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1.
Neural Netw ; 170: 506-520, 2024 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-38043371

RESUMO

The objective of this study is to investigate the synchronization criteria under the sampled-data control method for multi-agent systems (MASs) with state quantization and time-varying delay. Currently, a looped Lyapunov-Krasovskii Functional (LKF) has been developed, which integrates information from the sampling interval to ensure that the leader system synchronizes with the follower system, resulting in a specific condition in the form of Linear Matrix Inequalities (LMIs). The LMIs can be easily solved using the LMI Control toolbox in Matlab. Finally, the proposed approach's feasibility and effectiveness are demonstrated through numerical simulations and comparative results.


Assuntos
Redes Neurais de Computação , Fatores de Tempo
2.
Entropy (Basel) ; 25(8)2023 Jul 31.
Artigo em Inglês | MEDLINE | ID: mdl-37628175

RESUMO

The general delay Hopfield neural network is studied. We consider the case of time-varying delay, continuously distributed delays, time-varying coefficients, and a special type of a Riemann-Liouville fractional derivative (GRLFD) with an exponential kernel. The kernels of the fractional integral and the fractional derivative in this paper are Sonine kernels and satisfy the first and the second fundamental theorems in calculus. The presence of delays and GRLFD in the model require a special type of initial condition. The applied GRLFD also requires a special definition of the equilibrium of the model. A constant equilibrium of the model is defined. An inequality for Lyapunov type of convex functions with the applied GRLFD is proved. It is combined with the Razumikhin method to study stability properties of the equilibrium of the model. As a partial case we apply quadratic Lyapunov functions. We prove some comparison results for Lyapunov function connected deeply with the applied GRLFD and use them to obtain exponential bounds of the solutions. These bounds are satisfied for intervals excluding the initial time. Also, the convergence of any solution of the model to the equilibrium at infinity is proved. An example illustrating the importance of our theoretical results is also included.

3.
Entropy (Basel) ; 24(3)2022 Mar 05.
Artigo em Inglês | MEDLINE | ID: mdl-35327883

RESUMO

A model of gene regulatory networks with generalized proportional Caputo fractional derivatives is set up, and stability properties are studied. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are discussed, and also, their application to fractional order systems and the advantage of quadratic functions are pointed out. The equilibrium of the generalized proportional Caputo fractional model and its generalized exponential stability are defined, and sufficient conditions for the generalized exponential stability and asymptotic stability of the equilibrium are obtained. As a special case, the stability of the equilibrium of the Caputo fractional model is discussed. Several examples are provided to illustrate our theoretical results and the influence of the type of fractional derivative on the stability behavior of the equilibrium.

4.
Entropy (Basel) ; 23(7)2021 Jul 08.
Artigo em Inglês | MEDLINE | ID: mdl-34356412

RESUMO

In this work, we establish some integral inequalities involving metrics. Moreover, some applications to partial metric spaces are given. Our results are extension of previous obtained metric inequalities in the discrete case.

5.
Entropy (Basel) ; 23(8)2021 Aug 21.
Artigo em Inglês | MEDLINE | ID: mdl-34441226

RESUMO

This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations.

6.
Entropy (Basel) ; 23(4)2021 Apr 11.
Artigo em Inglês | MEDLINE | ID: mdl-33920402

RESUMO

As an effective tool to unify discrete and continuous analysis, time scale calculus have been widely applied to study dynamic systems in both theoretical and practical aspects. In addition to such a classical role of unification, the dynamic equations on time scales have their own unique features which the difference and differential equations do not possess and these advantages have been highlighted in describing some complicated dynamical behavior in the hybrid time process. In this review article, we conduct a survey of abstract analysis and applied dynamic equations on hybrid time scales, some recent main results and the related developments on hybrid time scales will be reported and the future research related to this research field is discussed. The results presented in this article can be extended and generalized to study both pure mathematical analysis and real applications such as mathematical physics, biological dynamical models and neural networks, etc.

7.
Entropy (Basel) ; 23(2)2021 Jan 20.
Artigo em Inglês | MEDLINE | ID: mdl-33498158

RESUMO

The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation are oscillatory. Our results complement some known results for neutral differential equations. An illustrative example is included.

8.
J Inequal Appl ; 2018(1): 143, 2018.
Artigo em Inglês | MEDLINE | ID: mdl-30137730

RESUMO

We state and prove new generalized Lyapunov-type and Hartman-type inequalities for a conformable boundary value problem of order α∈(1,2] with mixed non-linearities of the form (Tαax)(t)+r1(t)|x(t)|η-1x(t)+r2(t)|x(t)|δ-1x(t)=g(t),t∈(a,b), satisfying the Dirichlet boundary conditions x(a)=x(b)=0 , where r1 , r2 , and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0<η<1<δ<2 . Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative Tαa is replaced by a sequential conformable derivative Tαa∘Tαa , α∈(1/2,1] . The potential functions r1 , r2 as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.

9.
J Inequal Appl ; 2018(1): 179, 2018.
Artigo em Inglês | MEDLINE | ID: mdl-30137907

RESUMO

Some relaxed hybrid iterative schemes for approximating a common element of the sets of zeros of infinite maximal monotone operators and the sets of fixed points of infinite weakly relatively non-expansive mappings in a real Banach space are presented. Under mild assumptions, some strong convergence theorems are proved. Compared to recent work, two new projection sets are constructed, which avoids calculating infinite projection sets for each iterative step. Some inequalities are employed sufficiently to show the convergence of the iterative sequences. A specific example is listed to test the effectiveness of the new iterative schemes, and computational experiments are conducted. From the example, we can see that although we have infinite choices to choose the iterative sequences from an interval, different choice corresponds to different rate of convergence.

10.
J Inequal Appl ; 2018(1): 64, 2018.
Artigo em Inglês | MEDLINE | ID: mdl-29606841

RESUMO

In a real uniformly convex and uniformly smooth Banach space, some new monotone projection iterative algorithms for countable maximal monotone mappings and countable weakly relatively non-expansive mappings are presented. Under mild assumptions, some strong convergence theorems are obtained. Compared to corresponding previous work, a new projection set involves projection instead of generalized projection, which needs calculating a Lyapunov functional. This may reduce the computational labor theoretically. Meanwhile, a new technique for finding the limit of the iterative sequence is employed by examining the relationship between the monotone projection sets and their projections. To check the effectiveness of the new iterative algorithms, a specific iterative formula for a special example is proved and its computational experiment is conducted by codes of Visual Basic Six. Finally, the application of the new algorithms to a minimization problem is exemplified.

11.
J Inequal Appl ; 2018(1): 298, 2018.
Artigo em Inglês | MEDLINE | ID: mdl-30839795

RESUMO

The stability for a class of generalized Minty variational-hemivariational inequalities has been considered in reflexive Banach spaces. We demonstrate the equivalent characterizations of the generalized Minty variational-hemivariational inequality. A stability result is presented for the generalized Minty variational-hemivariational inequality with ( f , J ) -pseudomonotone mapping.

12.
J Inequal Appl ; 2017(1): 227, 2017.
Artigo em Inglês | MEDLINE | ID: mdl-28989255

RESUMO

In a real uniformly convex and p-uniformly smooth Banach space, a modified forward-backward splitting iterative algorithm is presented, where the computational errors and the superposition of perturbed operators are considered. The iterative sequence is proved to be convergent strongly to zero point of the sum of infinite m-accretive mappings and infinite [Formula: see text]-inversely strongly accretive mappings, which is also the unique solution of one kind variational inequalities. Some new proof techniques can be found, especially, a new inequality is employed compared to some of the recent work. Moreover, the applications of the newly obtained iterative algorithm to integro-differential systems and convex minimization problems are exemplified.

13.
J Inequal Appl ; 2017(1): 225, 2017.
Artigo em Inglês | MEDLINE | ID: mdl-28983180

RESUMO

In the present study, we work on the problem of the existence of positive solutions of fractional integral equations by means of measures of noncompactness in association with Darbo's fixed point theorem. To achieve the goal, we first establish new fixed point theorems using a new contractive condition of the measure of noncompactness in Banach spaces. By doing this we generalize Darbo's fixed point theorem along with some recent results of (Aghajani et al. (J. Comput. Appl. Math. 260:67-77, 2014)), (Aghajani et al. (Bull. Belg. Math. Soc. Simon Stevin 20(2):345-358, 2013)), (Arab (Mediterr. J. Math. 13(2):759-773, 2016)), (Banas et al. (Dyn. Syst. Appl. 18:251-264, 2009)), and (Samadi et al. (Abstr. Appl. Anal. 2014:852324, 2014)). We also derive corresponding coupled fixed point results. Finally, we give an illustrative example to verify the effectiveness and applicability of our results.

14.
J Inequal Appl ; 2017(1): 204, 2017.
Artigo em Inglês | MEDLINE | ID: mdl-28932102

RESUMO

In this paper, we consider random multi-normed spaces introduced by Dales and Polyakov (Multi-Normed Spaces, 2012). Next, by the fixed point method, we approximate the multiplicatives on these spaces.

15.
J Inequal Appl ; 2017(1): 108, 2017.
Artigo em Inglês | MEDLINE | ID: mdl-28553058

RESUMO

The inequality of Popoviciu, which was improved by Vasic and Stankovic (Math. Balk. 6:281-288, 1976), is generalized by using new identities involving new Green's functions. New generalizations of an improved Popoviciu inequality are obtained by using generalized Montgomery identity along with new Green's functions. As an application, we formulate the monotonicity of linear functionals constructed from the generalized identities, utilizing the recent theory of inequalities for n-convex functions at a point. New upper bounds of Grüss and Ostrowski type are also computed.

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