This article presents a study of Leslie–Gower predator–prey system to investigate the dynamics of disease transmission among predator species. The system includes the harvesting of infected predator. The positivity, boundedness of the solutions and permanence of the system are taken into consideration. The stability and Hopf bifurcation analyses around biologically feasible equilibria are scrutinized

For large-scale non-autonomous Stratonovich stochastic differential equations, we study a very general parallel waveform relaxation process which is on the basis of stochastic Runge–Kutta (SRK) method of mean-square order 1.0 in this literature. The convergence of the whole parallel numerical iterative scheme can be guaranteed and the scheme provides better properties in terms of decreasing the load

In this paper, we study the global asymptotic stability of following system of difference equations with quadratic terms: \(x_{n+1}=A+B\frac{y_{n}}{y_{n-1}^{2}}\), \(y_{n+1}=A+B\frac{x_{n}}{x_{n-1}^{2}}\) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

In this study, we have investigated local and global dynamics of a modified Leslie–Gower predator–prey model with Monod–Haldane functional response, where prey is subjected to quadratic harvesting. It is found that the solutions of the proposed system are positive and bounded uniformly. The feasible equilibrium points are also obtained for some suitable and predefined conditions. It is observed that

The fractional-order Bagley–Torvik equation has many applications in the field of life science and engineering. In this paper, we develop a new scheme based on the existing finite element method for the numerical solution of the Bagley–Torvik equation of order (0, 2). We adopt the formulation of the equation in a simple and generalized way. The existence and uniqueness of the solution and its error

The widespread problem of water pollution due to enhanced concentration of anthropogenic effluents is becoming a global issue. Public environmental awareness may be a plausible factor for the control of toxicants in the aquatic medium. The present paper is devoted to study the impact of awareness among human on reduction of environmental toxins affecting planktonic system. The provision of awareness

A compact quadratic spline collocation (QSC) method for the time-fractional Black–Scholes model governing European option pricing is presented. Firstly, after eliminating the convection term by an exponential transformation, the time-fractional Black–Scholes equation is transformed to a time-fractional sub-diffusion equation. Then applying \(L1 - 2\) formula for the Caputo time-fractional derivative

In a graph \(G=(V,E)\), a vertex \(v\in V\) is said to ve-dominate the edges incident on v as well as the edges adjacent to these incident edges on v. A set \(D\subseteq V\) is called a double vertex-edge dominating set if every edge of the graph is ve-dominated by at least two vertices of D. Given a graph G, the double vertex-edge dominating problem, namely Min-DVEDS is to find a minimum double vertex-edge

We discuss the superconvergence analysis of the Galerkin finite element method for the singularly perturbed coupled system of both reaction–diffusion and convection–diffusion types. The superconvergence study is carried out by using linear finite element, and it is shown to be second-order (up to a logarithmic factor) uniformly convergent in the suitable discrete energy norm. We have conducted some

Boreal forest in Canada has two main recurrent disturbances: one is fire and the other one is spruce budworm. The defoliation by spruce budworm, Choristoneura fumiferana (Clem.) (Lepidoptera: Tortricidae) was first started in British Columbia of Canada in 1957 near Liard River. Budworm outbreaks were observed in the 1960’s to 1970’s and from the mid 1980’s to the present. Spruce budworm disturbance

A limited memory q-BFGS (Broyden–Fletcher–Goldfarb–Shanno) method is presented for solving unconstrained optimization problems. It is derived from a modified BFGS-type update using q-derivative (quantum derivative). The use of Jackson’s derivative is an effective mechanism for escaping from local minima. The q-gradient method is complemented to generate the parameter q for computing the step length

In the present paper, a new fixed point iterative method is introduced based on Green’s function and it’s successfully applied to approximate the solution of boundary value problems. A strong convergence result is proved for the integral operator by using the proposed method. It is also showed that the newly defined iterative method has a better rate of convergence than the Picard–Green’s, Mann–Green’s

In this paper, we discuss the numerical solution of a class of linear integral equations of the second kind over an infinite interval. The method of solution is based on the reduction of the problem to a finite interval by means of a suitable family of mappings so that the resulting singular equation can be accurately solved using spectral collocation at the Jacobi-Gauss points. Several selected numerical

In this paper, we study \((1+2^{s-1}u)\)-constacyclic codes and a class of skew \((1+2^{s-1}u)\)-constacyclic codes of odd length over the ring \(R= {\mathbb {Z}}_{2^s}+u{\mathbb {Z}}_{2^s}\), \(u^2=0\), where \(s \ge 3\) is an odd integer. We have obtained the algebraic structure of \((1+2^{s-1}u)\)-constacyclic codes over R. Three new Gray maps from R to \({\mathbb {Z}}_2+u{\mathbb {Z}}_2\) have

Due to the immense applications of interconnection networks, various new networks are designed and extensively used in computer sciences and engineering fields. Networks can be expressed in the form of graphs, where node become vertex and links between nodes are called edges. To obtain the exact location of a specific node which is unique from all the nodes, several nodes are selected this is called

In this paper, we investigate the existence of monotone positive solutions for a fourth order boundary value problem with dependence on the derivative in nonlinearity under integral and multi-point boundary conditions. By applying the fixed point theorem in a cone, some criteria on the existence of positive solutions are acquired. These criteria are given by explicit conditions which are generally

Diabetes mellitus is a silent killer and major public health problem all over the world, but knowledge and awareness about diabetes are insufficient in middle and low-level socioeconomic countries. Awareness plays a vital role in understanding about causes factors of diabetes and its prevention. The world is not completely deterministic as there are biological fluctuations present within the population

In this paper, a nonlinear mathematical model of illicit drug use in a population is studied using dynamical system theory. The work is largely concerned with the analysis of asymptotic behaviour of solutions to a six-dimensional system of differential equations modeling the influence of illicit drug use in the population. The model is mathematically well-posed based on positivity and boundedness of

To explore the effect of direct cell-to-cell transmission on viral infection dynamics under the exposure of the non-cytolytic cure mechanism, a mathematical model integrating both the virus-to-cell and cell-to-cell transmissions with a non-cytolytic cure rate of infected cells in the presence of humoral immunity has been considered. Parameter variation experimentation suggests that a high cell-to-cell

In this article we propose a modified compartmental model describing the transmission of COVID-19 in Morocco. It takes account on the asymptomatic people and the strategies involving hospital isolation of the confirmed infected person, quarantine of people contacting them, and home containment of all population to restrict mobility. We establish a relationship between the containment control coefficient

In this paper, a fourth-order PDE model is proposed for image inpainting. This model is based on the mixture of Perona–Malik equation and Cahn–Hilliard equation. Using the idea of energy splitting, a numerical scheme is introduced for solving the proposed PDE model. Numerical experiments for testing the proposed model are provided at the end of the paper. The numerical results indicate that the proposed

The article introduces a new algorithm for solving a class of variational inequality problems for monotone operators and system of nonlinear variational inequalities problems for two inverse strongly monotone operators. We describe how to incorporate the extragradient like technique based on altering points technique with inertial effects. A weak convergence theorem is established for the proposed

A host-vector disease model with insecticide resistance genes is proposed as a system of differential equations. The resistance-induced reproduction number \({\mathcal {R}}_e\) is determined and qualitative stabilities analysis are provided. We use the model to study the effects of insecticide resistance of vectors on the spread of the disease. The resistance-induced reproduction number \({\mathcal

In this paper we construct quantum codes over \(\mathbb F_p\) by using cyclic and \(\lambda \)-cyclic codes over the ring \(R=\mathbb {F}_{p}+u\mathbb {F}_{p}+u^2\mathbb {F}_{p}+v\mathbb {F}_{p} +uv\mathbb {F}_{p}+u^2v\mathbb {F}_{p}+v^2\mathbb {F}_{p}+uv^2\mathbb {F}_{p} +u^2v^2\mathbb {F}_{p}\) where \(v^3=v , u^3=u , uv=vu\) and p is an odd prime integer. Using the idempotent decomposition method

In this paper, the partitioned second derivative general linear methods for solving separable Hamiltonian problems are derived which are G-symplectic, interchange symmetry and have zero parasitic growth factors. Order conditions for such methods based on the theory of rooted trees are provided and examples of partitioned pairs of order 2 and 3 are given. The experiments have been performed on some

In this article, we have presented the controllability relationship between the semilinear control system of fractional order (1, 2] with delay and that of the semilinear control system without delay. Suppose X and U be Hilbert spaces which are separable and \(Z=L_2[0,b;X],\;Z_h=L_2[-h,b;X],\;0\le h\le b\) and \(Y=L_2[0,b;U]\) be the function spaces. Let the semilinear control system of fractional

In the present work, a generalized fractional integral operational matrix is derived by using classical Legendre wavelets. Then, a numerical scheme based on this operational matrix and Lagrange multipliers is proposed for solving variational problems with fractional order. This approach has been applied on some illustrative examples. The results obtained for these examples demonstrate that the suggested

Brooks’ theorem states that for a graph G, if \(\varDelta (G)\ge 3\), then \(\chi (G)\le \max \{\varDelta (G),\omega (G)\}\). Borodin and Kostochka conjectured a result strengthening Brooks’ theorem, stated as, if \(\varDelta (G)\ge 9\), then \(\chi (G)\le \max \{\varDelta (G)-1,\omega (G)\}\). This conjecture is still open for general graphs. In this paper, we show that the conjecture is true for

The main purpose of this paper is to construct a semi-implicit difference scheme for the multi-term time-fractional Burgers-type equations. Firstly, the L2-discretization formula is applied to the discretization of the multi-term Caputo fractional derivatives. Secondly, the second-order spatial derivative is approximated by using the second-order central difference quotient approximation and the nonlinear

In this paper, we present an improvement of the Hexagonal Shepard method which uses functional and first order derivative data. More in details, we use six-point basis functions in combination with the modified local interpolant on six-points. The resulting operator reproduces polynomials up to degree 3 and has quartic approximation order. Several numerical results show the good accuracy of approximation

In the existing definition of a neutrosophic planar graph, there is a limitation. In that definition, the value of falsity in degree of planarity is 1, even then the crisp underline graph is planar. This limitation is removed in the proposed definition. In this study, an advanced concept of the neutrosophic planar graphs is given and investigated the generalized neutrosophic planar graphs (GNPG). The

The all-at-once system arising from fractional mobile/immobile advection–diffusion equations is studied. Firstly, the finite difference method with L1 formula is employed to discretize it. The resulting implicit scheme is a time-stepping scheme, which is not suitable for parallel computing. Based on this scheme, an all-at-once system is established, which will be suitable for parallel computing. Secondly

In this paper, a fractional order eco-epidemiological model with nonlinear incidence rate is studied. The populations are divided into healthy prey, infected prey and predator. A prey refuge was introduced in the healthy prey population to make the model more realistic. Various qualitative properties including local and global stability analysis of equilibrium points are investigated. The theoretical

The primary target of present research is to examine the application of OHAM (optimal homotopy asymptotic method) for a nanofluid transport through Darcy Forchheimer space toward the stagnation region by comparing stretching and straining forces. The porous matrix is suspended with nanofluid, and the flow field is under inconsistent heat source/sink influence. The solutions of guiding boundary layer

In the Distributed Storage Systems (DSSs), the encoded fraction of information is stored in a distributed fashion on different chunk servers. Recently a new paradigm of Fractional Repetition (FR) codes has been introduced, in which, encoded data information is stored on distributed servers using an encoding involving a Maximum Distance Separable (MDS) code and a Repetition code. In this work, we have

A complex neutrosophic set is a useful model to properly handle incomplete information of periodic nature. This is characterized by three complex-valued components: truth, indeterminacy and falsity membership functions, whose range is extended from [0, 1] to unit circle in the complex plane. In this article, we define the notion of generalized complex neutrosophic graphs of type 1 and discuss certain

The purpose of the paper is to elucidate by global-dual contact holonomy why one might expect the Foucault spherical pendulum’s spin echo-stabilized, symplectic swing-plane through the rotation axis of the spinning earth to follow a parallel vector field as time passes at a velocity depending on the latitude of the swivel’s location. The spinor geometric foundations of the paradigmatic Foucault spherical

The aim of this paper is to investigate the existence, uniqueness and continuous dependence of solutions for a class of third order iterative differential equations with integral boundary conditions. The method applied here is based on Schauder’s fixed point theorem. The main idea consists to convert the considered equation into an integral one before using the fixed point theorem. Moreover, an example

By making use of the preconditioned Hermitian and skew-Hermitian splitting (PHSS) iteration as the inner solver for the modified Newton method, we establish the modified Newton-PHSS method for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. Moreover, the local convergence theorem is proved under proper conditions. Numerical results

A boundary-value problem for singularly perturbed second order differential-difference equation with both the negative(delay) and positive(advance) shifts is considered and a new exponentially fitted three term finite difference scheme is proposed for the numerical approximation of its solution. An approximate version of the considered problem is constructed by the use of Taylor’s series expansion

In this paper, a general nonlinear Chikungunya virus (CHIKV) dynamics model is formulated and analyzed. We assume that, the production, removal and proliferation rates of all compartments as well as the incidence rate of infection are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The model is incorporated by two types of discrete time delays. We prove the nonnegativity

We investigate the solution of linear systems of equations that arise when singularly perturbed reaction–diffusion partial differential equations are solved using a standard finite difference method on layer adapted grids. It is known that there are difficulties in solving such systems by direct methods when the perturbation parameter, \(\varepsilon \), is small (MacLachlan and Madden in SIAM J Sci

Cigarette smoking on college campuses has become a significant public health issue, which in turn led to an increasing focus on establishing programs to reduce its prevalence. In this paper, a compartmental model depicting the spread and cessation of the smoking habit on college campuses, obtained using theoretical principles often employed in mathematical epidemiology, is proposed and analysed. The

This paper considers the exact solution of Burgers’ hierarchy of nonlinear evolution equations. We construct the general nth conservation law of the hierarchy and prove that these expressions may be transformed into ordinary differential equations. In particular, a coordinate transformation leads to the systematic reduction of the conservation law properties of the Burgers’ hierarchy. Such an approach

This article proposes a mathematical model based on ordinary nonlinear differential equations that describes the dynamics of population growth of the mosquito Aedes aegypti throughout its life cycle. Then, a modification is made to the model by implementing a time delay, initially constant and then distributed over time. In addition, h, the population growth threshold, is established, the equilibrium

This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we set this problem as an asymptotic target control problem under mixed state-control constraints, for a general class of ordinary differential equations

In this paper, we propose an improved finite difference/finite element method for the fractional Rayleigh–Stokes problem with a nonlinear source term. The second-order backward differentiation formula (BDF2) and weighted and shifted Grünwald-Letnikov difference (WSGD) formula are employed to discretize first-order time derivative and the time fractional-order derivative, respectively. Moreover, a linearized

In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund–Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem.

Mantle convection and melt migration are important processes for understanding Earth’s dynamics and how they relate to observations at the surface. Recently it has been established that melt migration can be modelled by coupling variable-viscosity Stokes flow and Darcy flow, where Stokes flow generally captures the long-term behaviour of the mantle and lithosphere, and Darcy flow models the two-phase

Globalization concepts for Newton-type iteration schemes are widely used when solving nonlinear problems numerically. Most of these schemes are based on a predictor/corrector step size methodology with the aim of steering an initial guess to a zero of f without switching between different attractors. In doing so, one is typically able to reduce the chaotic behavior of the classical Newton-type iteration

When seeking a solution to the interface problem, the potential theory to represent solution has been widely used. As the solution representation of the interface problem is only well-known for domains with simple inclusion, such as a disk, conformal mapping is often used to transform the arbitrary inclusion to a manageable inclusion to utilize the known solution representation. This paper proposes

Changes in morphology of a polycrystalline material may occur through interface motion under the action of a driving force. An important special case that is considered in this paper is the thermal grooving that occurs when a grain boundary intersects the flat surface of a recently solidified metal slab giving rise to the formation of a thin symmetric groove. In case the transient surface diffusion

Special number sequences play important role in many areas of science. One of them named as Fibonacci sequence dates back to 820 years ago. There is a lot of research on Fibonacci numbers due to their relation with the golden ratio and also due to many applications in Chemistry, Physics, Biology, Anthropology, Social Sciences, Architecture, Anatomy, Finance, etc. A slight variant of the Fibonacci sequence

The symmetric division deg index (or simply sdd-index) was proposed by Vukičević et al. as a remarkable predictor of total surface area of polychlorobiphenyls. It is one of discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. In this paper, we investigate some properties of this graph invariant in terms of

Let V(G) and E(G) be, respectively, the vertex set and edge set of a graph G. The general sum-connectivity index of a graph G is denoted by \(\chi _\alpha (G)\) and is defined as \(\sum \limits _{uv\in E(G)}(d_u+d_v)^\alpha \), where uv is an edge that connect the vertices \(u,v\in V(G)\), \(d_u\) is the degree of a vertex u and \(\alpha \) is any non-zero real number. A cactus is a graph in which

In this paper, let p be a prime with \(p\ge 7\). We determine the weight distributions of cyclic codes of length 6 over \(\mathbb {F}_q\) and the minimum Hamming distances of all repeated-root cyclic codes of length \(6p^s\) over \(\mathbb {F}_q\), where q is a power of p and s is an integer. Furthermore, we find all maximum distance separable codes of length \(6p^s\).

In this paper, a delayed SIQR epidemic model with vaccination and elimination hybrid strategies is analysed under a white noise perturbation. We prove the existence and the uniqueness of a positive solution. Afterwards, we establish a stochastic threshold \({\mathcal {R}}_s\) in order to study the extinction and persistence in mean of the stochastic epidemic system. Then we investigate the existence

The present study takes advantage of the white noise and the Lévy noise to portray the small and sudden environmental perturbations respectively, and puts forward a stochastic population model with Allee effects and Lévy jumps. First, it is confirmed that the model possesses a unique, global and positive solution. Then, permanence and extinction of the species are examined. Afterwards, the trajectory

This note discusses, in elementary terms, linear codes over \(\mathbb {Z}_2\) which are closed under 2-step cyclic shifts, and classifies them in terms of special linear combinations of polynomials. Codes which are preserved under order-reversing automorphisms are also discussed, and a classification result in terms of special linear combinations of polynomials is obtained.

By the combination of Lie symmetry analysis and dynamical system method, the (2+1)-dimensional dissipative long wave system is studied. First, we get Lie algebra and Lie symmetry group of the system. Then, by using the dynamical system method, the bifurcation and phase portraits of the corresponding traveling system of the system are obtained, it is shown that for different parametric space, the system