constitutes only a small mesh portion. • It can be realized by making relatively minor changes to the initial program. • The new method reduces the time consumption by 50%. [ABSTRACT FROM AUTHOR]

In the present paper, the machine repair problem (MRP) with real-life scenarios is investigated, which plays a significant role in the manufacturing process, industries, production lines, etc. An M ∖ M ∖ 1 ∖ K machine repair problem with retrial attempts under admission control policy F -policy and machine's feedback is considered in which a single repairman is available to repair the failed machines. The recursive technique is applied to solve the mathematical model and establish the probability distributions for different states, which are further used to develop the performance indices. The parametric non-linear programming (P-NLP) technique is employed to develop the MRP with F -policy in a fuzzy environment using the trapezoidal and sigmoidal fuzzy numbers. Zadeh's extension principle and parametric non-linear programming technique help us to find the α -cuts of the developed performance predictors of MRP. We frame and minimize the total cost of the system. The harmony search method (HSM) and quasi-Newton method are implemented to achieve the total minimum cost of the system corresponding to the optimal repair rate, which helps the system managers in the formulation of business policies in industries, including the automobile sector. A numerical example is also given, which produces several tables and graphs that show the validity of the model. [ABSTRACT FROM AUTHOR]

The price of a barrier option is often computed numerically. Due to the path dependency, the convergence rate of such numerical approximation is generally of order 1 / 2. In this paper, we show that the convergence order can be achieved at 1 under certain condition. This confirms a numerical analysis done previously by the third author with others. We consider the case where the underlying process is a Brownian motion with drift. The price of a barrier option coincides with the price of a vanilla option of the "symmetrized" diffusion, which has a discontinuous drift. The symmetrized diffusion is then approximated by a Markov chain and the corresponding option price is calculated. This approximation to the barrier option is shown to have a convergence order of 1 under some mild condition on the initial value of the process and the payoff function. [ABSTRACT FROM AUTHOR]

This paper focuses on the study of long-term behaviour of the stochastic logistic systems under Markov chain using delay feedback control based on discrete-time observations. Necessary conditions for extinction, persistence and boundedness in p th moment of the species in the time average is examined. Particularly, the upper bound of (τ + τ 0 ) of the time lag between two successive observations τ and the delay time τ 0 , is obtained. The stochastic comparison theorem and asymptotic analysis are the main techniques applied. It has been observed that, the delay feedback control has an impact on the persistence of the species. Synthetic examples and virtual realities are given to support the findings. [ABSTRACT FROM AUTHOR]

This paper addresses existence and Ulam–Hyers stability (UHS) problems for an impulsive Caputo–Hadamard fractional neutral functional stochastic differential equation with infinite delay (FNFSDEwID). We first prove the existence and uniqueness of the solution using Banach fixed point theorem and standard stochastic analysis techniques. We then tackle the UHS under a Lipschitz condition on a bounded and closed interval. We end up with an illustrative example that corroborates our theoretical findings. [ABSTRACT FROM AUTHOR]

In order to help regulators to control credit risk contagion effectively when the financial crisis happens, this paper first proposes a new nonlinear SIS/R (Susceptible–Infected–Susceptible/Removed) model to describe the real dynamic of risk spreading, which is more reasonable compared with traditional epidemic models. We provide a comprehensive nonlinear analysis of monotonicity, threshold conditions, stability properties, and asymptotic convergence for the SIS/R model. Moreover, we formulate a time-varying optimal dual control problem considering the macro-prudential tools and the easy monetary policy. By applying Pontryagin's minimum principle, we obtain the existence of a solution and its uniqueness for sufficient small regulatory deadlines. At last, the theoretical results are confirmed by numerical simulations. We show the effectiveness of the optimal dual regulatory strategy against the constant dual strategy and no control strategy. The sensitivity of the control cost to the model parameters is also shown. [ABSTRACT FROM AUTHOR]

This paper focuses on the construction and analysis of the structure-preserving algorithm for generalized fractional Schrödinger equation with wave operator. A fourth-order energy-conserving difference scheme is developed for the resulting equivalent system based on scalar auxiliary variable approach. The discrete energy conservation law, boundedness and convergence of difference solutions are proved in detail. Numerical experiments are performed to verify our theoretical analysis results. [ABSTRACT FROM AUTHOR]

In this paper, the optimal purchasing decisions of the option procurement of newsvendor-type commodities are studied. Based on the mismatch cost minimization criterion, the present study analyzes the option purchasing decisions of a risk-averse newsvendor under the measure of Conditional Value-at-Risk (CVaR). For the purpose of controlling the procurement risk, it is found that a newsvendor's optimal option purchasing decision under the CVaR measure increases at the quantile level under certain conditions. The result provides alternative explanations for a newsvendor's over-purchasing behaviors in reality. To mitigate the conservativeness of the CVaR measure, a combined objective defined as the mean-CVaR on mismatch cost is introduced, and the optimal option purchasing decision of a newsvendor minimizing the combined objective is derived. The combined objective can strike a balance between the minimization of CVaR of mismatch cost as well as the minimization of expected mismatch cost. In addition, a sensitivity analysis is performed to exhibit the results and managerial insights are presented to hedge against the potential risks for newsvendors in the option purchasing decision-making. [ABSTRACT FROM AUTHOR]

This paper focuses on developing a bounded real lemma (BRL) and designing a state-feedback controller which guarantees a prescribed H ∞ performance level for a class of memristor-based neural networks (MNNs) with unbounded time-varying delays. Firstly, a BRL for MNNs is presented by taking a new approach based on system solutions. This approach requires neither transformation of the model nor construction of Lyapunov–Krasovskii functionals, thereby reducing computational effort and complexity. In addition, the obtained BRL contains only a few simple inequalities, which can be easily solved by using MATLAB. Secondly, the condition for the existence of exponential H ∞ controller is given based on the obtained BRL. Finally, two simulation examples demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical and numerical investigation of stationary and oscillatory patterns in a spatial model of bacteria quiescence. The reaction–diffusion model consists of active and inactive microbial populations in a harsh environment accounting for the directed movement and switch of cells to dormancy at high concentration levels. We present a bifurcation analysis of the model and the interplay between Turing and Hopf instability is discussed. Numerical simulations supporting the existence of spatially homogeneous solutions, as well as stable spatial patterns and oscillatory patterns are presented. [ABSTRACT FROM AUTHOR]

In this paper, for the initial–boundary value problems of semi-linear reaction–diffusion equations with piecewise continuous argument in spatial derivative, we suggest Crank–Nicolson method, high-order compact difference (HOCD) method and HOCD-based Richardson extrapolation (RHOCD) method. Under the appropriate conditions, it is proved that HOCD (resp. RHOCD) method has the computational accuracy O (τ 2 + h 4) (resp. O (τ 4 + h 4)). This shows that RHOCD method improves the calculation accuracy of HOCD method in temporal direction. Moreover, we also analyze the stability of HOCD method and thus derive a global stability criterion of this method. Finally, with a series of numerical experiments, we further confirm the computational effectiveness and theoretical accuracy of the concerned methods. [ABSTRACT FROM AUTHOR]

This paper proposes a compact sixth-order accurate numerical method to solve Poisson equations with discontinuities across an interface. This scheme is based on two techniques for the second-order derivative approximation: a high-order implicit finite difference (HIFD) formula to increase the precision and an immersed interface method (IIM) to deal with the discontinuities. The HIFD formulation arises from Taylor series expansion, and the new formulas are simple modifications to the standard finite difference schemes. On the other hand, the IIM allows one to solve the differential equation using a fixed Cartesian grid by adding some correction terms only at grid points near the immersed interface. The two-dimensional equation is then solved by a nine-point compact sixth-order scheme named HIFD-IIM. Fourth- and second-order methods result in particular cases of the proposed method. Furthermore, the sixth-order method requires similar computational resources to a fourth-order formulation because the resulting matrices in both discretizations are the same. However, higher-order methods require the knowledge of more jump conditions at the interface. From the theoretical derivation of the proposed method, we expect fully six-order accuracy in the maximum norm. This order has been confirmed from our numerical experiments using nontrivial analytical solutions. [ABSTRACT FROM AUTHOR]

This paper introduces a deterministic fractional-order epidemic model (FOEM) for studying the transmission dynamics of the human immunodeficiency virus (HIV) and acquired immunodeficiency syndrome (AIDS). The model highlights the substantial role of unaware and undetected HIV-infected individuals in spreading the disease. Control strategies, such as wielding condoms, level of preventive measures to avoid infection, and self-strictness of susceptibles in sexual contact, have been incorporated into the study. The basic reproduction number ℛ 0 α has been derived, which suggests the conditions for ensuring the persistence and elimination of the disease. Further, to validate the model, actual HIV data taken from Mexico and India separately have been used. The disease dynamics and its control in both countries are analyzed broadly. The values of biological parameters are estimated at which numerical solutions better match the actual data of HIV patients in the case of fractional-order (FO) instead of integer-order (IO). Moreover, in the light of ℛ 0 α , our findings forecast that the disease will abide in the population in Mexico, and at the same time, it will die out from India after a long time. [ABSTRACT FROM AUTHOR]

In this paper, a three tier mathematical model describing the interactions between susceptible population, Covid-19 infected, diabetic population and Covid-19 infected, non diabetic population is proposed. Basic properties of such a dynamic model, namely, non negativity, boundedness of solutions, existence of disease-free and disease equilibria are studied and sufficient conditions are obtained. Basic reproduction number for the system is derived. Sufficient conditions on functionals and parameters of the system are obtained for the local as well as global stability of equilibria, thus, establishing the conditions for eventual prevalence of disease free or disease environment, as the case may be. The stability aspects are discussed in the context of basic reproduction number and vice versa. An important contribution of this article is that a novel technique is presented to estimate some key, influencing parameters of the system so that a pre-specified, assumed equilibrium state is approached eventually. This enables the society to prepare itself with the help of these key, influencing parameters so estimated. Several examples are provided to illustrate the results established and simulations are provided to visualize the examples. [ABSTRACT FROM AUTHOR]

The novelty of this paper is to derive a mean square solution of a second-order (Caputo) fractional linear differential equation in which the coefficients and initial conditions are random variables, and the forcing term is a second order stochastic process. Using the so-called mean square calculus and assuming mild conditions on the random variables of the equation together with an exponential growth condition on the forcing term, a mean square convergent generalized power series solution is constructed. As a result of this convergence, the sequences of the mean and correlation obtained from the truncated power series solution are convergent as well. The theory is illustrated with several examples in which different kind of distributions on the input parameters are assumed. [ABSTRACT FROM AUTHOR]

This paper studies the rotatory vibrating motion of a dynamically symmetric charged solid body (SB) connected with a spring around a fixed point as a novel model. The body is assumed to be influenced by a Newtonian force field (NFF) besides extrinsic moments like perturbing, restoring, and gyrostatic moment (GM). These moments are guided along the body's principal axes of inertia. The body is assumed to have a high starting angular velocity in the direction of the dynamic symmetry axis, and the perturbing moments (PM) are thought to be less than the restoring moment. These assumptions provide us with a tiny parameter, to use the averaging technique (AT), and to acquire the averaging system of the regulating one. Several applications are introduced to achieve the solutions of this system separately. These solutions are graphed to reveal the positive influences of the body's numerical values on the behavior of the body, taking into account the various impacts of the applied moments, the electromagnetic field, and the Newtonian one for all examined applications. The obtained results are considered a generalization of those which were obtained in related previous works. For the projections of the body angular velocity, the proportion of differences as a function of the investigated parameters varies between 17% and 35%, whereas the other parameters are varied between 0.0011% and 0.37%, respectively. Therefore, these outcomes are considered to be significant due to their applications in life specially that based on the theory of vibrating systems in physics and engineering fields. [ABSTRACT FROM AUTHOR]

Although many intelligent optimization algorithms have been applied to the multimodal multi-objective optimization problems (MMOPs) which are complex and difficult, challenges of MMOP such as loss of PS in decision space and low efficiency have not been well solved. To better solve these problems, an altruistic population algorithm (APA) which is based on the altruism behavior in some animal populations, is proposed in this paper. The proposed APA has five major operations: parent selection, procreation variation, altruistic nurturing, crowd competition and archive updating. A few important features of the proposed APA are: (1) The nurturing cost according to a pair of parents' condition is introduced. It can accelerate the convergence speed while maintaining the diversity of the Pareto optimal solutions (PS). (2) The application of altruism allows the transfer of nurturing cost between descendant siblings to improve the efficiency and decrease the unnecessary variations. (3) A selection strategy called neighboring selection based on the distance in the objective space is proposed. It is an effective way to delete the redundant individuals in the objective space. The experimental results reveal that APA preforms better than other existing algorithms for solving various MMOPs. • Based on the altruism, a novel meta-heuristic algorithm is proposed. • The nurturing process can balance the convergence speed and diversity of PS. • The application of altruism can improve the efficiency of evolutionary cost. • The proposed selection strategy is an effective way to delete the redundant. [ABSTRACT FROM AUTHOR]

Main focus of this paper is to introduce a new class of Fox–Wright type functions and obtain several new integral representations and various integral transforms such as Mellin transform, Whittaker transform, Jacobi transform, Gegenbauer transform, Laplace transform, Euler (Beta) transform, P δ , R ν and Hankel transform. Moreover, a new probability density function is also introduced and several properties are studied. As application, fractional derivative and fractional integration formula are established. The results obtained in this paper, are presumably new and their importance is illustrated by several interesting consequences and examples. Furthermore, numerical computation and graphical representations have been expressed to validate the results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical analysis of Fitzhugh–Nagumo (FHN) reaction–diffusion equations. The properties of numerical solutions of a semi-discrete and fully-practical piecewise linear finite element technique are provided. Moreover, for a semi-discrete and fully discrete finite element approximation, we establish a priori estimates and error bounds. We also introduce the results of some numerical examples in one and two dimensions, which confirm the theoretical findings of this paper. [ABSTRACT FROM AUTHOR]

This paper describes an analytical and numerical investigation of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton (TPP) and impulsive perturbations. White noise, impulsive perturbations, and TPP were incorporated into the system to stimulate natural aquatic ecological phenomena. The aim of this paper was to analyze how these factors affect the dynamics of the system. Mathematical derivations were utilized to investigate some key threshold conditions that ensure the existence and uniqueness of a global positive solution, population extinction, and persistence in the mean. In particular, we determined if there is a positive periodic solution for the system when the toxin liberation rate reaches a critical value. The numerical results indicated that both white noise and the impulsive control parameter can directly influence population extinction and persistence in the mean. Enhancing the toxin liberation rate of TPP increases the possibility of phytoplankton survival but reduces zooplankton biomass. These results improve our understanding of the dynamics of complex of aquatic ecosystems in a fluctuating environment. [ABSTRACT FROM AUTHOR]

In this paper, a new approach is proposed for parameter identification in seismically excited structures based on synchronization method and fuzzy logic. The main contribution of this paper is providing a general solution for the estimation of the identifier coefficients using fuzzy logic. These identifier coefficients adjust the convergence rate and accuracy of the identification. The fuzzy controller uses triangular membership functions as input and output. The input parameters to the fuzzy controller are functions of displacement and velocity of the top story subjected to earthquake excitation. By using appropriate fuzzy rules the results are obtained for identifier coefficients. Additionally, a novel and simple formulation to identify structural unknown parameters based on synchronization is presented. The performance of the proposed approach is investigated using different shear frames under various excitations. The sensitivity of the proposed method to different noise levels and modeling uncertainties is analyzed. Numerical examples indicate that the presented method can identify the unknown parameters of the structure with high accuracy and reasonable computational time. [ABSTRACT FROM AUTHOR]

Reasonable prediction of natural gas consumption and production in China is helpful for decision-makers formulate policies to solve the increasingly prominent contradiction between supply and demand of natural gas in China. Taking into account the data environment of China's small sample, this paper considers using the grey prediction model with characteristic of small sample modeling to study the consumption and production of natural gas in China. To achieve accurate prediction, this paper developed a novel discrete fractional nonlinear grey Bernoulli model with power term (DFNGBM(1,1, α)), and used the latest equilibrium optimizer to solve the hyper-parameters of the model. The proposed model has the advantages of most existing grey prediction models, such as fractional-order accumulation operation and time power term. In addition, the proposed model is a unified expression form of many other grey forecasting models. The consumption and production of natural gas in China from 2003 to 2020 are used as examples to verify the feasibility and validity of the proposed model compared with other competitive models that have been used to study natural gas. It turns out that the prediction ability of the proposed model is better than other models. Therefore, the feasibility and effectiveness of the proposed model have been confirmed. Finally, the DFNGBM (1,1, α) model is used to predict China's natural gas consumption and production in the next few years, and some corresponding recommendations are given based on the prediction results. [ABSTRACT FROM AUTHOR]

This article deals with global μ -stabilization of quaternion-valued inertial bidirectional associative memory neural networks (QVIBAMNNs) with time-varying delays via time-delayed impulsive control. Firstly, the existence and uniqueness of the equilibrium point are proved by the homeomorphism mapping method. Then, based on an improved differential inequality, sufficient conditions for global μ -stabilization of QVIBAMNNs via time-delayed impulsive control are obtained. Significantly, the activation function in this paper is an extension of Lipschitz condition, which is superior to general quaternion-valued activation function. And quaternion is not required to be decomposed into real or complex values in this paper. Ultimately, some numerical simulations have proved the feasibility of the theorems. [ABSTRACT FROM AUTHOR]

Solving the convergence problem in the world of computing is needed to find an optimization solution. Many researchers propose a meta-heuristic approach in solving problems quickly using the results of the approach. This method is used because of its flexibility and fast search rate. Each meta-heuristic method has its own characteristics and is not necessarily able to solve the problem for all cases. This paper proposes a meta-heuristic method that is inspired by the way in which leaders are chosen in the chimpanzee community. The leader in the chimpanzee community is always the alpha male chimpanzee and has relationships with all chimps, both male and female. The principle of Chimpanzee Leader Election Optimization (CLEO) is the phase of improving performance and social relations with community members. The chimp performance improvement phase is based on the age aspect, which affects the memorize's ability of the chimps, which are inverted U-shaped. Meanwhile, the social relations/mating phase has been analogized in this CLEO algorithm. This paper has also evaluated the performance of the proposed algorithm, both to find the optimal value in the minimum and maximum search. This algorithm has also been compared with various other meta-heuristic algorithms. The results of the CLEO algorithm are quite competitive with other meta-heuristic algorithms in multi-high dimensional. [Display omitted] • Meta-heuristic. • Optimization. • Computational Modeling. [ABSTRACT FROM AUTHOR]

This paper studies the delay-dependent conditions for finite-time extended dissipativity based non-fragile feedback control for neural networks with mixed interval time-varying delays. By applying Jensen's inequality, an extended Jensen's double integral inequality, and a free matrix form inequality to the Lyapunov–Krasovskii functional (LKF), delay-dependent conditions are derived and solved by the Matlab control toolbox in terms of linear matrix inequalities (LMIs). By stability criteria, this paper is less conservative than the other works. In addition, we demonstrate the advantage of our obtained methods by five numerical examples. One practical example shows a real-world approach: the quadruple-tank process system (QTPS). • This research is the first time studying the finite-time extended dissipative performance and the design of non-fragile feedback controller on the neural networks with distributed and interval time-varying delays model. • In Theorem 2, we provide new sufficient conditions for extended dissipative performance based on Theorem 1. The corresponding model is finite-time extended dissipative. • Based on Theorem 2, we design the non-fragile controller. The corresponding model is finite-time extended dissipative via the nonfragile feedback controller in Theorem 3. • We construct new LKF and apply several inequalities for estimation of integral terms from the derivative of Lyapunov–Krasovskii functionals (LKFs) to achieve the upper bound of the interval time-varying delay greater than [7, 10, 13, 32]. • Finally, we provide an example to show the effectiveness of our result applied with a practical implementation: the quadruple-tank process system (QTPS) and desirable into engineering. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish the stability results based on the approach of Linear Matrix Inequality (LMI) for the addressed mathematical model using Caputo–Fabrizio operator (CF operator). Firstly, we extend some existing results of Caputo fractional derivative in the literature to a new fractional order operator without using singular kernel which was introduced by Caputo and Fabrizio. Secondly, we have created a mathematical model to increase Cytoplasmic Incompatibility (CI) in Aedes Aegypti mosquitoes by releasing Wolbachia infected mosquitoes. By this, we can suppress the population density of A.Aegypti mosquitoes and can control most common mosquito-borne diseases such as Dengue, Zika fever, Chikungunya, Yellow fever and so on. Our main aim in this paper is to examine the behaviours of Caputo–Fabrizio operator over the logistic growth equation of a population system then, prove the existence and uniqueness of the solution for the considered mathematical model using CF operator. Also, we check the α -exponential stability results for the system via linear matrix inequality technique. Finally a numerical example is provided to check the behaviour of the CF operator on the population system by incorporating the real world data available in the known literature. [ABSTRACT FROM AUTHOR]