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An analysis of an existing mathematical framework that describes the epidemiology of the Hepatitis A Virus (HAV) via dual modes of transmission is done in this paper. Sanitation and vaccination are taken into account by the model as mitigating techniques. Using the Homotopy perturbation method, the relevant six compartments like susceptible, vaccinated, latent, infectious, recovered and HAV population (S-V-L-I-R-P) of the model are solved analytically. For each of the six compartments, specific analytical formulations are provided. Several types of model parameters are illustrated graphically to demonstrate their impacts. Comparing the results with the numerical simulation (MATLAB) yields a good fit. [ABSTRACT FROM AUTHOR]

In this paper, we study a three-species predator-prey model with modified LG-Holling type II with Lévy jumps, and we take the competition among predators into consideration. First, We use an Ornstein-Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system by mathematical analysis skills such as comparison theorem. Futhermore, the extinction or persistence in the mean of each species under different conditions is obtained. Finally, some numerical simulations are carried out to support our main results. [ABSTRACT FROM AUTHOR]

This paper proposes a new method to improve re performance of intra-field interpolation which is the mos~ important element of deinterlacing method. Traditional edge- based methods were poor at determining accurate edge iirection which decides interpolation performance. The 7roposed method decides the direction and slope of edge based on locally adaptive-thresholded binary image to mprove efficiency and accuracy, and it also increased the ~orizontal size of search window to 15 for better direction ietermination at gentle slope. Compared to traditional edge- based methods, interpolation based on binary image, which is ,`enerated using the proposed method, leads to great erformance improvement. With computer simulations for a ~`ariety of images, this paper shows the new approach is much ~etter than traditional methods.. [ABSTRACT FROM AUTHOR]

From the facts that numerous regions with initially similar economic conditions end up with different levels of entrepreneurial agglomeration, this paper constructs a model assuming that the sequential entrants make their career choices based on existing entrepreneurial ratio and describing the dynamics of entrepreneurial agglomeration formation. After mathematical analysis and numerical simulation using NetLogo, it is found that under social selection, a nonlinear Polya process with self-reinforcing and path-dependency characters will emerge, and the repeated entrants' career choices will lead to the agglomeration of entrepreneurship; the agent's risk compensation value, the initial population of agents, the number of role models in the early stage and the initial entrepreneurial ratio are determinants to the formation of entrepreneurial agglomeration. The findings confirm that entrepreneurship has "memory" and the entrepreneurial history could have influence on the future. In order to forge the entrepreneurial agglomeration, our suggestions include exerting influence on the determinants from an early age, and improving the individual's risk-taking abilities. [ABSTRACT FROM AUTHOR]

To have a more realistic model, in this paper, This manuscript is devoted to investigating a fractional-order mathematical model of Kouidere et al. That describes the dynamics of spread of African swine fever virus (ASFV). The aim of this work is to protect susceptible pigs from the virus, In our model, by including three controls which represent: the iron fencing and spraying pesticides and get rid. The aims of this paper is to reduce the number of infected pigs and ticks by using optimal control strategy and fractinal order derivation. Pontryagin's maximal principle is used to describe optimal controls with Caputo time-fractional derivative and the optimal system is resolved in an iterative manner. Numerical simulations are presented based on the presented method. We finished tis article with a conclusion. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical framework using multiple reconfigurable intelligent surfaces (RISs) for enhancing the secrecy performance of wireless systems. In particular, multiple RISs are exploited to support transmitter-legitimate user communication under the existence of an eavesdropper. Two practical scenarios are investigated, i.e., there are only transmitter-eavesdropper links (case 1) and there are both transmitter-eavesdropper and transmitter-RIS-eavesdropper links (case 2). We mathematically obtain the closed-form expressions of the average secrecy capacity (ASC) of the considered system in these two investigated cases over Nakagami-m fading channels. The impacts of the system parameters, such as the locations of the RISs, the number of REs, and the Nakagami-m channels, are deeply evaluated. Computer simulations are used to validate our mathematical analysis. Numerical results clarify the benefits of using multiple RISs for improving the secrecy performance of wireless systems. Specifically, the ASCs in cases 1 and 2 are significantly higher than that in the case without RISs. Importantly, when the locations of the RISs are fixed, we can arrange the larger RSIs near either the transmitter or legitimate user to achieve higher ASCs. In addition, when the numbers of reflecting elements (REs) in the RISs increase, the ASCs in cases 1 and 2 are greatly enhanced. [ABSTRACT FROM AUTHOR]

This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor. [ABSTRACT FROM AUTHOR]

This paper introduces a single-phase multi-function converter (MFC) circuit that can perform the power electronics functions of a DC–DC, a DC–AC, an AC–AC, and an AC–DC boost converter. The power circuit of the proposed converter contains only four bi-directional switches, which is sufficient side by side with a switched logic-based control system to execute converter functions. The proposed converter can implement the boosting converter function, which is a drawback of the conventional single-phase matrix converter, which is limited to performing the buck converter functions. The mathematical analysis of each converter function is presented. A state space averaging technique is employed to obtain the time-invariant state space model for a better understanding of the converter characteristics. The frequency response approach is used to demonstrate the effect of circuit parameters on converter stability using the time-invariant state-space model. Moreover, the performance analysis of the system is checked through the building of a simulation model of the proposed converter via MATLAB/Simulink and MATLAB/Simscape toolbox integration. Additionally, the actual performance of the proposed converter is verified through a laboratory prototype experimental study. The experimental results confirm those obtained by computer simulation, clearly demonstrating the successful operation of the proposed circuit as a multi-function converter with acceptable levels of total harmonic distortion (THD). [ABSTRACT FROM AUTHOR]

In this paper, we discuss the competition of two species for a single essential growth-limiting nutriment with viral infection that affects only the first species. Although the classical models without viral infection suggest competitive exclusion, this model exhibits the stable coexistence of both species. We reduce the fourth-dimension proposed model to a three-dimension one. Thus, the coexistence of the two competing species is demonstrated using the theory of uniform persistence applied to the three-variable reduced system. We prove that there is no coexistence of both species without the presence of the virus and the satisfaction of some assumptions on the growth rates of species. Finally, we give some numerical simulations to confirm the obtained theoretical findings. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is the numerical analysis of a class of mathematical models that describe the contact between a thermo-piezoelectric body and a conductive foundation. Under the assumption of a static process, the material's behavior is modeled with a linear thermo-electro-elastic constitutive law and the frictional contact with Signorini's and Tresca's laws. A variational problem is derived and the existence of a unique weak solution is proved by combining arguments from the theory of variational inequalities with linear strongly monotone Lipschitz continuous operators. A successive iteration technique to linearize the problem by transforming it into an incremental recursive form is proposed, and its convergence is established. An Augmented Lagrangian variant, known as the Alternating Direction Multiplier Method (ADMM), is employed to split the original problem into two subproblems, resolve them sequentially, as well as update the dual variables at each iteration. To illustrate the performance of the proposed approach, several numerical simulations on two-dimensional test problems are carried out. [ABSTRACT FROM AUTHOR]

• A coupling mechanism model of an FSDB unit is developed and verified. • Mathematical analysis is explored to reveal the coupling mechanism of an FSDB system. • Rigid and elastic motions of disk and cyclic blades induce diagonal and cross-coupling terms. • The motion patterns of cyclic blades are classified and clarified. • Effects of motion patterns of cyclic blades on NFs and CSs are applied to interpret and validate the dynamic coupling. This paper focuses on the influence mechanism of cyclic blades on the dynamic coupling of a flexible shaft-disk-blade (FSDB) system through mathematical analysis and numerical simulation. Firstly, a coupling mechanism model of an FSDB unit is developed through a Lagrange method and the assumed mode method (AMM), after considering the coupling behavior among shaft bending, shaft torsion, disk vibration, and blade bending. The modal comparison results between the proposed model and FEM affirm the validity of the model. Then the analytical interpretation is explored by decomposing and discussing the diagonal coupling and cross-coupling matrices of the FSDB system. The mechanism discussion reveals that the coupling matrices originate from the rigid and elastic motions of flexible disk and cyclic blades, indicating that the motions of cyclic blades play an important role in dynamic coupling. Therefore, the motions of cyclic blades are classified and analyzed, and their effects on natural frequencies (NFs) and critical speeds (CSs) are applied to further interpret and validate the dynamic coupling through numerical simulation. The numerical results indicate that motions of cyclic blades can increase, decrease, and eliminate the magnitude of dynamic coupling significantly. [ABSTRACT FROM AUTHOR]

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1 < d < 2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model. [ABSTRACT FROM AUTHOR]

In this paper, we study the mathematical analysis of a nonlinear age-dependent predator–prey system with diffusion in a bounded domain with a non-standard functional response. Using the fixed point theorem, we first show a global existence result for the problem with spatial variable. Other results of existence concerning the spatial homogeneous problem and the stationary system are discussed. At last, numerical simulations are performed by using finite difference method to validate the results. [ABSTRACT FROM AUTHOR]

This paper focuses on the convergence analysis for a patch structure Nicholson's blowflies system involving an oscillating death rate and multiple different time-varying delays. By using inequality techniques and concise mathematical analysis proof, some sufficient criteria are established to guarantee the global exponential convergence of the zero equilibrium point for the addressed system. Our results are novel and supplement some existing ones. Furthermore, the effectiveness and feasibility of the obtained results are demonstrated by some numerical simulations. [ABSTRACT FROM AUTHOR]

In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to tackle a variety of computing tasks, among them the computation of shortest paths and the design of efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. In this paper, we generalize the dynamics to the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterizations of the optimum solution. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of global μ -synchronization of impulsive pantograph neural networks. In this paper, new concept of ν -asymptotic periodic impulsive interval T a s y ν is proposed for pantograph networks. By employing the Lyapunov method combined with the mathematical analysis approach for impulsive systems, some useful criteria are derived to guarantee the global μ -synchronization of coupled pantograph neural networks when the asymptotic logarithmic periodic impulsive interval T a s y ln < ∞ and T a s y ln = ∞ , respectively. Especially when T a s y ln = ∞ , as long as the networks are unstable, impulsive control cannot achieve synchronization regardless of the size of the impulse gain. Numerical simulations are exploited to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Cortical circuits process information by rich recurrent interactions between excitatory neurons and inhibitory interneurons. One of the prime functions of interneurons is to stabilize the circuit by feedback inhibition, but the level of specificity on which inhibitory feedback operates is not fully resolved. We hypothesized that inhibitory circuits could enable separate feedback control loops for different synaptic input streams, by means of specific feedback inhibition to different neuronal compartments. To investigate this hypothesis, we adopted an optimization approach. Leveraging recent advances in training spiking network models, we optimized the connectivity and short-term plasticity of interneuron circuits for compartment-specific feedback inhibition onto pyramidal neurons. Over the course of the optimization, the interneurons diversified into two classes that resembled parvalbumin (PV) and somatostatin (SST) expressing interneurons. Using simulations and mathematical analyses, we show that the resulting circuit can be understood as a neural decoder that inverts the nonlinear biophysical computations performed within the pyramidal cells. Our model provides a proof of concept for studying structure-function relations in cortical circuits by a combination of gradient-based optimization and biologically plausible phenomenological models. Author summary: The brain contains billions of nerve cells—neurons—that can be classified into different types depending on their shape, connectivity and activity. A particularly diverse group of neurons is that of inhibitory neurons, named after their suppressive effect on neural activity. Presumably, their diverse properties allow inhibitory neurons to fulfil different functions, but what these functions are is currently unclear. In this paper, we investigated if a particular function can explain the existence and properties of the two most common inhibitory cell classes: The need to regulate activity in different physical parts (compartments) of the neurons they target. We investigated this function in a computer model, using optimization to find the neuron properties best-suited for compartment-specific inhibition. Our key result is that after the optimization, model neurons largely fell into two classes that resembled the two types of biological neurons. In particular, the optimized neurons were connected to only one compartment of other neurons. This suggests that the diversity of inhibitory neurons is well suited for compartment-specific inhibition. In the future, our approach of optimizing neural properties might be used to investigate other functions (or dysfunctions) of neuron diversity. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a deterministic mathematical model to analyze effective interventions for meningitis and pneumonia coinfection as well as to make a rational recommendation to public healthy, policy or decision makers and programs implementers. We have introduced the epidemiology of infectious diseases, the epidemiology of meningitis, the epidemiology of pneumonia, and the epidemiology of infection of meningitis and pneumonia. The positivity and boundedness of the sated model was shown. Our model elucidate that, the disease free equilibrium points of each model are locally asymptotically stable if the corresponding reproduction numbers are less than one and globally asymptotically stable if the corresponding reproduction numbers are greater than one. Additionally, we have analyzed the existence and uniqueness of the endemic equilibrium point of each sub models, local stability and global stability of the endemic equilibrium points for each model. By using standard values of parameters we have obtained from different studies, we found that the effective reproduction numbers of meningitis R e f f (m) = 9 and effective reproduction numbers of pneumonia R e f f (p) = 11 that lead us to the effective reproduction number of the meningitis and pneumonia co-infected model is m a x R e f f m , R e f f (p) = 9 . Applying sensitivity analysis, we identified the most influential parameters that can change the behavior of the solution of the meningitis pneumonia coinfection dynamical system are α 1 , α 2 and π . Biologically, decrease in α 1 and increasing in π is a possible intervention strategy to reduce the infectious from communities. Finally, our numerical simulation has shown that vaccination against those diseases, reducing contact with infectious persons and treatment have the great effect on reduction of these silent killer diseases from the communities. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a mathematical model of cancer including tumor cells, immune cells, and normal cells is investigated when a delay term is induced. Though the model was originally proposed by De Pillis et al. (Math. Comput. Model. 37:1221–1244, 2003), to make the model more realistic, we have added a delay term into the model, and it has incorporated novelty in our present work. The stability of existing equilibrium points in the delay-induced system is studied in detail. Global stability conditions of the tumor-free equilibrium point have been found. It is shown that due to this delay effect, the coexisting equilibrium point may lose its stability through a Hopf bifurcation. The implicit function theorem is applied to characterize a complex function in a neighborhood of delay terms. Additionally, the presence of Hopf bifurcation is demonstrated when the transversality conditions are satisfied. The length of delay for which the solutions preserve the stability of the limit cycle is estimated. Finally, through a series of numerical simulations, the theoretical results are formally examined. [ABSTRACT FROM AUTHOR]

We argue that, despite the fact that the field of multiscale modelling and simulation has enjoyed significant success within the past decade, it still holds many open questions that are deemed important but so far have barely been explored. We believe that this is at least in part due to the fact that the field has been mainly developed within disciplinary silos. The principal topics that in our view would benefit from a targeted multidisciplinary research effort are related to reaching consensus as to what exactly one means by 'multiscale modelling', formulating a generic theory or calculus of multiscale modelling, applying such concepts to the urgent question of validation and verification of multiscale models, and the issue of numerical error propagation in multiscale models. Moreover, we believe that this would, in principle, also lay the foundation for more efficient, well-defined and usable multiscale computing environments. We believe that multidisciplinary research to fill in the gaps is timely, highly relevant, and with substantial potential impact on many scientific disciplines. [ABSTRACT FROM AUTHOR]

In this paper, we consider a fractional-order model of a brushless DC motor. To develop a mathematical model, we use the concept of the Liouville–Caputo noninteger derivative with the Mittag-Lefler kernel. We find that the fractional-order brushless DC motor system exhibits the character of chaos. For the proposed system, we show the largest exponent to be 0.711625. We calculate the equilibrium points of the model and discuss their local stability. We apply an iterative scheme by using the Laplace transform to find a special solution in this case. By taking into account the rule of trapezoidal product integration we develop two iterative methods to find an approximate solution of the system. We also study the existence and uniqueness of solutions. We take into account the numerical solutions for Caputo Liouville product integration and Atangana–Baleanu Caputo product integration. This scheme has an implicit structure. The numerical simulations indicate that the obtained approximate solutions are in excellent agreement with the expected theoretical results. [ABSTRACT FROM AUTHOR]

In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stages. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R H and R P ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R P and R H ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection model R H P is less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is max 7 , 17 = 17. Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates β 1 and β 2 , respectively. The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence. [ABSTRACT FROM AUTHOR]

As a new efficient rock-breaking technology, harmonic impact drilling technology has received great attention, but the research on its rock-breaking mechanism is insufficient, which limits its development. Based on the theory of vibration, a simplified model of high-frequency harmonic vibration impact system is established in this paper. The numerical model was solved by Matlab and the motion equations of drill bit and rock at different stages of motion are obtained, respectively. Based on the factor analysis of the mathematical model, the dynamic characteristics of the impact system under harmonic excitation are studied. Finally, numerical simulations are carried out to further analyze the drilling effect of harmonic impact drilling and verify the correctness of the simplified model. The results show that when the excitation frequency equals the resonance frequency of rock, the vibration displacement of rock reaches the peak value. The drilling speed is greatly increased by harmonic impact drilling compared with conventional drilling. [ABSTRACT FROM AUTHOR]

In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, a predator–prey model with prey-stage structure and prey-taxis is proposed and studied. Firstly, the local stability of non-negative constant equilibria is analyzed. It is shown that non-negative equilibria have the same stability between ODE system and self-diffusion system, and self-diffusion does not have a destabilization effect. We find that there exists a threshold value ξ 0 such that the positive equilibrium point of the model becomes unstable when the prey-taxis rate ξ < ξ 0 , hence the taxis-driven Turing instability occurs. Furthermore, by applying Crandall–Rabinowitz bifurcation theory, the existence, the stability and instability, and the turning direction of bifurcating steady state are investigated in detail. Finally, numerical simulations are provided to support the mathematical analysis. [ABSTRACT FROM AUTHOR]

When experimental resources are significantly constrained, resolution V fractional factorial designs are often prohibitively large for experiments with 6 or more factors. Resolution IV designs may also be cost prohibitive, as additional experimentation may be required to de-alias active 2-factor interactions (2FI). This paper introduces 20-run no-confounding screening designs for 6 to 12 factors as alternatives to resolution IV designs. No-confounding designs have orthogonal main effects, and since no 2FI is completely confounded with another main effects or 2FI, the experimental results can be analyzed without follow-on experimentation. The paper concludes with the results of a Monte Carlo simulation used to assess the model-fitting accuracy of the recommended designs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a non-autonomous convection-reaction diffusion system (CDI) with a nonlinear reaction source function. This model refers to the quantification and the distribution of antibiotic resistant bacteria (ARB) in a river. The main contributions of this paper are: (i) the determination of the limit set of the system by applying the semigroups theory, it is shown that it is reduced to the solutions of the associated elliptic system (CDI)e, (ii) sufficient conditions for the existence of a positive solution of (CDI)e based on the Leray-Schauder's degree theory. Numerical simulations which support our theoretical analysis are also given. [ABSTRACT FROM AUTHOR]

The low-density lipoprotein (LDL)/high-density lipoprotein (HDL)-cholesterol ratio has been shown to have a high correlation with the cardiovascular risk assessment. Is it possible to quantify the correlation mathematically? In this paper, we develop a bifurcation analysis for a mathematical model of the plaque formation with a free boundary in the early stage of atherosclerosis. This bifurcation analysis, to the ratio of LDL/HDL, is based on explicit formulations of radially symmetric steady-state solutions. By performing the perturbation analysis to these solutions, we establish the existence of bifurcation branches and derive a theoretical condition that a bifurcation occurs for different modes. We also analyze the stability of radially symmetric steady-state solutions and conduct numerical simulations to verify all theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a Holling-Tanner predator-prey model with ratio-dependent functional response and non-linear prey harvesting is analyzed. The mathematical analysis of the model includes existence, uniqueness and boundedness of positive solutions. It also includes the permanence, local stability and bifurcation analysis of the model. The ratio-dependent model always has complex dynamics in the vicinity of the origin; the dynamical behaviors of the system in the vicinity of the origin have been studied by means of blow up transformation. The parametric conditions under which bionomic equilibrium point exist have been derived. Further, an optimal harvesting policy has been discussed by using Pontryagin maximum principle. The numerical simulations have been presented in support of the analytical findings. [ABSTRACT FROM AUTHOR]

This paper concerns the mathematical analysis of a mathematical model for price formation. We take a large number of rational buyers and vendors in the market who are trading the same good into consideration. Each buyer or vendor will choose his optimal strategy to buy or sell goods. Since markets seldom stabilize, our model mimics the real market behavior. We introduce three models. All of them are modifications of the original J.-M. Lasry and P. L. Lions evolution model. In the first modified model, a random term is added to mimic the randomness of trading in the real market. This reflects markets with low volatility, where it might be difficulty to buy or sell goods at specific price. In the second model, we use cumulative density function instead of density function. We give numerical simulations on these two models in order to have a general picture on the solution. In the third model, we add a term associated with the parameter R to destabilize the original Larsy–Lions model and study oscillations and wave solutions depending on different values of R. We also study existence and uniqueness of the solution. Moreover, Several plots are given to demonstrate these results corresponding to the theoretical prediction. [ABSTRACT FROM AUTHOR]

This paper is concerned with a reaction‐advection‐diffusion system, which is a continuous version of statistical model for criminal activity proposed by Short et al (Math. Models Methods Appl. Sci., 8 (2008), 1249‐1267). From very recently results, it is known that the classical solution of the corresponding initial‐boundary value problem exists globally. On the other hand, Rodriguez (Phys. D, 260 (2013), 191‐200) asserted the uniform‐in‐time boundedness of classical solution; however, there is a gap in the proof. In this work, we first solve this open problem by establishing some crucial a priori estimates. Then, invoking the uniform boundedness, we present that the classical solution converges exponentially to the steady state. Our results are consistent with the experiment observation and numerical simulation in the existing literatures. [ABSTRACT FROM AUTHOR]

In this paper, we provide a new method for constructing chaotic Hopfield neural networks. Our approach is based on structuring the domain to form a special set through the discrete evolution of the network state variables. In the chaotic regime, the formed set is invariant under the system governing the dynamics of the neural network. The approach can be viewed as an extension of the unimodality technique for one-dimensional map, thereby generating chaos from higher-dimensional systems. We show that the discrete Hopfield neural network considered is chaotic in the sense of Devaney, Li–Yorke, and Poincaré. Mathematical analysis and numerical simulation are provided to confirm the presence of chaos in the network. [ABSTRACT FROM AUTHOR]

The current paper is devoted to the time–space fractional Ginzburg–Landau equation driven by fractional Brownian motion. The spatial–temporal regularity of the nonlocal stochastic convolution is firstly established, and then the existence and uniqueness of the global mild solution are obtained by the Banach fixed point theorem and Mittag-Leffler functions. Finally, the numerical simulations for the time-fractional stochastic Ginzburg–Landau equation are provided to verify the mathematical analysis results. [ABSTRACT FROM AUTHOR]

In this paper we studied the dynamics of one ammensal and two mutualistic species. A distributed time lag is induced in the interaction of ammensal and two mutual species. Local and global stability analysis is discussed at co-existing state. Numerical simulation with different delay kernel strengths are illustrated and proved that delay kernels play a significant role in the growth of two mutual species populations. [ABSTRACT FROM AUTHOR]

Microgrid can operate in both grid-connected and islanded modes. Islanding can be scheduled or unscheduled. In the event of unscheduled islanding, the microgrid should be able to maintain its sustainability. Therefore, it is necessary to determine and supply the amount of required spinning reserve for stable islanding. In this paper, a two-stage strategy for optimal scheduling of the microgrid is proposed while uncertainties of renewable generations and demand are considered. In the first stage, co-optimization of power and reserve is carried out with the presence of distributed generations and batteries. Therefore, in the second stage, the demand is also used as reserve to provide required reserve for stable islanding. In order to determine the optimal amount of reserve of demand, a novel objective function is proposed. The objective function minimizes the sum of the standby reserve cost, expected cost of called reserve, and expected cost of emergency curtailment. One of the salient features of the proposed model is its modularity. That is, it can be added easily to any scheduling model in which the demand is not considered as reserve. Mathematical analysis and numerical simulations show the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

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

In this paper, we study theoretically and experimentally the far-field diffraction of amplitude vortex grating. The analytic expression of the diffraction intensity distribution is deduced according to Bessel function and its recursion formula, and the dependence relation of the diffraction on the parameters of grating is exhibited. The numerical simulations indicate the diffraction patterns consist of two characteristic components, namely, the inner spot and the periphery turbine-like fringes. The number of grating lines and their rotation direction determine the structure of the periphery turbine-like fringes. The density of the grating lines influences the radial size of the turbine-like fringe structure, and the hard-edged aperture controls the compaction of the fringes besides limiting the diffraction intensity. The practical experimental results verify these conclusions. The study of this paper will be helpful for the understanding the diffraction characteristics of vortex grating and regulating artificially the intensity distribution of the beam. [ABSTRACT FROM AUTHOR]

In this paper we propose a nonlinear reaction-diffusion system describing the interaction between toxin-producing phytoplankton and fish population. We analyze the effect of self- and cross-diffusion on the dynamics of the system. The existence, uniqueness and uniform boundedness of solutions are established in the positive octant. The system is analyzed for various interesting dynamical behaviors which include boundedness, persistence, local stability, global stability around each equilibria based on some conditions on self- and cross-diffusion coefficients. The analytical findings are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

Highlights • We propose a variable weight test for both rare and common variants association based on affected sib pairs. • The variable weight structure makes it possible to analyze rare and common variants simultaneously. • The new method can improve the power of simultaneously detecting rare and common variants. • The proposed method is more powerful than the existing and related methods for detecting effects of rare and common variants. Abstract Current genome-wide association analysis has identified a great number of rare and common variants associated with common complex traits, however, more effective approaches for detecting associations between rare and common variants with common diseases are still demanded. Approaches for detecting rare variant association analysis will compromise the power when detecting the effects of rare and common variants simultaneously. In this paper, we extend an existing method of testing for rare variant association based on affected sib pairs (TOW-sib) and propose a variable weight test for rare and common variants association based on affected sib pairs (abbreviated as VW-TOWsib). The VW-TOWsib can be used to achieve the purpose of detecting the association of rare and common variants with complex diseases. Simulation results in various scenarios show that our proposed method is more powerful than existing methods for detecting effects of rare and common variants. At the same time, the VW-TOWsib also performs well as a method for rare variant association analysis. [ABSTRACT FROM AUTHOR]

An important problem in network analysis is to identify significant communities. Most of the real-world data sets exhibit a certain topological structure between nodes and the attributes describing them. In this paper, we propose a new community detection criterion considering both structural similarities and attribute similarities. The clustering method integrates the cost of clustering node attributes with the cost of clustering the structural information via the normalized modularity. We show that the joint clustering problem can be formulated as a spectral relaxation problem. The proposed algorithm is capable of learning the degree of contributions of individual node attributes. A number of numerical studies involving simulated and real data sets demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we formulate a deterministic, nonlinear model of cholera with age structure which integrates the direct transmission and the indirect transmission of the disease. The vaccination and the demographic movements are also taken into account in this model. The propounded model is an initial/boundary-value problem constituted of four partial differential equations of first order describing the transmission dynamics of human hosts and of two ordinary differential equations representing the bacterial dynamics in the environment. We conduct a rigorous mathematical analysis of this model and we prove that it admits a unique positive bounded solution. The existence of a unique equilibrium which is infection-free in the absence of the transmission disease and endemic in the presence of the transmission disease is also established. We determine a threshold parameter ℜ 0 such that this equilibrium is locally asymptotically stable when ℜ 0 < 1 and unstable when ℜ 0 > 1. Also, a parameter ℜ 0 ⋆ is determined such that when ℜ 0 > 1 and ℜ 0 ⋆ < 1 , the number of the infected individuals of the equilibrium becomes less than 1. At the end, we use Wendland’s Compactly Supported Radial Basis Functions (CSRBFs) method to find the numerical solution of the formulated model. This numerical solution is used to conduct the numerical simulation allowing us thus to check our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a delayed differential system to model labor force (occupied labor force and unemployed) evolution. The mathematical analysis of our model focuses on the local behavior of the labor force around a positive equilibrium position; the existence of a branch of periodic solutions bifurcated from the positive equilibrium is then analyzed according to the Hopf bifurcation theorem. Finally, we performed numerical simulations to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we give a theoretical and numerical analysis of a model for small vertical vibrations of an elastic membrane coupled with a heat equation and subject to linear mixed boundary conditions. We establish the existence, uniqueness, and a uniform decay rate for global solutions to this nonlinear non-local thermoelastic coupled system with linear boundary conditions. Furthermore, we introduced a numerical method based on finite element discretization in a spatial variable and finite difference scheme in time which results in a nonlinear system to be solved by Newton's method. Numerical experiments for one-dimensional and two-dimensional cases are presented in order to estimate the rate of convergence of the numerical solution that confirm our analysis and show the efficiency of the method. [ABSTRACT FROM AUTHOR]

Highlights • A joint stiffening element is proposed to simulate lattice structures fabricated by additive manufacturing. • The influence of the joint on the stiffness of the lattice structure can be considered in the proposed model. • A parametric study is conducted to quantify the influence of the joint on a certain lattice structure and to find the optimal parameters of the joint stiffening element. • Three-point bend testing is conducted, and it shows that the accuracy is significantly improved by the proposed model for bending dominant lattice structures. • The computational cost of the proposed model is much lower than the tetrahedral element model. Abstract In this paper, a concept called joint stiffening element is proposed to represent the influence of the joint on the stiffness of lattice structures fabricated by additive manufacturing. Four parameters are defined in the proposed element to quantify the increment of the stiffness caused by the lattice joint. Then, three-point-bend testing is used to validate the proposed model. The lattice structures with Cubic-center and Vintiles topologies are designed and fabricated for the experiment. As-fabricated material properties are obtained by tensile specimens to eliminate the influence caused by the manufacturing process and to isolate the joint stiffening effect. The result shows that models with the solid element and the proposed element are both accurate, but the proposed model has a significantly less computational cost than the solid element model. Furthermore, compared to the beam element model, the proposed model can more accurately estimate the stiffness of lattice structures, especially for the Vintiles topology. It is also found that the joint stiffening effect is more significant on the bending dominant topology than the stretching dominant topology. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

The heat shock proteins (HSPs) protect the other proteins in the process of folding under stressful conditions such as oxygen deprivation, hypothermy or presence of alcohol. They have also an important role in tumour invasion. In this paper, the existence, uniqueness and permanence properties for the solution of the mathematical model which focuses on the synthesis of HSP70 is proved. Moreover the numerical simulations are performed by using FDM, namely a combination of backward and forward Euler methods, and the results confirm the expected behaviour of the solution. [ABSTRACT FROM AUTHOR]