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The main aim of this paper is to investigate Hardy-Littlewood type Theorems and a Hopf type lemma on functions induced by a differential operator. We first prove more general Hardy-Littlewood type theorems for the Dirichlet solution of a differential operator which depends on α ∈ (- 1 , ∞) over the unit ball B n of R n with n ≥ 2 , related to the Lipschitz type space defined by a majorant which satisfies some assumption. We find that the case α ∈ (0 , ∞) is completely different from the case α = 0 due to Dyakonov (Adv. Math. 187 (2004), 146–172). Then a more general Hopf type lemma for the Dirichlet solution of a differential operator will also be established in the case α > n - 2 . [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we use differential operator to present new identities and provide alternative proofs for certain established identities related to geometric polynomials. Additionally, by using the differential operator associated with geometric polynomials, Rolle’s theorem and a theorem of Wang and Yeh, we present some results on the real rootedness of polynomials. [ABSTRACT FROM AUTHOR]

In the current paper, we define some subclasses of holomorphic functions in the open disk u that are defined by the differential operator. These subclasses are defined in the open disk u. We make some estimates for the bounds of the Fekete-Szego inequality as well as the coefficients | a2 | and | a3 | for functions that belong to these subclasses. Also, some of the results of these subclasses have been generalized, particularly those that involve the majorization and quasi-subordination concepts. [ABSTRACT FROM AUTHOR]

We introduce a regularization method with two differential operators for solving a linear ill-posed operator equation system. The existence and uniqueness of regularized solutions to the problem are derived. With an a priori as well as an a posteriori parameter choice strategy, convergence and convergence rates of the regularized solution are also obtained. As an application, we apply the regularization to a simultaneous inversion of the source term and the initial value problem for a heat conduction equation, numerical experiments are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract The discrete analog of the differential operator plays a significant role in constructing interpolation, quadrature, and cubature formulas. In this work, we consider a discrete analog D m ( h β ) $D_{m}(h\beta )$ of the differential operator d 2 m d x 2 m + 1 $\frac{d^{2m}}{dx^{2m}}+1$ designed specifically for even natural numbers m. The operator’s effectiveness in constructing an optimal quadrature formula in the L 2 ( 2 , 0 ) ( 0 , 1 ) $L_{2}^{(2,0)}(0,1)$ space is demonstrated. The errors of the optimal quadrature formula in the W 2 ( 2 , 1 ) ( 0 , 1 ) $W_{2}^{(2,1)}(0,1)$ space and in the L 2 ( 2 , 0 ) ( 0 , 1 ) $L_{2}^{(2,0)}(0,1)$ space are compared numerically. The numerical results indicate that the optimal quadrature formula constructed in this work has a smaller error than the one constructed in the W 2 ( 2 , 1 ) ( 0 , 1 ) $W_{2}^{(2,1)}(0,1)$ space.

In this paper, we present a new class of linear fractional differential operators that are based on classical Gaussian hypergeometric functions. Then, we utilize the new operators and the concept of differential subordination to construct a convex set of analytic functions. Moreover, through an examination of a certain operator, we establish several notable results related to differential subordination. In addition, we derive inclusion relation results by employing Briot–Bouquet differential subordinations. We also introduce a perspective study for developing subordination results using Gaussian hypergeometric functions and provide certain properties for further research in complex dynamical systems. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Bloch eigenvalues, band functions and bands of the self-adjoint differential operator L generated by the differential expression of odd order n with the m × m periodic matrix coefficients, where n > 1. We study the localizations of the Bloch eigenvalues and continuity of the band functions and prove that each point of the set (2 π N) n , ∞ ∪ (- ∞ , (- 2 π N) n ] belongs to at least m bands, where N is the smallest integer satisfying N ≥ π - 2 M + 1 and M is the sum of the norms of the coefficients. Moreover, we prove that if M ≤ π 2 2 - n + 1 / 2 , then each point of the real line belong to at least m bands. [ABSTRACT FROM AUTHOR]

In this paper, we consider the necessary and sufficient conditions for the subharmonicity of functions of two variables representable as a product of two functions of one variable in the Cartesian coordinate system or in the polar coordinate system in domains on the plane. We establish a connection of such functions with functions that are convex with respect to solutions of second-order linear differential equations, that is, convex with respect to two functions. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to show that if u ∈ W m , p (R n) is a weak solution of Q u = f where f ∈ X p , k r , q (R n) , then u ∈ X p , k m + r , q (R n) with 1 < p , q < ∞ , 0 < r < 1 , k is a temperate weight function in the Hörmander sense, Q = ∑ | β | ≤ m c β ∂ β is a linear partial differential operator of order m ≥ 0 with non-zero constant coefficients c β , and where X p , k r , q (R n) is either the weighted Triebel-Lizorkin or the weighted Besov space. The way to prove this result is based on the boundedness of the continuous wavelet transform with rotations. [ABSTRACT FROM AUTHOR]

In this paper, we construct higher-order modular differential equations for elliptic modular forms, holomorphic Jacobi forms, and skew-holomorphic Jacobi forms by using the Rankin-Cohen brackets extended to the Eisenstein series of weight two. Rankin-Cohen brackets are typical tools in the construction of modular forms by differential operators. We introduce the extended Rankin-Cohen brackets for holomorphic or skew-holomorphic Jacobi forms paired with elliptic modular forms. They provide a unified method of construction of higher-order modular differential equations for the modular forms above. In particular, with these extended Rankin-Cohen brackets, we can reproduce the modular differential equations of previous studies. [ABSTRACT FROM AUTHOR]

For a quasi-split Satake diagram, we define a modified q-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding ıquantum group. In other words, we provide a differential operator approach to ıquantum groups. Meanwhile, the oscillator representations of ıquantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed. [ABSTRACT FROM AUTHOR]

The discrete analog of the differential operator plays a significant role in constructing interpolation, quadrature, and cubature formulas. In this work, we consider a discrete analog D m (h β) of the differential operator d 2 m d x 2 m + 1 designed specifically for even natural numbers m. The operator's effectiveness in constructing an optimal quadrature formula in the L 2 (2 , 0) (0 , 1) space is demonstrated. The errors of the optimal quadrature formula in the W 2 (2 , 1) (0 , 1) space and in the L 2 (2 , 0) (0 , 1) space are compared numerically. The numerical results indicate that the optimal quadrature formula constructed in this work has a smaller error than the one constructed in the W 2 (2 , 1) (0 , 1) space. [ABSTRACT FROM AUTHOR]

Due to inherent operating constraints, wireless sensor networks (WSNs) need help assuring network security. This problem is caused by worms entering the networks, which can spread uncontrollably to nearby nodes from a single node infected with computer viruses, worms, trojans, and other malicious software, which can compromise the network’s integrity and functionality. This article discusses a fractional SE1E2IR{\mathsf{S}}{{\mathsf{E}}}_{1}{{\mathsf{E}}}_{2}{\mathsf{I}}{\mathsf{R}} model to explain worm propagation in WSNs. For capturing the dynamics of the virus, we use the Mittag–Leffler kernel and the Atangana–Baleanu (AB) Caputo operator. Besides other characteristics of the problem, the properties of superposition and Lipschitzness of the AB Caputo derivatives are studied. Standard numerical methods were employed to approximate the Atangana–Baleanu–Caputto fractional derivative, and a detailed analysis is presented. To illustrate our analytical conclusions, we ran numerical simulations.

Solutions to problems arising from much scientific and applied research conducted at the world level lead to integral and differential equations. They are approximately solved, mainly using quadrature, cubature, and difference formulas. Therefore, in the current work, we consider a discrete analogue of the differential operator 1 − 1 2 π 2 d 2 d x 2 m in the Hilbert space H 2 μ R , called D m β . We modify the Sobolev algorithm to construct optimal quadrature formulas using a discrete operator. We provide a weighted optimal quadrature formula, using this algorithm for the case where m = 1 . Finally, we construct an optimal quadrature formula in the Hilbert space H 2 μ R for the weight functions p x = 1 and p x = e 2 π i ω x when m = 1 . [ABSTRACT FROM AUTHOR]

Let B g (r) be the moduli space of triples of the form (X , K X 1 / 2 , F) , where X is a compact connected Riemann surface of genus g, with g ≥ 2 , K X 1 / 2 is a theta characteristic on X, and F is a stable vector bundle on X of rank r and degree zero. We construct a T ∗ B g (r) -torsor H g (r) over B g (r) . This generalizes on the one hand the torsor over the moduli space of stable vector bundles of rank r, on a fixed Riemann surface Y, given by the moduli space of algebraic connections on the stable vector bundles of rank r on Y, and on the other hand the torsor over the moduli space of Riemann surfaces given by the moduli space of Riemann surfaces with a projective structure. It is shown that H g (r) has a holomorphic symplectic structure compatible with the T ∗ B g (r) -torsor structure. We also describe H g (r) in terms of the second order matrix valued differential operators. It is shown that H g (r) is identified with the T ∗ B g (r) -torsor given by the sheaf of holomorphic connections on the theta line bundle over B g (r) . [ABSTRACT FROM AUTHOR]

In this paper, we obtain the coefficient bounds and closure properties for a class of analytic functions defined using q-differential operator which are closely related to the classes of α-spiralike and convex α-spiral functions. Also we investigate convolution properties and necessary and sufficient conditions for functions in the defined class. [ABSTRACT FROM AUTHOR]

In this paper, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. These properties are established by first proving a new second-order Hardy-type inequality, where the weights are the coefficients of the equation and the operator. This new inequality, in its turn, is established for functions satisfying certain boundary conditions that depend on the boundary behavior of one of its weights at infinity and at zero. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the representation of the symbolic n-plithogenic differential operator for many different values of n by classical algebraic matrices and plithogenic matrices. We present many examples about the representation of symbolic n-plithogenic differential operators by matrices. As well as, we compute the symbolic 2-plithogenic, 3-plithogenic, and 4-plithogenic Wronsckian, and anti-Wronsckian.

The main goal of this paper is to study the representation of the symbolic n-plithogenic differential operator for many different values of n by classical algebraic matrices and plithogenic matrices. We present many examples about the representation of symbolic n-plithogenic differential operators by matrices. As well as, we compute the symbolic 2-plithogenic, 3-plithogenic, and 4-plithogenic Wronsckian, and anti-Wronsckian. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm that, given a differential operator of order 2, detects if this operator comes from a simpler operator under a non-trivial change of variables. [ABSTRACT FROM AUTHOR]

In this paper, we present a new class of linear fractional differential operators that are based on classical Gaussian hypergeometric functions. Then, we utilize the new operators and the concept of differential subordination to construct a convex set of analytic functions. Moreover, through an examination of a certain operator, we establish several notable results related to differential subordination. In addition, we derive inclusion relation results by employing Briot–Bouquet differential subordinations. We also introduce a perspective study for developing subordination results using Gaussian hypergeometric functions and provide certain properties for further research in complex dynamical systems.

In this paper the authors combine the quantum calculus applications regarding the theories of differential subordination and superordination with fuzzy theory. These results are established by means of an operator defined as the $ q $-analogue of the multiplier transformation. Interesting fuzzy differential subordination and superordination results are derived by the authors involving the functions belonging to a new class of normalized analytic functions in the open unit disc $ U $ which is defined and investigated here by using this $ q $-operator.

In this paper, we explore the intricate connection between orthogonal polynomials and norm attainable operators within a Hilbert space. We give examples of this relationship by associating Hermite, Laguerre, and Jacobi orthogonal polynomials with second-order differential operators. These associations are substantiated by demonstrating various properties, notably the assertion that if a second-order differential operator is expressed in a specific form with continuous coefficients and smooth functions, then it qualifies as self-adjoint. Further-more, we establish that when the coefficients of such an operator are real-valued functions ensuring positivity, an eigen-value problem associated with it yields eigenfunctions forming an orthonormal basis, and consequently, the operator is normal. [ABSTRACT FROM AUTHOR]

In this paper, we classify the family of entire functions { ρ , σ } such that the induced weighted composition map A ρ , σ , is a conjugation namely J b , α , where b is an arbitrary complex number and α is a real number such that 0 < α < 1. In the last section, we characterize the J b , α -symmetric maximal differential operators on the Fock space α 2 . [ABSTRACT FROM AUTHOR]

In this paper, we characterize a new second-order Hardy-type inequality and find a two-sided estimate for its least constant. As applications of this new inequality, we study oscillatory properties of a fourth-order differential equation and spectral properties of a corresponding differential operator. [ABSTRACT FROM AUTHOR]

The accurate simulation of anisotropic media is critical in seismic imaging and inversion. In recent years, some scholars have dedicated efforts to the study of precise elastic waves in anisotropic media; however, it is easy to separate P-wave and S-wave from elastic wave fields in isotropic media but difficult to separate them in anisotropic media. To address this issue, others have proposed pseudo-pure-wave equations based on the theory of wave-mode separation, but shear wave interference still exists. Therefore, we derived the first-order pure quasi-P-wave equation with no shear wave component in orthorhombic anisotropic media (ORT) which is common in the Earth’s crust and has very important research value. The presence of a pseudodifferential operator in the equation poses a challenge for solving. In order to solve the pure wave equation, we decomposed the original pseudodifferential operator into an elliptic differential operator and a scalar operator, both of which are easily solvable. In addition, we extended the equation from ORT media to tilted ORT (TORT) media. The example results indicate that our pure quasi-P-wave equation can yield a more stable and accurate P-wave field. The pure wave equation we propose can be applied in reverse time migration (RTM), the least squares RTM (LSRTM), and even the full waveform inversion (FWI).

It is known that discrete analogs of differential operators play an important role in constructing optimal quadrature, cubature, and difference formulas. Using discrete analogs of differential operators, optimal interpolation, quadrature, and difference formulas exact for algebraic polynomials, trigonometric and exponential functions can be constructed. In this paper, we construct a discrete analogue D m (h β) of the differential operator d 2 m d x 2 m + 2 d m d x m + 1 in the Hilbert space W 2 (m , 0) . We develop an algorithm for constructing optimal quadrature formulas exact on exponential-trigonometric functions using a discrete operator. Based on this algorithm, in m = 2 , we give an optimal quadrature formula exact for trigonometric functions. Finally, we present the rate of convergence of the optimal quadrature formula in the Hilbert space W 2 (2 , 0) for the case m = 2 . [ABSTRACT FROM AUTHOR]

Magnetic fields of different astrophysical objects are generated by the dynamo mechanism. Dynamo is based on the alpha-effect and differential rotation, which are described using a system of parabolic equations. Their solution is an important problem in magnetohydrodynamics and mathematical physics. They can be solved assuming exponential growth of the solution, which leads to an eigenvalue problem for a differential operator connected with spatial coordinates. Here, we describe a system of equations connected with the generation of magnetic field in discs, which are associated with galaxies and binary systems. For an ideal case of an infinitely thin disc, the eigenvalue problem can be precisely solved. If we take into account the finite thickness of the disc, the problem becomes more difficult. The solution can be found using asymptotical methods based on perturbations of the eigenvalues. Here, we present two different models which describe field evolution for different cases. For the first, we find eigenvalues taking into account linear and quadratic terms for the perturbations in the eigenvalue problem. For the second, we find eigenvalues using only linear terms; this is quite sufficient. Results were verified through numerical modeling, and basic computational tests show proper correspondence between different methods. [ABSTRACT FROM AUTHOR]

By making use of the concept of basic (or q-) calculus, a subclass of q-starlike functions with reference to symmetric points, which is associated with the q-exponential function, is introduced in the open unit disc. Further, we derived upper bounds for the third-order Hankel determinant for the defined class. For the validity of our results, relevant connections with those in earlier works are also pointed out. [ABSTRACT FROM AUTHOR]

In this paper the authors combine the quantum calculus applications regarding the theories of differential subordination and superordination with fuzzy theory. These results are established by means of an operator defined as the q -analogue of the multiplier transformation. Interesting fuzzy differential subordination and superordination results are derived by the authors involving the functions belonging to a new class of normalized analytic functions in the open unit disc U which is defined and investigated here by using this q -operator. [ABSTRACT FROM AUTHOR]

In this work, we propose a mathematical model to depict the conversion of groundwater flow from confined to unconfined aquifers. The conversion problem occurs due to the heavy pumping of confined aquifers over time, which later leads to the depletion of an aquifer system. The phenomenon is an interesting one, hence several models have been developed and used to capture the process. However, one can point out that the model has limitations of its own, as it cannot capture the effect of fractures that exist in the aquitard. Therefore, we suggest a mathematical model where the classical differential operator that is based on the rate of change is substituted by a non-conventional one including the differential operator that can represent processes following the power law to capture the memory effect. Moreover, we revise the properties of the aquitard to evaluate and capture the behaviors of flow during the process in a different aquitard setting. Numerical analysis was performed on the new mathematical models and numerical solutions were obtained, as well as simulations for various fractional order values.

Solutions to problems arising from much scientific and applied research conducted at the world level lead to integral and differential equations. They are approximately solved, mainly using quadrature, cubature, and difference formulas. Therefore, in the current work, we consider a discrete analogue of the differential operator 1−12π2d2dx2m in the Hilbert space H2μR, called Dmβ. We modify the Sobolev algorithm to construct optimal quadrature formulas using a discrete operator. We provide a weighted optimal quadrature formula, using this algorithm for the case where m=1. Finally, we construct an optimal quadrature formula in the Hilbert space H2μR for the weight functions px=1 and px=e2πiωx when m=1.

In this paper we introduce the Ruscheweyh-Bernardi differential-integral operator Tm : A → A defined by Tm [f](z) = (1 - λ) Rm [f](z) + λBm [f] (z), z ∈ U, where Rm is the Ruscheweyh differential operator (Definition 1.3) and Bm is the Bernardi integral operator (Definition 1.1). By using the operator Tm, the class of univalent functions denoted by Tm (λ, β), 0 ≤ λ ≤ 1, 0 ≤ β < 1, is defined and several differential subordinations are studied. [ABSTRACT FROM AUTHOR]

Zadeh's fuzzy set theory offers a logical, adaptable solution to the challenge of defining, assessing and contrasting various sustainability scenarios. The results presented in this paper use the fuzzy set concept embedded into the theories of differential subordination and superordination established and developed in geometric function theory. As an extension of the classical concept of differential subordination, fuzzy differential subordination was first introduced in geometric function theory in 2011. In order to generalize the idea of fuzzy differential superordination, the dual notion of fuzzy differential superordination was developed later, in 2017. The two dual concepts are applied in this article making use of the previously introduced operator defined as the convolution product of the generalized Sălgean operator and the Ruscheweyh derivative. Using this operator, a new subclass of functions, normalized analytic in U, is defined and investigated. It is proved that this class is convex, and new fuzzy differential subordinations are established by applying known lemmas and using the functions from the new class and the aforementioned operator. When possible, the fuzzy best dominants are also indicated for the fuzzy differential subordinations. Furthermore, dual results involving the theory of fuzzy differential superordinations and the convolution operator are established for which the best subordinants are also given. Certain corollaries obtained by using particular convex functions as fuzzy best dominants or fuzzy best subordinants in the proved theorems and the numerous examples constructed both for the fuzzy differential subordinations and for the fuzzy differential superordinations prove the applicability of the new theoretical results presented in this study. [ABSTRACT FROM AUTHOR]

In this paper, the author combines the geometric theory of analytic function regarding differential superordination and subordination with fuzzy theory for the convolution product of Ruscheweyh derivative and multiplier transformation. Interesting fuzzy inequalities are obtained by the author. [ABSTRACT FROM AUTHOR]

Motivated by the pivotal role played by linear operators, many years ago Rota proposed to determine algebraic operator identities satisfied by linear operators on associative algebras, later called Rota's Program on Algebraic Operators. Recent progresses on this program have been achieved in the contexts of operated algebra, rewriting systems and Gröbner-Shirshov bases. These developments also suggest that Rota's insight can be applied to determine operator identities on Lie algebras, and thus to put the various linear operators on Lie algebras in a uniform perspective. This paper carries out this approach, utilizing operated polynomial Lie algebras spanned by nonassociative Lyndon-Shirshov bracketed words. The Lie algebra analog of Rota's program is formulated in terms convergent rewriting systems and equivalently in terms of Gröbner-Shirshov bases. The relation of this Lie algebra analog of Rota's program with Rota's program for associative algebras is established. Applications are given to modified Rota-Baxter operators, differential type operators and Rota-Baxter type operators. [ABSTRACT FROM AUTHOR]

On a uniform grid of nodes on the semiaxis , a generalization is considered of Yu. N. Subbotin's problem of local extremal functional interpolation of numerical sequences that have bounded generalized finite differences corresponding to a linear differential operator of order and whose first terms , are predefined. Here it is required to find an times differentiable function such that which has the least norm of the operator in the space . For linear differential operators with constant coefficients for which all roots of the characteristic polynomial are real and pairwise distinct, it is proved that this least norm is finite only in the case of . [ABSTRACT FROM AUTHOR]

The results obtained by the authors in the present article refer to quantum calculus applications regarding the theories of strong differential subordination and superordination. The q-analogue of the multiplier transformation is extended, in order to be applied on the specific classes of functions involved in strong differential subordination and superordination theories. Using this extended q-analogue of the multiplier transformation, a new class of analytic normalized functions is introduced and investigated. The convexity of the set of functions belonging to this class is proven and the symmetry properties derive from this characteristic of the class. Additionally, due to the convexity of the functions contained in this class, interesting strong differential subordination results are proven using the extended q-analogue of the multiplier transformation. Furthermore, strong differential superordination theory is applied to the extended q-analogue of the multiplier transformation for obtaining strong differential superordinations for which the best subordinants are provided. [ABSTRACT FROM AUTHOR]

In the present paper, we study a new subclasses of harmonic univalent functions by using differential operator in the unit disc U = {z 2 C: |z| < 1}. Also we obtain the coefficient bounds, convex combination, extreme points and convolution conditions. [ABSTRACT FROM AUTHOR]

The results obtained by the authors in the present paper refer to quantum calculus applications regarding the theories of differential subordination and superordination. These results are established by means of an operator defined as the q-analogue of the multiplier transformation. Interesting differential subordination and superordination results are derived by the authors involving the functions belonging to a new class of normalized analytic functions in the open unit disc U, which is defined and investigated here by using this q-operator. [ABSTRACT FROM AUTHOR]

In this paper, we consider the continuity of the band functions and Bloch functions of the differential operators generated by the differential expressions with periodic matrix coefficients. [ABSTRACT FROM AUTHOR]

The symmetric Schur process has many different types of formals, such as the functional differential, functional integral, and special functional processes based on special functions. In this effort, the normalized symmetric Schur process (NSSP) is defined and then used to determine the geometric and symmetric interpretations of mathematical expressions in a complex symmetric domain (the open unit disk). To obtain more symmetric properties involving NSSP, we consider a symmetric differential operator. The outcome is a symmetric convoluted operator. Geometrically, studies are presented for the suggested operator. Our method is based on the theory of differential subordination. [ABSTRACT FROM AUTHOR]

Beam models are widely applied in civil engineering, transport, and industry because the beams are basic structural elements. When dealing with the high-order modes of beam in the context of applying the modal analysis method, the numerical instability issue affects the numeric simulation accuracy in many boundary conditions. There are two solutions in literature to overcome this shortcoming, namely refinement of the asymptotic form for the high order modes and reshaping the terms within the equation of the modes to eliminate the source of the numerical instability. In this paper, the numerical instability issue is signalled when the standard form of Green's function, which includes hyperbolic functions, is applied to a free-free Timoshenko length-long beam. A new way is proposed based on new set of eigenfunctions, including an exponential function, to construct a new form of Green's function. To this end, it starts from a new general form of Green's function and the characteristic equation is obtained; then, based on the boundary condition, the Green's function associated to the differential operator of the free-free Timoshenko beam is distilled. The numerical stability of the new form of the Green's function is verified in a numerical application and the results are compared with those obtained by using the standard form of the Green's function. [ABSTRACT FROM AUTHOR]

We present an innovative piecewise smooth mapping of the plane as a parametric discrete-time chaotic system that has robust chaos over a share of its significant organization parameters and includes the generalized Henon and Lozi schemes as two excesses and other arrangements as an evolution in between. To obtain the fractal Henon and Lozi system, the generalized Henon and Lozi system is defined by adopting the fractal idea (FHLS). The recommended system's dynamical performances are investigated from many angles, such as global stability in terms of the set of fixed points.