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A nonlinear dynamical model is developed in this paper that depicts interactions among vultures, human, animals and their carcasses. Diseases such as plague, anthrax and rabies are spreading due to the cascade impact caused by the catastrophic drop in the vulture population, particularly in Africa and Asia. The built model is theoretically studied using qualitative differential-equation theory to demonstrate the system's rich dynamical features, which are critical for maintaining the ecosystem's equilibrium. According to the qualitative findings, depending on the parameter combinations, the system not only displays stability of many equilibrium states but also experiences transcritical and Hopf bifurcations. By keeping an eye on the variables causing the decline of the vulture population, the model's outputs may assist in maintaining balance with the prevention of the spread of disease through carcasses. Hopf-bifurcation results in the bifurcation of the limit cycle through the threshold, supporting the idea that interactions between humans and vultures may also be periodic. [ABSTRACT FROM AUTHOR]

We consider state and parameter estimation for compartmental models having both timevarying and time-invariant parameters. In this manuscript, we first detail a general Bayesian computational framework as a continuation of our previous work. Subsequently, this framework is specifically tailored to the susceptible-infectious-removed (SIR) model which describes a basic mechanism for the spread of infectious diseases through a system of coupled nonlinear differential equations. The SIR model consists of three states, namely, the susceptible, infectious, and removed compartments. The coupling among these states is controlled by two parameters, the infection rate and the recovery rate. The simplicity of the SIR model and similar compartmental models make them applicable to many classes of infectious diseases. However, the combined assumption of a deterministic model and time-invariance among the model parameters are two significant impediments which critically limit their use for long-term predictions. The tendency of certain model parameters to vary in time due to seasonal trends, non-pharmaceutical interventions, and other random effects necessitates a model that structurally permits the incorporation of such time-varying effects. Complementary to this, is the need for a robust mechanism for the estimation of the parameters of the resulting model from data. To this end, we consider an augmented state vector, which appends the time-varying parameters to the original system states whereby the time evolution of the time-varying parameters are driven by an artificial noise process in a standard manner. Distinguishing between time-varying and time-invariant parameters in this fashion limits the introduction of artificial dynamics into the system, and provides a robust, fully Bayesian approach for estimating the timeinvariant system parameters as well as the elements of the process noise covariance matrix. This computational framework is implemented by leveraging the robustness of the Markov chain Monte Carlo algorithm permits the estimation of time-invariant parameters while nested nonlinear filters concurrently perform the joint estimation of the system states and time-varying parameters. We demonstrate performance of the framework by first considering a series of examples using synthetic data, followed by an exposition on public health data collected in the province of Ontario. [ABSTRACT FROM AUTHOR]

In this article, two accurate nonlinear methods are proposed to calculate non-symmetrical locking ranges of the Injected Cross-Coupled Oscillator (ICCO) with the parallel RLC tank and series RL with a parallel C tank for both weak and strong injection levels. By writing governing differential equations of circuit elements of the ICCO, graphical presenting of current vectors, and using the averaging method for solving nonlinear equations, equations of the ICCO are simplified. Then, exact non-symmetrical locking ranges are calculated using the iterative method. Moreover, the describing function of the oscillator's nonlinear part, an inverse tangent function, is applied to the model. The inverse tangent function generates complicated governing differential equations of circuit elements that are accurate. Then, it is solved to ICCO for the first time and has novel results for calculating non-symmetrical locking ranges. There is a good agreement between theoretical and simulation results. The proposed non-symmetrical locking ranges are accurate in both weak and strong injections. The absolute percent of errors for various levels of the injection signal is less than 20%. In the bargain, proposed locking ranges are the most accurate compared to previously published results. [ABSTRACT FROM AUTHOR]

This article proposes and analyses a viscosity scheme for an enriched nonexpansive mapping. The scheme is incorporated with the implicit midpoint rule of stiff differential equations. We deduce some convergence properties of the scheme and establish that a sequence generated therefrom converges strongly to a fixed point of an enriched nonexpansive mapping provided such a point exists. Furthermore, we provide some examples of the implementation of the schemes with respect to certain enriched mappings and show the numerical pattern of the scheme. [ABSTRACT FROM AUTHOR]

We provide new sharp results on the action of Toeplitz operators from Triebel and Besov spaces to new BMOA-type function spaces on the unit disk. In this paper, we consider s ≥ 1 case in previous papers s < 1 was covered for BMOAs,q and BMOAsp spaces. We modify a little our previously known proofs. [ABSTRACT FROM AUTHOR]

Nowadays, the world of communication and information has undergone many changes, the rapidly growing trend of computer systems in terms of computing and storage and retrieval methods on the one hand and on the other hand a slow or almost constant trend in computer networks and non-response to The current needs of companies, organizations, telecommunication service providers as well as network designers face a series of limitations such as complexity, lack of scalability and lack of coordination between market needs and network capabilities and the introduction of cloud services and virtual servers. Network designers have taken a big step forward in the development of networks, and the solution to achieve this progress in networks is the use of software-based networks. In recent years, despite much research in the field of this type of network, there is still a need for optimizations in this area. One of the challenges that currently needs work and development is the issue of fault tolerance and failure in these networks. In this paper, various failure tolerance methods in software-defined networks are introduced. [ABSTRACT FROM AUTHOR]

In this study, we apply an algebraic approach to solve a class of fractional partial differential equations (FPDEs) by utilizing conformable fractional derivatives. This method has been successfully utilized to study and achieve analytical solutions for Drinfeld-Sokolov-Wilson equations. In this approach, we use a suitable fractional transformation and the principles of fractional calculus to simplify fractional partial differential equations into ordinary differential equations. [ABSTRACT FROM AUTHOR]

Biometrics is concerned with the identification and verification of people using their physiological and behavioral characteristics which are enduring and distinctive and these characteristics can distinguish one person from another. Systems for biometric recognition integrate intricate technological, operational, and definitional choices in a variety of scenarios. These systems combined with biometric strategies and authentication techniques will help to enhance the security of applications that rely on user collaboration. They aid in locating a specific person inside a set of industrial networks, office buildings, and control systems. This paper focused on convolutional neural networks, deep learning in biometrics, Unimodal and Multimodal Biometrics, template security, and general challenges of biometrics. This article examines a comprehensive and in-depth survey that succinctly and methodically on fingerprint and vein biometrics, analyzed, and compared to determine which is more effective in verifying the identification of a specific user and to highlight a biometric authentication system and the challenges of biometrics. We discuss each method and dataset used as well as their efficacy. The key difficulties in using these biometric recognition models as well as prospective directions for future study in this area are also covered. [ABSTRACT FROM AUTHOR]

In this article, firstly we investigate some properties of the boundary curvature of the numerical range. In the next, we define M(T) as the smallest constant such that dist(λ, σ(T)) ≤ M(T)Rλ(T); for all λ ∈∂W(T), where Rλ(T), the radius curvature at the point λ, is defined. Also, we investigate for non-convexoid T, M(T) = sup dist(λ, σ(T))/Rλ(T), where the supremum on the right-hand side is taken along all points λW(T) with finite non-zero curvature. Finally, the value of M(T) will be calculated for the self-inverse operators. [ABSTRACT FROM AUTHOR]

In this paper, we first establish the bicomplex version of Rouche's theorem. Also, a new approach is given to prove the maximum modulus principle for bicomplex holomorphic functions. Our proof is based on the direct method and extends the result proved by Luna-Elizarraras et al. Finally, we generalize the Hurwitz's theorem to bicomplex space. [ABSTRACT FROM AUTHOR]

In this paper, we establish Jensen's inequality for (p-q)-convex functions. By using Jensen's inequality we obtain some Hermite-Hadamard type inequality and several sharp inequalities. Some examples are given. [ABSTRACT FROM AUTHOR]

We prove optimal existence results for entropy solutions to some anisotropic boundary value problems like {... DiAi(x, w, &#8711, w) = f -- div F(w) in Ω, in Ω, on ∂Ω, where f ∈ L1(Ω), F = (F1, ..., FN) satisfies F ∈ (C0(ℝ))N and Ω is a bounded, open subset of ℝN, N ≥ 2, and the function Ai(x, s, ξ) verify the large monotonicity condition. The construction of the proof of our theorem is done by using Minty's Lemma in its modified version. [ABSTRACT FROM AUTHOR]

We study in this paper the existence and uniqueness of solutions to initial value problems for semilinear differential equations involving ψ-Caputo differential derivatives of an arbitrary l ∈ (0,1), using the fixed theorem. We do analyse further the M-L-U-H stability and the M-L-U-H-R stability. Then we conclude with an example to illustrate the result. [ABSTRACT FROM AUTHOR]

In the present study, we have investigated the steady mixed convection nonaxisymmetric Homann stagnation-point flow in the presence of a magnetic field over a vertical flat wall immersed in a viscous and incompressible fluid. The magnetic field is applied in the normal direction to the plate. The governing equations are reduced to a system of nonlinear ordinary differential equations with suitable boundary conditions by applying similarity transformations to the equations and the boundary conditions. Using an efficient shooting method, the transformed equations are numerically solved. The solution involves the dimensionless governing parameters: representing the shear-to-strain-rate ratio, a mixed convection parameter γ, a magnetic field parameter M, and Prandtl number Pr. An important observation is that dual solutions exist for a certain range of mixed convection parameter γ. It is noticed that critical values γc of γ are found in opposing flow, which produce two solution branches by making saddle-node bifurcation at γ = γc. Numerical results are obtained for representative values of, γ, and M and are explored in depth. Through the use of graphs, the properties of the flow and temperature profiles for various values of the governing parameters, γ, andM are examined. Also, we examined how the solution varied with γ for representative values of M (magnetic field parameter). A parametric analysis is conducted to investigate how different governing parameters affect the characteristics of fluid flow and temperature. Also, we derive asymptotic results for large γ. [ABSTRACT FROM AUTHOR]

The article introduces a generalization of the Khalouta transform to conformable fractional order. Topics include the derivation and proof of fundamental properties and theorems related to the conformable fractional Khalouta transform, its application in solving fractional differential equations to demonstrate its efficiency and validity, and its relevance in modeling complex phenomena across fields like fluid dynamics, quantum mechanics, and wave theory.

In this work, we use two unique methodologies, the homotopy perturbation transform method and Yang transform decomposition method, to solve the fractional nonlinear seventh-order Kaup–Kupershmidt (KK) problem. The physical phenomena that arise in chemistry, physics, and engineering are mathematically explained in this equation, in particular, nonlinear optics, quantum mechanics, plasma physics, fluid dynamics, and so on. The provided methods are used to solve the fractional nonlinear seventh-order KK problem along with the Yang transform and fractional Caputo derivative. The results are significant and necessary for exploring a range of physical processes. This paper uses modern approaches and the fractional operator to develop satisfactory approximations to the offered problem. To solve the fractional KK equation, we first use the Yang transform and fractional Caputo derivative. He's and Adomian polynomials are useful to manage nonlinear terms. It is shown that the suggested approximate solution converges to the exact one. In these approaches, the results are calculated as convergent series. The key advantage of the recommended approaches is that they provide highly precise results with little computational work. The suggested approach results are compared to the precise solution. By comparing the outcomes with the precise solution using graphs and tables we can verify the efficacy of the offered strategies. Also, the outcomes of the suggested methods at various fractional orders are examined, demonstrating that the findings get more accurate as the value moves from fractional order to integer order. Moreover, the offered methods are innovative, simple, and quite accurate, demonstrating that they are effective for resolving differential equations. [ABSTRACT FROM AUTHOR]

This work addresses the qualitative analysis of a novel non-linear coupled system of fractional differential problems (FDPs) using Caputo and Liouville–Riemann fractional derivatives. Fractional calculus has demonstrated significant applicability across various fields, including financial systems, optimal control, epidemiological models, chaotic systems, and engineering. The proposed model builds on existing research by formulating a non-linear coupled fractional boundary value problem with mixed boundary conditions. The primary advantages of our method include its ability to capture the dynamics of complex systems more accurately and its flexibility in handling different types of fractional derivatives. The model's solution was derived using advanced mathematical techniques, and the results confirmed the existence and uniqueness of the solutions. This approach not only generalizes classical differential equation methods but also offers a robust framework for modeling real-world phenomena governed by fractional dynamics. The study concludes with the validation of the theoretical findings through illustrative examples, highlighting the method's efficacy and potential for further applications. [ABSTRACT FROM AUTHOR]

This paper is devoted to studying a class of fuzzy fractional switched implicit differential equations (FFSIDEs) with non-instantaneous impulses that there are few papers considering this issue. Considering switching law and the memory property of fractional calculus, we first present a formula of solution for FFSIDEs with non-instantaneous impulses. Subsequently, based on a sequence of Picard functions, we explore the existence of solutions for the addressed equations by successive approximation. Furthermore, Ulam–Hyers (U–H) stability for this considered equations is derived. The main results are obtained using fuzzy-valued fractional calculus and nonlinear analysis. Finally, two numerical examples illustrating the theoretical result are given. [ABSTRACT FROM AUTHOR]

In this article, we consider nonlinear neutral Volterra integro‐differential equations (NVIDEs) including infinite delay. We prove three new theorems with regard to the stability, the uniform stability, and the instability of zero solution of the NVIDEs. The new results of this article include sufficient conditions and the technique of the proofs is based on the Lyapunov‐Krasovskiĭ functional (LKF) approach. By this article, some results that can be found in the literature are extended and improved from the linear case to nonlinear cases and contributed. [ABSTRACT FROM AUTHOR]

We investigate the structure of rank-to-rank elementary embeddings at successor rank, working in ZF set theory without the Axiom of Choice. Recall that the set-theoretic universe is naturally stratified by the cumulative hierarchy, whose levels V α are defined via iterated application of the power set operation, starting from V 0 =∅, setting V α+1 =P(V α), and taking unions at limit stages. Assuming that j:V α+1 →V α+1 is a (non-trivial) elementary embedding, we show that V α is fundamentally different from V α+1: we show that j is definable from parameters over V α+1 iff α+1 is an odd ordinal. The definability is uniform in odd α+1 and j. We also give a characterization of elementary j:Vα+2 → Vα+2 in terms of ultrapower maps via certain ultrafilters. For limit ordinals λ, we prove that if j:Vλ→Vλ is Σ1-elementary, then j is not definable over Vλ from parameters, and if β < λ and j:Vβ → Vλ is fully elementary and ∈-cofinal, then j is likewise not definable. If there is a Reinhardt cardinal, then for all sufficiently large ordinals α, there is indeed an elementary j: Vα → Vα, and therefore the cumulative hierarchy is eventually periodic (with period 2). [ABSTRACT FROM AUTHOR]

In this two-paper series, we prove the invariance of the Gibbs measure for a threedimensional wave equation with a Hartree nonlinearity. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. In this paper, we focus on the dynamical aspects of our main result. The local theory is based on a paracontrolled approach, which combines ingredients from dispersive equations, harmonic analysis, and random matrix theory. The main contribution, however, lies in the global theory. We develop a new globalization argument, which addresses the singularity of the Gibbs measure and its consequences. [ABSTRACT FROM AUTHOR]

We present an algorithm for the result of differential equations (DEs) by using linearly independent Hosoya polynomials of trees. With the newly adopted strategy, the desired outcome is expanded in the form of a collection of continuous polynomials over an interval. Nevertheless, compared to other methods for solving differential equations, this method's precision and effectiveness relies on the size of the collection of Hosoya polynomials, and the process is easier. Excellent agreement between the exact and approximate solutions is obtained when the current scheme is used to crack linear and nonlinear equations. Potentially, this method could be used in more intricate systems for which there are no exact solutions. [ABSTRACT FROM AUTHOR]

In this paper, we will present existence and localization fixed point theorems and stability results for the fixed point problem involving some very general classes of operators (singlevalued and multi-valued), namely for Ćirić type operators. Then, an application to homotopy principles is given. Our results complement and extend the works in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the authors studied sufficient conditions to understand the oscillatory behavior of solutions of nonlinear neutral delay (and advanced) differential equation (E) with deviating arguments. Employing Banach fixed point theorem, the authors established the existence of bounded positive solutions of (E). The authors solved various examples using MATLAB software to understand the applications of the main theorems. Moreover, the authors analyzed the effect of delay terms on the behavior of solutions of (E). This paper has improved the results obtained in Basu [2] and Chatzarakis [11]. [ABSTRACT FROM AUTHOR]

Due to the restrictive growth and/or monotonicity requirements inherent in their employment, classical iterative fixed-point theorems are rarely used to approximate solutions to an integral operator with Green's function kernel whose fixed points are solutions of a boundary value problem. In this paper, we show how one can decompose a fixed-point problem into multiple fixed-point problems that one can easily iterate to approximate a solution of a differential equation satisfying one boundary condition, then apply a bisection method in an intermediate value theorem argument to meet a second boundary condition. Error estimates on the iterates are also established. The technique will be illustrated on a second-order right focal boundary value problem, with an example provided showing how to apply the results. [ABSTRACT FROM AUTHOR]

The main purpose of this work is to present an accurate computational approach for solving the singularly perturbed Burger-Huxley equations. The quasilinearization technique linearizes the nonlinear term of the differential equation. The finite difference approximation is formulated to approximate the derivatives in the differential equations and then accelerate its rate of convergence to improve the accuracy of the solution. Numerical experiments were conducted to sustain the theoretical results and to show that the presented method produces a more correct solution than some surviving methods in the literature. [ABSTRACT FROM AUTHOR]

The Harmonic BalanceMethod (HBM) is one of the most often applied semi-analytic approximation methods in nonlinear dynamics. In earlier publications, the two coauthors already observed for the softening Duffing oscillator and other systems that especially low ansatz order HBM solutions may contain larger errors for some solution branches, and called this artifacts. In the present work, this problem is studied systematically with a new implementation of the method and applied again to the example of the softening Duffing oscillator. In conjunction with a mathematical definition for HBM artifacts we discuss and present possible a posteriori and a priori HBM error measures. [ABSTRACT FROM AUTHOR]

Summary: In the paper, a nonlinear analysis of RC phase‐shift oscillator with operational amplifier is done. Using Kirchhoff's laws, a nonlinear system of three differential equations that describes the behavior of the oscillator is obtained. This system is analyzed using the Poincaré–Andronov–Hopf bifurcation theory. The basic principles of the Poincaré–Andronov–Hopf bifurcation theory are presented in advance, including the Center Manifold Theory and the Theory of Normal Forms. It was found that, under certain conditions, the oscillator system has a limit cycle, which means that the oscillator under consideration generates periodic oscillations. The period, amplitude, and stability of the generated periodic oscillations are determined theoretically. The obtained analytical results are confirmed by a numerical analysis of the nonlinear system of differential equations performed by MATLAB. [ABSTRACT FROM AUTHOR]

In this paper, we extend the block hybrid method with equally spaced intra-step points to solve linear and nonlinear third-order initial value problems. The proposed block hybrid method uses a simple iteration scheme to linearize the equations. Numerical experimentation demonstrates that equally spaced grid points for the block hybrid method enhance its speed of convergence and accuracy compared to other conventional block hybrid methods in the literature. This improvement is attributed to the linearization process, which avoids the use of derivatives. Further, the block hybrid method is consistent, stable, and gives rapid convergence to the solutions. We show that the simple iteration method, when combined with the block hybrid method, exhibits impressive convergence characteristics while preserving computational efficiency. In this study, we also implement the proposed method to solve the nonlinear Jerk equation, producing comparable results with other methods used in the literature. [ABSTRACT FROM AUTHOR]

Multilayer fluid models play a crucial role in comprehending fluid–fluid and fluid– nanoparticle interactions within the petroleum industry, geophysics, and plasma physics due to their diverse industrial applications. The current research aims to investigate the impact of a heat source/sink on a non-Newtonian hybrid nanofluid that saturates a porous medium positioned between a transparent viscous fluid filling a vertical channel. The model governing nonlinear coupled differential equations are nondimensionalized using appropriate fundamental quantities. Subsequently, the regular perturbation method is employed to solve the transformed dimensionless governing equations. Upon comparing the data, it is evident that current results closely align with the previously published findings. The parameter Q2 causes an increase in both θs(ζ) and θt(ζ) across all three regions. Increasing Casson parameter leads to a decrease in θt(ζ). [ABSTRACT FROM AUTHOR]

Thermal buckling of a shear deformable circular plate made of functionally graded materials (FGM) is studied using an exact analytical method in the Hamiltonian system. Fundamental equations for the thermal buckling of the plate under transversely nonuniform temperature rising are established based on the first-order shear deformation theory. Subsequently, by introducing the symplectic method, the differential equations are converted into canonical equations in the Hamiltonian system. Buckling loads and buckling modes correspond to symplectic eigenvalues and eigen solutions, respectively. The expressions of complete buckling modes in the form of special functions are achieved by solving canonical equations and boundary conditions analytically and exactly. The symplectic eigenvalues are obtained simultaneously and the buckling temperature increments are calculated using the inverse solution. Finally, the influences of the gradient characteristics, geometric parameters, boundary conditions, and type of thermal loading on the buckling temperature increments are discussed through parameter research. [ABSTRACT FROM AUTHOR]

The large‐amplitude vibration of initially stressed functionally graded material (FGM) rectangular plates with porosities is investigated in this paper. All edges of the plate are simply supported and uncompressed edges are tangentially restrained. Initial stresses are caused by in‐plane compressive load acting on freely movable edges or thermally induced forces at restrained edges. Pores present in FGM through even and uneven distributions. Material properties are assumed to be temperature‐dependent and, due to the presence of the pores, the effective properties of FGM are determined using a modified rule of mixture. Governing equations in terms of deflection and stress function are established based on the classical plate theory taking into account von Kármán nonlinearity and initial geometric imperfection. These equations are solved using approximate analytical solutions along with the Galerkin method to obtain a time differential equation containing quadratic and cubic nonlinear terms. Nonlinear frequencies are determined by means of numerical integration employing the fourth‐order Runge–Kutta scheme. Parametric studies are carried out to analyze the effects of material and geometry properties, porosity volume fraction and distribution, pre‐existent compressive and thermal loads, imperfection and degree of tangential constraints of unloaded edges on the natural frequencies and nonlinear to linear frequency ratio of FGM plates. [ABSTRACT FROM AUTHOR]

This paper delves into the asymptotic and oscillatory behavior of all classes of solutions of fourth-order nonlinear neutral delay differential equations in the noncanonical form with damping terms. This research aims to improve the relationships between the solutions of these equations and their corresponding functions and derivatives. By refining these relationships, we unveil new insights into the asymptotic properties governing these solutions. These insights lead to the establishment of improved conditions that ensure the nonexistence of any positive solutions to the studied equation, thus obtaining improved oscillation criteria. In light of the broader context, our findings extend and build upon the existing literature in the field of neutral differential equations. To emphasize the importance of the results and their applicability, this paper concludes with some examples. [ABSTRACT FROM AUTHOR]

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Present work explores quadratic extrapolation (QE) technique for large deformation flexure study of FGM plate with five variables higher-order shear deformation theory (HSDT). Rule of mixtures is utilized in achieving effective material properties across the thickness. Governing differential equations (GDEs) and boundary conditions have been acquired using the principle of virtual work. Quadratic extrapolation (QE) and Newton-Raphson (NR) linearization techniques are considered and compared with respect to computational time. Von-Karman type nonlinearity is used in the present work. Multiquadric radial basis function (RBF) based meshfree technique discretizes GDEs in displacement form. FGM plates with different boundary conditions are investigated under different patch loadings. Present results are validated with some previously published results after a convergence study. Some new results are produced for the flexural response of the FGM plate under patch loads. Effect of types of loads, grading index, patch load location, and boundary conditions are presented. [ABSTRACT FROM AUTHOR]

In this study, we solve fractional order PDEs with free parameters that regulate wave motion in a low-pass electrical transmission line equation (LPET) using the unified technique. To convert the governing equation into an ordinary differential equation (ODE), we have used a simple linear fractional transformation. The unified technique can therefore be used to find various single and extracting wave solutions to the equation of attention. Using Maple-18 software, all of the established solutions are validated and verified. By selecting appropriate values for the fractional order and free parameters, the two dimensional (2D) and three dimensional (3D) profiles of some of the assimilation solutions demonstrating kink, singular kink, cross kink, bright-dark kink, lump type kink, anti-kink, dark-anti kink, singular periodic, periodic, singular soliton solutions are displayed. The effect of free parameters and fractionality on the dynamical properties of the precise and exploited solutions are graphically illustrated and discussed in detail. We have also compared our results to those found in the literature review. Wherever possible, the judgment demonstrates no significant differences between our realized and published solutions. The results of this investigation show that the adopting technique is both productive and powerful in extracting wave solutions to nonlinear evolution problems that arise in the areas of applied mathematics, mathematical physics, and engineering. [ABSTRACT FROM AUTHOR]

In the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. We scrutinize how diffusion impacts the model's stability. By analysing the stability of the model's uniform equilibrium state, we identify a condition leading to Turing instability. The study delves into how diffusion influences pattern formation within a predator-prey system. Our findings reveal that various spatiotemporal patterns, such as patches, spots, and even chaos, emerge based on species diffusion rates. We derive the amplitude equation by employing the weak nonlinear multiple scales analysis technique and the Taylor series expansion. A novel sinc interpolation approach is introduced. Numerical simulations elucidate the interplay between diffusion and Turing parameters. In a two-dimensional domain, spatial pattern analysis illustrates population density dynamics resulting in isolated groups, spots, stripes, or labyrinthine patterns. Simulation results underscore the method's effectiveness. The article concludes by discussing the biological implications of these outcomes. [ABSTRACT FROM AUTHOR]

Stiffness properties of structural members, such as beam, plate and shell, can change drastically in the presence of axial forces due to geometric effects of the nonlinear strain components. In this paper, the stability behaviour of beam-column is investigated using the governing differential equation and compared with the geometrically nonlinear finite element analysis. The lateral deflection obtained from the theoretical model matches quite accurately with the numerical values for wide range of axial to critical load ratio P/Pcr. It is shown that bending stiffness decreases linearly with the axial load. By extending the theory, an expression for the membrane stiffness of the beam-column is presented in this paper. The geometrically nonlinear finite element analysis can capture exactly the parabolic variation of the membrane stiffness as per the derived expression. It increases initially up to P/Pcr = 0.35 and decreases rapidly to negligible value near the critical load indicating buckling instability. [ABSTRACT FROM AUTHOR]

We investigate the non-trivial solutions for a partial discrete Dirichlet nonlinear problem with p-Laplacian by applying Ricceri's variational principle and a two non-zero critical points theorem. In addition, we identify open intervals of the parameter ≥ under appropriate constraints imposed on the nonlinear term. This allows us to ensure that the nonlinear problem has at least one or two non-trivial solutions. [ABSTRACT FROM AUTHOR]

In the current study, a new numerical algorithm is presented to solve a class of nonlinear fractional integral-differential equations with weakly singular kernels. Cubic hat functions (CHFs) and their properties are introduced for the first time. A new fractional-order operational matrix of integration via CHFs is presented. Utilizing the operational matrices of CHFs, the main problem is transformed into a number of trivariate polynomial equations. Error analysis and the convergence of the proposed method are evaluated, and the convergence rate is addressed. Ultimately, three examples are provided to illustrate the precision and capabilities of this algorithm. The numerical results are presented in some tables and figures. [ABSTRACT FROM AUTHOR]

This paper discusses the S-asymptotically periodic problem of fractional evolution equation with delay. By introducing a new noncompact measure theory involving infinite interval, we study the existence of S-asymptotically periodic mild solutions under the situation that the relevant semigroup is noncompact and the nonlinear term satisfies more general growth conditions instead of Lipschitz-type conditions. Moreover, by establishing a new Gronwall-type integral inequality corresponding to fractional differential equation with delay, we consider the global asymptotic behavior of S-asymptotically periodic mild solutions, which will make up for the blank of this field. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a multi-order -Hilfer fractional pantograph implicit differential equation on unbounded domains . The existence and uniqueness of solution are established for a such problem by utilizing the Banach fixed point theorem in an applicable Banach space. In addition, stability of the types Ulam-Hyers ( ), Ulam-Hyers-Rassias ( ) and semi-Ulam-Hyers-Rassias (s- ) are discussed by using nonlinear analysis topics. Finally, a concrete example includes some particular cases is enhanced to illustrate rightful of our results. [ABSTRACT FROM AUTHOR]

Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. We have converted assumed PDE into nonlinear ODE by using the optimal system. The new auxiliary scheme is used to find the Travelling wave solutions, while graphical behaviour visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, and fundamental principles in physics that assert certain quantities remain constant over time. [ABSTRACT FROM AUTHOR]

For the neutral functional differential equation with two types controls and the discontinuous initial condition, whose right-hand side are linear with respect to the prehistory of the phase velocity, theorems on the continuous dependence of a solution with respect to perturbations of the initial data and the right-hand side are proposed. Under the initial data we imply the collection of delay parameters, initial functions, initial vector and control functions. In the work, two cases are considered, when perturbation of the nonlinear term in the right-hand side are small in the integral and Euclidean topologies. Discontinuity at the initial moment means that at the initial moment values of the initial function and trajectory, in general, do not coincide, this situation may be related to the instant change in a dynamical process (changes of investment, environment and so on). Such type theorems play an important role in proving of necessary conditions of optimality in the optimization problem, in proving variation formulas of solution and in the sensitivity analysis of mathematical models. [ABSTRACT FROM AUTHOR]

A Bass diffusion model is defined on an arbitrary network, with the additional introduction of behavioral compartments, such that nodes can have different probabilities of receiving the information/innovation from the source and transmitting it to other nodes. The dynamics are described by a large system of non-linear ordinary differential equations, whose numerical solutions can be analyzed in dependence on diffusion parameters, network parameters, and relations between the compartments. For example, in a simple case with two compartments (Enthusiasts and Sceptics about the innovation), we consider cases in which the "publicity" and imitation terms act differently on the compartments, and individuals from one compartment do not imitate those of the other, thus increasing the polarization of the system and creating sectors of the population where adoption becomes very slow. For some categories of scale-free networks, we also investigate the dependence on the features of the networks of the diffusion peak time and of the time at which adoptions reach 90% of the population. [ABSTRACT FROM AUTHOR]

A qualitative analysis for a nonlinear system of fractional pantograph evolution differential equations (FPEDEs) has been established. Conditions about the solution of the underlying equations have been established in the direction of the existence and uniqueness of the solution. Using results of fixed‐point theorems of Krasnoselskii iterations in Banach spaces, we develop the required results. This research work is enriched by establishing the results related to Ulam–Hyers (UH) stability of the problem under consideration via the tools of nonlinear analysis. To validate the reliability of the obtained results, some pertinent examples are given in the manuscript. [ABSTRACT FROM AUTHOR]

This paper considers blow-up and global existence for a semilinear space-time fractional pseudo-parabolic equation with nonlinear memory in a bounded domain. We determine the critical exponents of the Cauchy problem when α < γ and α ≥ γ , respectively. The results obtained in this study are noteworthy extension to the results of time-fractional differential equation. The critical exponent is consistent with the corresponding Cauchy problem for the time-fractional differential equation with nonlinear memory, which illustrates that the diffusion effect of the third order term is not strong enough to change the critical exponents. [ABSTRACT FROM AUTHOR]