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This paper describes the ongoing research on the physical modeling of AssiDoma¨n paper mill in Fro¨vi (Sweden). This project includes the developing of a Modelica base library for thermohydraulic, pulp and paper systems. Up to now, the model includes the wet end part of the paper process, that is the approaching system from the mixing chests to the cyclone systems, the headboxes and the wires. [Copyright &y& Elsevier]

One of the most important characteristics of the photovoltaic (PV) modules is their long lifetime (around 25 years). However, recent investigations have shown that PV modules may suffer significant degradation before that time; that is why the development of diagnostic techniques is important for the customers of PV systems. In this paper two indicators to quantify the degradation of a PV module are presented. Such indicators use the single-diode model to represent a PV module without degradation and combine such information with the experimental measurements to estimate the increase in the series resistance and/or the decrease in the parallel resistance with respect to reference values. The estimation of those variations allows the quantification of the module degradation. Simulation results comparing the proposed indicators with the fill factor (a traditional indicator to quantify the electrical quality of a PV module), and other indicators to estimate the series resistance are presented to illustrate the advantages of the proposed indicators. [ABSTRACT FROM AUTHOR]

This paper deals with smart grid concept and its reliability in presence of renewable energies. Around the globe an adjustment of electric energy is required to limit CO2 gas emission, preserve the greenhouse, limit pollution, fight climate change and increase energy security. Subsequently renewable energy expansion is the real test for designers and experts of smart grid system. This initiative has made significant progress toward the modernization and growth of the electric utility infrastructure and aims to integrate it into today's advanced communication era, both in function and in architecture. The study is focused on the difference between a conventional grid and a smart grid concept and the integration of renewable energy in a smart grid system where grid control is a must for energy management. Assuring a good grid reliability, taking the right control measures in order to preserve continuous electricity supply for the customers are challenges highlighted in the present paper. [ABSTRACT FROM AUTHOR]

In this paper, we consider Constrained Pseudoconvex Nonsmooth Optimization Problems (CPNOPs), which are a class of nonconvex optimization problems. Due to their nonconvexity, classical convex optimization algorithms are unable to solve them, while existing methods, i.e., numerical integration methods, are inadequate in terms of computational performance. In this paper, we propose a novel approach for solving CPNOPs that combines neurodynamic optimization with deep learning. We construct an initial value problem (IVP) involving a system of ordinary differential equations for a CPNOP and use a surrogate model based on a neural network to approximate the IVP. Our approach transforms the CPNOP into a neural network training problem, leveraging the power of deep learning infrastructure to improve computational performance and eliminate the need for traditional optimization solvers. Our experimental results show that our approach is superior to numerical integration methods in terms of both solution quality and computational efficiency. [ABSTRACT FROM AUTHOR]

This paper presents the synthesis of a state observer for the 1 D × 1 D Vlasov–Poisson (VP) equations. To derive the LPV (linear parameter-varying) formulation of the system, the Vlasov equation is approximated using the discontinuous Galerkin method and the Poisson problem is approximated using the Raviart–Thomas mixed finite element approach. The paper demonstrates the asymptotic and exponential stability of the discretized VP system. Furthermore, the synthesis is extended to include H ∞ state estimation. A simulation code has been developed to validate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel pseudospectral (PS) method for solving a new class of initial-value problems (IVPs) of time-dependent one-dimensional fractional partial differential equations (FPDEs) with variable coefficients and periodic solutions. A main ingredient of our work is the use of the recently developed periodic RL/Caputo fractional derivative (FD) operators with sliding positive fixed memory length of Bourafaet al. (2021) or their reduced forms obtained by Elgindy (2023) as the natural FD operators to accurately model FPDEs with periodic solutions. The proposed method converts the IVP into a well-conditioned linear system of equations using the PS method based on Fourier collocations and Gegenbauer quadratures. The reduced linear system has a simple special structure and can be solved accurately and rapidly by using standard linear system solvers. A rigorous study of the computational storage requirements as well as the error and convergence of the proposed method is presented. The idea and results presented in this paper are expected to be useful in the future to address more general problems involving FPDEs with periodic solutions. [ABSTRACT FROM AUTHOR]

To date, a large number of research papers have been written on malware classification, identification, classification into different families, and the distinction between malware and goodware. These works have been based on captured malware samples and have attempted to analyse malware and goodware using various techniques like the analysis of malware using malware visualization. These works usually convert malware samples capturing the malware structure into image structures which are then subject to image processing. In this paper, we propose an unconventional and novel approach to malware visualization based on its dynamical analysis, subsequent complex network conversion and fractal geometry, e.g. Julia sets visualization. Very interesting images being subsequently used to classify as malware and goodware. The classification is done by deep learning network. The results of the presented experiments of fractal conversion and subsequent classification are based on a database of 6,589,997 goodware, 827,853 potentially unwanted applications and 4,174,203 malware samples provided by ESET. 1 1 https://www.eset.com. This paper aims to show a new direction in visualizing malware using fractal geometry and possibilities in analysis and classification. [Display omitted] • Introduction of a new method for malware visualization based on fractal geometry. • Show interesting results when visualy comparing classified samples using fractal geometry. • Test novel malware image classification using deep learning. • To point out and define new research directions in visual malware analysis opened by our method. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a technique that utilizes both dynamical mechanisms and machine learning to reduce dimensionality in high-dimensional complex systems. Specifically, the method employs Hopf bifurcation theory to establish a model paradigm and use machine learning to train location parameters. The effectiveness of the proposed method is evaluated by testing the Van Der Pol equation and it is found that it possesses good predictive ability. In addition, simulation experiments are conducted using a hunting motion model, which is a well-known practice in high-speed rail, demonstrating positive results. To ensure the robustness of the proposed method, we tested it on noisy data. We introduced simulated Gaussian noise into the original dataset at different signal-to-noise ratios (SNRs) of 10 db, 20 db, 30 db, and 40 db. All data and codes used in this paper have been uploaded to GitHub. [ABSTRACT FROM AUTHOR]

This paper proposes a new method for determining the simulation parameters of the Jiles–Atherton Model used to simulate the first magnetisation curve and hysteresis loop in ferromagnetic materials. The Jiles–Atherton Model is an important tool in engineering applications due to its relatively simple differential formulation. However, determining the simulation parameters for the anhysteretic curve is challenging. Several methods have been proposed, primarily based on mathematical aspects of the anhysteretic and first magnetisation curves and hysteresis loops. This paper focuses on finding the magnetic moments of the material, which are used to define the simulation parameters for its anhysteretic curve. The proposed method involves using the susceptibility of the material and a linear approximation of a paramagnet to find the magnetic moments. The simulation parameters can then be found based on the magnetic moments. The method is validated theoretically and experimentally and offers a more physical approach to finding simulation parameters for the anhysteretic curve and a simplified way of determining the magnetic moments of the material. [ABSTRACT FROM AUTHOR]

This paper aims to obtain less conservative stability and stabilization conditions for sampled-data linear systems with multiple sampling rates. To this end, three novel delay-dependent states resulting from sampling are introduced in the augmented state, enabling the exploitation of the sawtooth-type characteristics of the sampling-induced delay in both stability and stabilization processes. Additionally, a novel discontinuous function is included in Lyapunov–Krasovskii-based functional to enhance the capacity to extract more information from specific sampling pattern for each state. Especially, to strengthen the interdependence among the components of the augmented state, supplementary zero equalities are incorporated into the stability analysis conditions. Furthermore, by including a novel weighted state derivative in the augmented state, this paper proposes an effective method that can transform the parameter-dependent stability conditions into stabilization conditions formulated in terms of linear matrix inequalities. Finally, the validity and practicality of the proposed method are demonstrated through two illustrative examples. [ABSTRACT FROM AUTHOR]

This paper discusses the process of optimizing the shape of systems that are controlled by the Stokes flow with threshold leak boundary conditions. In the theoretical part it focuses on studying the stability of solutions to the state problem in relation to a specific set of domains. In order to facilitate computation, the slip term and impermeability condition are regulated. In the computational part, the optimized portion of the boundary is defined using Bézier polynomials, in order to create a finite dimensional optimization problem. The paper also includes numerical examples to demonstrate the computational efficiency of this approach. [ABSTRACT FROM AUTHOR]

In this paper, the elastostatic and elastodynamic problems are analyzed by using the meshless generalized finite integration method (GFIM). The idea of the GFIM is to construct the integration matrix and the arbitrary functions by piecewise polynomial with Kronecker product, which leads to a significant improvement in accuracy and convenience. However, the traditional direct integration in the GFIM is difficult to deal with a large number of arbitrary functions generated in elastic problems. In order to tackle this problem, a special technique is proposed to construct relationships among arbitrary functions in this paper. Also, the Laplace transform method and the Durbin's inversion technique are adopted to deal with the variables of time in the elastodynamic problem. Several numerical examples are presented to demonstrate the accuracy and stability of the GFIM. [ABSTRACT FROM AUTHOR]

The paper focuses on pricing European-style options on multiple underlying assets under the Black–Scholes model represented by a nonstationary partial differential equation. The numerical solution of such equations is challenging in dimensions exceeding three, primarily due to the so-called curse of dimensionality. The main contribution of the paper is the design and analysis of the method based on combining the sparse wavelet-Galerkin method and the Crank–Nicolson scheme with Rannacher time-stepping enhanced by Richardson extrapolation, which helps overcome the curse of dimensionality. The next contribution is constructing a new orthogonal cubic spline wavelet basis on the interval and a sparse tensor product wavelet basis on the unit cube, which is suitable for the proposed method. The resulting method brings the following important advantages. The method is higher-order convergent with respect to both temporal and spatial variables, and the number of basis functions is significantly reduced compared to a full grid. Furthermore, many matrices involved in the computation are identity matrices, which results in a considerable simplification of the algorithm. Moreover, we prove that the condition numbers of discretization matrices are uniformly bounded and do not depend on the dimension, even without preconditioning, which leads to a small number of iterations when solving the resulting linear system. Numerical experiments are presented for several types of European-style options. [ABSTRACT FROM AUTHOR]

This study introduces a novel approach for integrating a compact mechanism into the Marine Predator Algorithm (MPA), subsequently proposing innovative parallel and communication strategies. The synergistic combination of these methodologies substantially augments the global search efficiency and accelerates the convergence rate of the original MPA. The paper culminates in presenting an enhanced version of the Marine Predator Algorithm, termed PCMPA, which leverages compact parallel technology. The performance of PCMPA, alongside a range of comparative algorithms, is rigorously evaluated using the CEC2013 benchmark test functions. These comparative algorithms encompass recent variants of MPA, PSO, DE, and other newly developed algorithms. Evaluation results reveal that PCMPA outperforms its counterparts in a more extensive array of test functions. To corroborate PCMPA's efficacy in real-world scenarios, the algorithm is applied to parameter optimization in Backpropagation neural network (BNN) and targeted engineering optimization challenges. This application demonstrates that PCMPA consistently achieves enhanced performance in practical implementations. • The study presents a novel variant of the Marine Predators Algorithm, dubbed PCMPA. • The paper benchmarks PCMPA against other Marine Predators Algorithm variants and other Algorithms. • The research applies PCMPA to optimize parameters of BNNs and to tackle engineering optimization challenges. [ABSTRACT FROM AUTHOR]

This paper aims to obtain the numerical solution of a one-dimension fourth-order Kuramoto-Sivashinsky (KS) equation, which has application in the context of flame propagation. This study combines the implementation of two new mechanisms quintic Uniform Algebraic Hyperbolic (QUAH) tension B-spline and quintic Uniform Algebraic Trigonometric (QUAT) tension B-spline with a renowned method known as Differential Quadrature Method (DQM). DQM is used to approximate the derivatives. Then, to obtain the weighting coefficients both quintic splines QUAH and QUAT are implemented with DQM and the original boundary value problem was then transformed into an ordinary differential equation. The Runge-Kutta 43 technique was used to solve the resultant ODE. With this approach, the outcomes are precise and close to the exact solution. The differential quadrature technique has a significant advantage over the previous approaches because it prevents the perturbation in order to find the better results for the given nonlinear equations. The accuracy of the suggested method is then illustrated numerically resolving four test problems and calculating the error norms L 2 and L ∞. Calculated results are displayed graphically and in tabular format for quick and simple access. This paper introduces an original work, to the best of the author's knowledge. The obtained solution and graphical observations show that QUAH and QUAT tension B-splines with DQM is a strong and dependable methods for estimating nonlinear problem solutions. Quintic B-splines are higher-order interpolation method compared to lower-degree B-splines, which results in more accurate approximations, and provides smooth and continuous representations of functions. Moreover, DQM when combined with quintic B-splines, can help reduce numerical dispersion, and can be applied to a wide range of problems. • Two new regimes of order six, referred as Uniform Algebraic Trigonometric and Uniform Algebraic Hyperbolic are proposed. • The Kuromoto-Sivashinsky equation (KS) is numerically solved by combining DQM with splines. • Four test problems have been resolved to gauge how well the current approach works. • Error norms and convergence order are calculated to evaluate the precision and efficiency of the approach. • The unconditional stability of the suggested technique has been proved. [ABSTRACT FROM AUTHOR]

Aiming at the second-order tracking system with arbitrary initial shifts, this paper presents a multi-phase iterative learning control strategy. Firstly, utilizing the form of solution of the second-order non-homogeneous linear differential equation with constant coefficients and the initial shifts, we can select the appropriate control gain to ensure that the second-order systems are stable and reach the stable output after a fixed time. Secondly, on the premise that the second-order systems have reached the fixed output, two methods are proposed for rectifying the fixed shift, namely, shifts rectifying control and varied trajectory control. Theoretical analysis shows that the multi-stage iterative learning control strategy proposed in this paper can ensure that the second-order systems achieve complete tracking in the specified interval. Finally, the simulation examples affirm the validation of the designed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we construct an improved Implicit–Explicit (IMEX) numerical scheme based on the conservation form of the advection–diffusion equations and study the numerical stability of the method in case of a nonlinear advection–diffusion Lotka–Volterra model. The classical numerical methods might be unsuitable for providing accurate numerical results for advection–diffusion problem in which advection dominates diffusion. An improved numerical scheme is proposed, which can preserve the positivity for arbitrary stepsizes. The convergence, boundedness, existence and uniqueness of the numerical solutions are investigated in paper. A threshold value denoted by R 0 Δ x , is introduced in the stability analysis. It is shown that the numerical semi-trivial equilibrium is locally asymptotically stable if R 0 Δ x < 1 and unstable if R 0 Δ x > 1. Moreover, the limiting behaviors of the threshold value are exhibited. Finally, some numerical simulations are given to confirm the conclusions. [ABSTRACT FROM AUTHOR]

This paper deals with the non-linear Susceptible–Infected–Hospitalized–Recovered model with Holling type II incidence rate, treatment with saturated type functional response for the prevention and control of disease with limited healthcare facilities. The well-posedness of the model is ensured with the help of the non-negativity and boundedness of the solution of the system. The feasibility of the model with DFE (Disease-free equilibrium) and EE (endemic equilibrium) is analysed. The local and global stability are discussed with the help of the computed basic reproduction number R 0. At R 0 = 1 , we use the Centre manifold theory to analyse the transcritical bifurcation exhibited by the system. It is found that the disease is not eradicated even if R 0 < 1 due to the occurrence of backward bifurcation. The occurrence condition of Hopf bifurcation is obtained. The optimal control theory is used to analyse the effects of the minimum possible medical facilities, hospital beds, and awareness creation on the population dynamics. The Hamiltonian function is constructed with the extended optimal control model and solved by Pontryagin's maximum principle to get the minimum possible expenditure. Different types of control strategies are shown by numerical simulation. The sensitivity analysis is discussed with the help of a crucial parameter that depends on the reproduction number. Further, the model is simulated numerically to support the theoretical studies. This paper emphasizes the significance of treatment intensity, the total number of hospital bed available and their occupancy rate as vital parameters for prevention of disease prevalence. • A nonlinear model is proposed to study the spread and control of infectious diseases with limited healthcare facilities. • Due to backward bifurcation, R 0 < 1 is insufficient to eliminate the disease, and the system exhibits periodic oscillation due to the emergence of Hopf bifurcation. • Using Pontryagin's maximum principle, effects of the limited medical facilities, hospital beds, and awareness-building initiatives are examined to determine the minimum possible expenses. • Sensitivity analysis is used to determine the appropriate control parameter and cost-effectiveness analysis is used for finding most optimal strategy. [ABSTRACT FROM AUTHOR]

The Fibonacci sequence is significant because of the so-called golden ratio, which describes predictable patterns for everything. Fibonacci polynomials are related to Fibonacci numbers, and in this paper we extend their applicability by using them to solve fractional differential equations (FDEs) and systems of fractional differential equations (SFDEs). With the help of the Riemann–Liouville fractional integral operator for the fractional-order hybrid function of block-pulse functions and the Fibonacci polynomials defined in this paper, the solution of the considered FDE and SFDE is reduced to a system of algebraic equations, which can be solved by Newton's iterative method. The fractional order is obtained by transforming x into x α , with α > 0. Compared to other models, our method in some situations is better by twelve orders of magnitude. There are situations when we get the exact solution. The presented method proves to be simple and effective in solving nonlinear problems with given initial values. [ABSTRACT FROM AUTHOR]

In this paper, the asymptotic solutions about the origin and infinity are formulated via Laplace transform for a two-term linear Caputo fractional differential equation. The asymptotic expansion about the origin describes the complete singular information of the solution, which is also a good approximation of the solution near the origin. The expansion at infinity exhibits the structure of the solution, as well as the stable or unstable property of the solution, which becomes more accurate as the variable tends to larger. Based on the asymptotic solution about the origin, a singularity-separation Legendre collocation method is designed to validate the methods in this paper. Numerical examples show the easy calculation and high accuracy of the truncated expansions and their Padé approximations when the variable is suitably small or sufficiently large. As an application, the method is used to solve the initial value problem of the Bagley–Torvik equation, and the oscillatory property of the solution is displayed. • The series solutions with logarithms about the origin and infinity are formulated. • The series solution at the origin is used to design a Legendre collocation method. • The expansion at infinity reveals the stable or unstable property of the solution. • The method can be applied to solve general multi-term linear fractional problems. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a three-dimensional Lotka–Volterra attractor in the frame of the Caputo fractional derivative to examine its dynamics. The theoretical concepts like existence and uniqueness and boundedness of the solution are analyzed. To regulate the chaos in this fractional-order system, we have developed a sliding mode controller and conditions for global stability of the controlled system with and without uncertainties and outside disruptions are derived. The ability of the designed controller is examined in terms of both commensurate and non-commensurate fractional order derivatives for all the aspects. The Lyapunov exponent is the novelty of this paper which is used to illustrate the behavior of the chaos and demonstrate the dissipativeness of the considered chaotic system. We have examined the effect of fractional order derivatives in this system. With the help of numerical simulations, the theoretical claims regarding the impact of the controller on the system are established. [ABSTRACT FROM AUTHOR]

In this paper we formulate various mathematical models to describe the processes of anaerobic digestion of an organic waste treatment plant, based on its chemical kinetics, stoichiometry and on the biological aspects that influence the chemical reactions of anaerobic digestion. The latter is a process of degradation of the organic substance by microorganisms in the absence of oxygen, used in plants that have the purpose of producing biomethane and compost. This type of process is very complex and for its realization different chemical phases are involved as well as the presence of different bacterial families. The chemical reaction reagent represents the digester substrate; the products are biogas (methane and carbon dioxide) and digestate (degraded organic substances, from which compost is obtained). The populations modeled here are the reactants of chemical reactions and their products, as well as microorganisms. The latter play an important role as they carry the reactions inside the anaerobic reactor in which they live. Each mathematical model formulated consists of a system of ordinary differential equations, numerically integrated with the use of MATLAB software. The models are formulated both in non-operational and operational conditions. In the first case, in which neither new daily organic waste inputs nor product releases are expected, the system variables are studied at steady state as functions of the parameters. The operating models, on the other hand, also consider the daily input and output of the plant. • The paper contains four models for the organic biodigester of a waste treatment plant. • Their behaviors are compared via simulations in the static case. • The models are extended to account for operational conditions. • Their behaviors are also tested against the available data in operational conditions. [ABSTRACT FROM AUTHOR]

This paper studies an optimization problem for the unsteady partial differential equations (PDEs) with convection term, widely used in continuous casting process. Considering the change of casting speed, a dynamic optimization method based on new DY-HS hybrid conjugate gradient algorithm (DY-HSHCGA) is proposed. In the DY-HSHCGA, the Dai–Yuan and the Hestenes–Stiefel conjugate gradient algorithms are convex combined, and a new conjugate parameter θ k is obtained through the condition of quasi-Newton direction. Moreover, Lipschitz continuity of the gradient of cost function, as an important conditions for convergence, is analyzed in this paper. On the basis on this condition, the global convergence of DY-HSHCGA is proved. Finally, the effectiveness of DY-HSHCGA is verified by some instances from the steel plant. Comparing with other algorithms DY-HSHCGA obviously accelerates the convergence rate and reduces the number of iteration. The optimizer based on the DY-HSHCGA shows a more stable results. • Optimization problem of an unsteady PDEs is investigated. • A new DY-HS hybrid conjugate gradient algorithm (DY-HSHCGA) is presented. • The global convergence of the DY-HSHCGA is analyzed. • The Lipschitz continuity of the gradient of cost function is proved • The effectiveness of DY-HSHCGA is verified by experimental simulations. [ABSTRACT FROM AUTHOR]

Recently, a time-splitting Fourier pseudo-spectral (TSFP) scheme for solving numerically the Klein–Gordon–Dirac equation (KGDE) has been proposed (Yi et al., 2019). However, that paper only gives numerical experiments and lacks rigorous convergence analysis and error estimates for the scheme. In addition, the time symmetry of the scheme has not been proved. This is not satisfactory from the perspective of geometric numerical integration. In this paper, we proposed a new TSFP scheme for the KGDE with periodic boundary conditions by reformulating the Klein–Gordon part into a relativistic nonlinear Schrödinger equation. The new scheme is time symmetric, fully explicit and conserves the discrete mass exactly. We make a rigorously convergence analysis and establish error estimates by comparing semi-discretization and full-discretization using the mathematical induction. The convergence rate of the scheme is proved to be second-order in time and spectral-order in space, respectively, in a generic norm under the specific regularity conditions. The numerical experiments support our theoretical analysis. The conclusion is also applicable to high-dimensional problems under sufficient regular conditions. Our scheme can also serve as a reference for solving some other coupled equations or systems such as Klein–Gordon–Schrödinger equation. [ABSTRACT FROM AUTHOR]

Time-fractional diffusion equation is an important transport dynamical model for simulating fractal time random walk. This article is devoted to investigating the a priori and a posteriori error estimates for this model equation. A Petrov–Galerkin spectral method is revisited in this paper to address our problem, which the generalized Jacobi functions and Fourier-like basis functions are utilized as basis for constructing efficient and accurate space–time spectral approximations. Rigorous proofs are given for the stability of our spectral scheme. And then the convergence of the proposed method is proved by establishing an a priori error estimate. Specifically, an efficient and reliable a posteriori error estimator is introduced, and we derive that the residual-based error indicator provides an upper bound and a lower bound for the numerical error. Finally, several numerical experiments are provided to examine our theoretical claims. • An available Petrov–Galerkin spectral method is proposed to approximate the TFDEs. • The spectral accuracy is confirmed by error analysis, along with numerical tests. • An a posteriori error estimate is derived, and numerical tests support our results. [ABSTRACT FROM AUTHOR]

The paper is concerned with three types of cubic splines over a triangulation that are characterized by three degrees of freedom associated with each vertex of the triangulation. The splines differ in computational complexity, polynomial reproduction properties, and smoothness. With the aim to make them a versatile tool for numerical analysis, a unified representation in terms of locally supported basis functions is established. The construction of these functions is based on geometric concepts and is expressed in the Bernstein–Bézier form. They are readily applicable in a range of standard approximation methods, which is demonstrated by a number of numerical experiments. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-time synchronization (FTS) issue for stochastic complex networks (SCNs) with/without time-delay under impulsive effects subject to denial of service (DoS) attacks. Firstly, a novel distributed dynamic event-triggered controller (DETC) is designed to realize the FTS for SCNs without delays, and the FTS conditions are addressed in the form of the algebraic inequalities. The Zeno behavior can be excluded for the proposed dynamic event-triggered mechanism (DETM). Secondly, a new feedback controller is designed to achieve the FTS for SCNs with time-varying delay. In addition, by applying Lyapunov stability theory and stochastic analysis technology, the FTS conditions are derived. Finally, two numerical examples are provided to illustrate the feasibility of the designed control strategies and the correctness of the stated theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the exponential synchronization problem for multi-link and multi-delayed inertial neural networks with Markov jump (MMDINNMJ) using an aperiodically intermittent adaptive control strategy. Different from most research on inertial neural networks, we take multi-link, multi-delay and Markov jump into account. The obstacle caused by the coexistence of Markov jump and multi-delay is avoided by using the delayed integral method while considering the exponential synchronization of MMDINNMJ. Additionally, under graph theory, Lyapunov stability theory and the developed control scheme, some novel sufficient conditions for synchronization at exponential rate in p th (p > 0) moment of underlying networks are determined, which are strongly related to multi-link topological structure, time delay, and Markov jump. Finally, two examples are given to demonstrate the viability of the theoretical conclusions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the role of plankton populations in the aquatic reservoir on the transmission dynamics of acute cholera within the human communities. To this, we develop a nonlinear six dimensional mathematical model that combines the plankton populations with the epidemiological SIR-type human subpopulations and the V. cholerae bacterial population in the aquatic reservoir. It is assumed that the susceptible humans become infected either by ingesting zooplankton, which serves as a reservoir for the cholera pathogen, by free-living V. cholerae in the water, or by cholera-infected individuals. We explore the existence and stability of all biologically plausible equilibria of the system. Also, we determine basic reproduction number (R 0) and introduced an additional threshold, named planktonic factor (E 0), that is found to significantly affect the cholera transmission. Furthermore, cholera-free equilibrium encounters transcritical bifurcation at R 0 = 1 within the planktonic factor's unitary range. We perform some sensitivity tests to determine how the epidemic thresholds R 0 and E 0 will respond to change in the parametric values. The existence of saddle–node bifurcation is shown numerically. Our findings reveal that there are strong connections between the planktonic blooms and the cholera epidemic. We observe that even while eliminating cholera from the human population is very difficult, we may nevertheless lessen the epidemic condition by enhancing immunization, treatment and other preventive measures. [ABSTRACT FROM AUTHOR]

This paper examines the asymptotic stability of nonlinear fractional-order switched systems (FOSSs) under a mode-dependent event-triggered delayed impulsive mechanism (MDETDIM). The impulses and switched signals are asynchronous. A novel MDETDIM is proposed to determine the impulsive sequence, which can prevent the Zeno phenomenon. Lyapunov-based asymptotic stability conditions for general FOSSs are derived using the proposed MDETDIM. The theoretical results are then applied to a fractional-order Hopfield neural network (FOHNN) with event-based delayed impulses and switching effects. Two examples are provided to demonstrate the effectiveness of our proposed results. [ABSTRACT FROM AUTHOR]

The present paper aims to develop a stable multistep numerical scheme for the non-linear generalized time-fractional diffusion equations (GTFDEs) with non-smooth solutions. Mesh grading technique is used to discretize the temporal direction, which results in 2 − α order of convergence (0 < α < 1). The spatial direction is discretized using a second order difference operator and the non-linear term is approximated using Taylor's series. Theoretical stability and convergence analysis is established in the L 2 -norm. Moreover, some random noise perturbations are added to investigate the numerical stability of the developed scheme. Finally, numerical simulations are performed on three test examples to verify the robustness and efficiency of the scheme. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of nonlinear BVP involving fractional derivative in the ψ -Riemann–Liouville sense with nonlocal boundary conditions. By means of some properties of the Green's function and fixed point theorems due to Banach, Boyd-Wong, and Rus, existence of a unique solution is obtained. We have some examples that prove the theory is true. [ABSTRACT FROM AUTHOR]

Proposing new metaheuristic methods is crucial for continuous algorithmic improvement and the ability to effectively address increasingly complex real-world optimization problems. On the other hand, Evolutionary Game Theory analyzes how trough competition is possible to modify the strategies of individuals within a population in order to spread successful mechanisms and reduce or remove less successful strategies. This paper introduces a novel optimization approach based on the principles of evolutionary game theory. In the proposed method, all individuals are initialized using the Metropolis–Hasting technique, which sets the solutions at a starting point closer to the optimal or near-optimal regions of the problem. An original strategy is then assigned to each individual in the population. By considering the interactions and competition among different agents in the optimization problem, the approach modifies the strategies to improve search efficiency and find better solutions. To evaluate the performance of the proposed technique, it is compared with eight well-known metaheuristic algorithms using 30 benchmark functions. The proposed methodology demonstrated superiority in terms of solution quality, dimensionality, and convergence when compared to other approaches. [ABSTRACT FROM AUTHOR]

In this paper, stochastic predictive computing networks are exploited to investigate the dynamics of the SIS with vaccination impact based epidemic model (SISV-EM) represented by nonlinear systems of stochastic differential equations (SDEs) by exploitation of artificial neural networks (ANNs) with the backpropagated Levenberg-Marquardt technique (BLMT) i.e., (ANNs-BLMT) to approximate the solution behavior. The stochastic nonlinear SISV-EM is governed with three classes: susceptible, infectious, and vaccinated populations. The referenced or target datasets for ANNs-BLMT are constructed by employing Euler-Maruyama (EM) scheme for solving stochastic differential systems in case of sufficiently various nonlinear SISV-EM scenarios by varying the percentage of vaccination for newly born, the coefficient of transmission, the natural mortality rates, the infectious rates of recovery, the rate at which vaccinated people lose their immunity, the rate of death caused by disease, the proportion of vaccinated against susceptible and the white noise in the environment. Based on arbitrary training, testing, and validation samples from the referenced dataset, the ANNs-BLMT provides an approximate solution for the stochastic nonlinear SISV-EM, with significant correlations to the referenced results. Exhaustive simulation-based results using error histograms, mean square errors, and regression analyses further demonstrate that the proposed ANNs-BLMT is efficient, consistent, and accurate for solving SISV-EM. • A two-layer framework of ANNs-BLMT is proposed as an innovative technique based on a stochastic computing paradigm to investigate the dynamics of stochastic nonlinear SISV-EM. • Innovative technique based on a stochastic computing ANNs-BLMT to investigate the dynamics of stochastic nonlinear SISV-EM Reference dataset for ANNs -BLMT is developed with Euler-Maruyama (EM) scheme nonlinear SISV-EM with varying parametersMean square error criteria is used for training of ANNs-BLMT to find approximate solutions to a variety of SISV-EM scenarios Computation of error histogram illustration, regression metrics, and MSE learning curves prove the performance of ANNs-BLMT. • The mean square error criteria are effectively utilized in approximation theory to develop an objective function for training the ANNs-BLMT to determine approximate solutions to a variety of stochastic nonlinear SISV-EM scenarios. • The computation of error histogram illustration, regression metrics, and MSE learning curves significantly improve the performance, precision, and consistency of the ANNs-BLMT for solving the stochastic nonlinear SISV-EM. [ABSTRACT FROM AUTHOR]

The existing chaotic systems exhibit chaos degradation phenomena because of the limited chaotic precision in the real number field. In response to this deficiency, this paper proposes a chaotic bits XOR system (CBXS) in the integer field satisfying Devaney's chaos. That is, CBXS has the property of sensitivity of initial value, topological transitivity, and periodic point density. Then, a series of chaotic and random test results illustrate that the sequences generated by CBXS with linear feedback shift register (LFSR) in the finite field G F (2) have good random and chaotic performance. It can overcome the chaos degradation problem because it is generated in the integer field and can avoid the limited precision in the real number field. Finally, we employ the proposed CBXS to image encryption with the optimized Arnold's transformation. The experimental results verify that even after simple encryption, the cipher image still exhibits good encryption effect and efficiency, which illustrates the effectiveness of CBXS. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the pricing of European crude oil options under nonlinear dynamics with stochastic behaviour and jump risks, incorporating the features of arising convenience yield of crude oil and potential extreme fluctuation in the dynamics of crude oil prices. We present a closed-form solution to European crude oil option prices under an incomplete market setting, after deriving the pricing kernel with the equilibrium method and determining the risk neutral dynamics of crude oil prices. We extend our model to a mean-reverting stochastic volatility case, which also admits an analytical formula for the equilibrium price of European crude-oil options. Finally, our model is shown to be consistent with a number of interesting facts documented in the recent literature. [ABSTRACT FROM AUTHOR]

In this paper, a linearized numerical scheme of nonlinear variable-order fractional diffusion equation with time delay is constructed. We apply the L 2 − 1 σ formula to discretize the temporal derivative and second-order central difference scheme to discretize the spatial derivative. The proposed method is unconditionally stable and convergent with O τ 2 + h 2 , where τ and h are the time and space steps, respectively. Numerical experiment demonstrates the effectiveness and accuracy of the numerical scheme. [ABSTRACT FROM AUTHOR]

The dissemination of public health information through television and social media posts is essential for informing the public about the transmission of contagious diseases, which is crucial in preventing the spread of various infectious diseases. In this paper, we propose a non-linear mathematical model to assess the effect of advertisements through social media in creating awareness and limiting treatment on spreading infectious diseases. These initiatives may alter population behaviour and divide the susceptible population into subgroups. In addition, to comprehend these dynamics better, we use half-saturation constant rates for media coverage and treatment. The model's well-posedness and feasibility are evaluated. The possible biological equilibrium points are calculated. Local and global stability are carried out. The objective of our study is to produce the model's bifurcation. Transcritical, Saddle–node, Hopf bifurcation of codimension 1 and Cusp, Generalized-Hopf (Bautin), and Bogdanov–Takens (BT) bifurcation of codimension 2 are studied for this purpose. Due to the limited medical resources and supply efficiency, the model exhibits backward bifurcation, resulting in bistability. Moreover, the occurrence condition for stability and direction of Hopf bifurcation is discussed. This model study demonstrates that the system is significantly influenced by the pace with which awareness programmes are implemented and that raising this value above a threshold may result in continuous oscillation. Sensitivity analysis employs the normalized forward sensitivity index of the basic reproduction number to provide a comprehensive understanding of the effect of various parameters on accelerating and limiting disease spread. Further, the minimum possible cost is determined by formulating an optimal control system based on sensitivity analysis and applying Pontryagin's maximum principle. Methods of cost-effectiveness, such as ACER and ICER, are used to determine the most cost-effective control intervention strategy among all the strategies. Numerical simulations have been done to support all theoretical findings. • A non-linear model is proposed to assess the effect of advertisements through social media and limiting treatment on infectious diseases. • Due to backward bifurcation, R 0 ¡ 1 is insufficient to eliminate the sickness, and additionally, the model displays Hopf, Saddle–node, Bogdanov–Takens, and Generalized Hopf bifurcation. • Strategies having the highest infection-averted capacity using treatment and media implementation as control parameters are obtained. • Different control techniques are compared using numerical simulation, and sensitivity analysis is used to determine the appropriate control parameter. • Using method like ACER and ICER, we determine the most cost-effective strategy. [ABSTRACT FROM AUTHOR]

In this paper, a cortex-basal ganglia model about Parkinson's disease with two time delays is studied, and the critical conditions for Hopf bifurcation are derived. The results show that time delays can change the state of basal ganglia. The basal ganglia is stable when the delays are small. However, when the time delay is greater than the corresponding bifurcation critical point, different types of oscillations occur in the basal ganglia. The larger the time delays, the more active the neuronal clusters in the basal ganglia. Furthermore, the bidirectional Hopf bifurcation is found by studying the connection weights between different neural nuclei. Finally, the influence of connection weight and time delay which are related to the internal segment of the globus pallidus on its oscillation is discussed. Research shows that reducing the connection weight and the corresponding time delay in excitatory neuronal clusters, or increasing the connection weight and decreasing the corresponding time delay in inhibitory neuronal clusters, can improve the oscillation of Parkinson's disease. [ABSTRACT FROM AUTHOR]

In this paper, we consider an enriched cut finite element method (ECFEM) with interface-unfitted meshes for solving Stokes interface equations consisting of two incompressible fluids with different viscosities. By approximating the velocity with the enriched P 1 element and the pressure with the P 0 element, and stabilizing the Galerkin variational formulation with suitable ghost penalty terms, we propose the new ECFEM and prove that it is well-posed and has the optimal a priori error estimate in the energy norm. All derived results are independent of the interface position. Moreover, compared with other conforming finite element methods with the optimal rate in convergence, the proposed scheme here not only has the minimum degrees of freedom, but also avoids using the derivative of the pressure in the penalty term. The presented numerical examples validate the theoretical predictions. [ABSTRACT FROM AUTHOR]

In this paper, we derive an efficient numerical scheme for approximating the energy eigenvalues and corresponding wavefunctions of the radial Schrödinger eigenproblems defined on a semi-infinite domain for arbitrary values of the angular momentum number. The numerical scheme is based on the Chebyshev spectral collocation differentiation matrix method. In this scheme, at first, we redefine the radial Schrödinger eigenproblem on a finite interval by adopting an appropriate change of the independent variable. Then, by expanding the wavefunctions of the problem as a series of the Chebyshev polynomials of the first kind, as well as employing the differentiation matrices in order to determine the derivatives of Chebyshev polynomials at the collocation points, considered problem becomes a generalized eigenvalue problem. The convergence behavior and excellent performance of the proposed technique are illustrated through some numerical experiments of the most significant potentials in quantum mechanics. Compared with exact solutions (when available), and those reported previously in the literature, the current scheme achieves higher accuracy and efficiency even when high-index energy eigenvalues are computed. [ABSTRACT FROM AUTHOR]

In this paper, we study the split common fixed point problem for two nonlinear mappings in p -uniformly convex and uniformly smooth Banach spaces. We propose an algorithm which uses dynamic stepsize, it allows to be easily implemented without prior information about operator norm. We further apply our result to solve the split variational inclusion problem, equilibrium problem and convexly constrained linear inverse problem. Moreover, we provide numerical examples to verify efficiency of our algorithm. • Presents an iteration process for splitting problems, with dynamic choosing step size. • Implement the result for solving wide classes of mathematical engineering problems. • Includes nontrivial example with computer simulation to compare our findings with existing ones. [ABSTRACT FROM AUTHOR]

In this paper, we study the time-fractional Euler–Poisson–Darboux equation with the Bessel fractional derivative. The Laplacian operator of this equation is considered in the ordinary and fractional derivatives and also in different coordinates. For the multi-dimensional Euler–Poisson–Darboux equation in the infinite domain (the whole space), we use the joint modified Meijer–Fourier transforms and establish a complex inversion formula for deriving the fundamental solution. The fractional moment of this solution is also presented in different dimensions. For studying the time-fractional Euler–Poisson–Darboux equation by the numerical methods in finite domain, we sketch the semi- and fully-discrete methods along with the matrix transfer technique to analyze the equation with fractional Laplacian operators in the cartesian, polar and spherical coordinates. The associated error and convergence theorems are also discussed. The illustrative examples are finally presented to verify our results in different coordinates. [ABSTRACT FROM AUTHOR]

In this paper, a supervisory interval type-2 fuzzy adaptive sliding mode control scheme is addressed for cable robots. In the proposed control scheme, intelligent methods are combined with conventional sliding mode control to achieve optimal adjustment of control parameters. This approach ensures accurate tracking performance, despite the structural constraints of cable robots. These constraints include the production of purely tensile forces and the effects due to inherent elasticity, which will make the design of the controller challenging. For this purpose, the internal force concept is utilized to ensure the tension style of cables. Additionally, considering a compensator part in the proposed controller and applying the singular perturbation theorem, the vibration effects of elastic cables are handled, and stability is proved through the second Lyapunov method. Therefore, the desired performance of the control system will be guaranteed for the movements that stimulate the vibration modes of cables. An interval type-2 fuzzy logic controller is proposed to adjust the control gain, effectively reducing the chattering level. Moreover, a supervisory interval type-2 fuzzy logic control system is introduced to regulate the gains within the sliding surface. The Grasshopper Optimization Algorithm is employed to select the optimal parameters for the membership functions of the fuzzy system. The results of the conducted simulations show that the desired tracking performance is provided, despite different uncertain parameters and the structural constraints of the considered cable robot. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the classical chemostat model where the consumption function of the species, in both cases Monod and Haldane, is perturbed by real random fluctuations. Once the existence and uniqueness of non-negative global solution of the corresponding random systems is ensured, we prove the existence of a deterministic compact attracting set, whence we are able to find conditions to guarantee either the extinction or the persistence of the species, the most important aim in real applications. In addition, we depict several numerical simulations to illustrate the theoretical framework, standing out our contributions, providing the biological interpretation of every result and comparing with similar works in the literature. [ABSTRACT FROM AUTHOR]

This paper tackles the problem of nonfragile state estimation for semi-Markovian switching complex-valued networks with time-varying delay. The concerned transition rates of the semi-Markov process are uncertain, including both the completely unknown ones and the inaccurately known ones with known bounds. To reduce the communication burden, a particular event-triggered generator is constructed, which depends on the latest available measurement output and a predefined positive threshold. Combining the stochastic analysis method with the Lyapunov stability theory, some less conservative criteria are obtained to ascertain the global asymptotic stability of the estimation error system in the mean-square sense. In addition, by solving some matrix inequalities, the desired nonfragile estimator gains are explicitly designed. Finally, a numerical example with simulations is given to illustrate effectiveness of the established estimation scheme. [ABSTRACT FROM AUTHOR]

The Barndorff–Nielsen and Shephard (BNS) model is a representative jump-type stochastic volatility model. Still, no method exists to compute option prices numerically for the non-martingale case with infinite active jumps. In this paper, selecting the minimal martingale measure (MMM) as a representative martingale measure, we develop two simulation methods for the BNS model under the MMM. The first method simulates the asset price at maturity and the Radon–Nikodym density of the MMM separately. On the other hand, the second method directly computes the asset price distribution under the MMM. In addition, we implement some numerical experiments to evaluate the performance of our simulation methods. [ABSTRACT FROM AUTHOR]

This paper presents an innovative event-triggered control scheme for addressing the stabilization problem of polynomial fuzzy systems under the influence of Denial-of-Service (DoS) attacks. The proposed controller utilizes a sampling-based event-triggered mechanism to reduce communication resources and avoid Zeno behavior. Furthermore, a novel polynomial fuzzy model-based control system is developed to investigate the impact of periodic DoS attacks and the addressed event-triggered mechanism on system stability. To improve system performance, control gains are updated at each triggering instant. The exponential stability criteria are formulated in the form of sum-of-square constraints, supported by a triggering instant dependent piecewise Lyapunov-Krasovskii functional and an online asynchronous premise reconstruction approach. Finally, the efficiency and usefulness of the theoretical findings are validated through simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, a new consensus protocol is designed for linear agents in the presence of a time-variant communication topology. Furthermore, we aim to present a fully distributed unified consensus protocol. Using the proposed protocol, each agent within a communication network can iteratively update its state to the maximum state of its neighbors, change it to the minimum state of the neighboring agents, or keep its state constant. In contrast to conventional consensus protocols, which strongly require the weights of communication graph links to have a positive lower bound for reaching consensus, our proposed protocol is not restricted by such a requirement and is able to make the agents converge under more general conditions. To accelerate the convergence rate and reduce the computational time relative to other conventional protocols, various operating modes (i.e., Tracker, Following, and Cross) are assigned to each agent within the communication network. Finally, to prove the practical merits of the proposed protocol and validate its performance, two numerical examples are presented here, one for a consensus problem, and another for a consensus-based formation problem. [ABSTRACT FROM AUTHOR]

In this paper we determine the necessary and sufficient conditions for asymptotically stability of periodic cycles for periodic difference equations by using the Jury's conditions. Such conditions are obtained using the information of the Jacobian matrices of the individual maps, avoiding thus the computation of the Jacobian matrix of the composition operator, which in higher dimension can be an a very difficult task. We illustrate our ideas by using models in population dynamics and in economics game theory. • Coefficients of a characteristic polynomial. • Necessary and sufficient conditions for local stability of periodic maps. • Periodic Cournot Duopoly game model. • 3D periodic Ricker competition model. • Periodic delayed logistic model. [ABSTRACT FROM AUTHOR]