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In this paper, we ponder a kind of discrete-time fractional-order complex-valued fuzzy BAM neural network. Firstly, in order to guarantee the quasi-projective synchronization of the considered networks, an original quantitative control strategy is designed. Next, by virtue of the relevant definitions and properties of the Mittag-Leffler function, we propose a novel discrete-time fractional-order Halanay inequality, which is more efficient for disposing of the discrete-time fractional-order models with time delays. Then, based on the new lemma, fractional-order h-difference theory, and comparison principle, we obtain some easy-to-verify synchronization criteria in terms of algebraic inequalities. Finally, numerical simulations are provided to check the accuracy of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we primarily concentrate on the quasi-projective synchronization of master–slave discrete-time BAM neural networks. Without using the LMI and matrix measure methods, by applying discrete inequalities and the Lyapunov sequences, constructing a discrete inequality group, then solving the inequality group, two novel criteria to guarantee the quasi-projective synchronization are obtained for the considered networks. The controllers designed, the approach, and the results in the paper are fully novel, which advance the development of the study of synchronization of discrete neural networks. [ABSTRACT FROM AUTHOR]

We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings.

We focused on the quasi-projective synchronization (QPS) and finite-time synchronization (FNTS) for a class of fractional-order memristive complex-valued delay neural networks (FOMCVDNNs). Rather than decomposing the complex-valued system into its real and imaginary components, we adopted a more streamlined approach by introducing a lemma associated with the complex-valued sign function. This innovative technique enabled us to design a simpler discontinuous controller. Then, based on the finite-time Lemma, measurable selection theorem, Lyapunov function theory, properties of the Mittag-Leffler function, and the fractional-order Razumikhin theorem, various substantial results were derived using a novel hybrid control scheme. In conclusion, we presented numerical simulations to illustrate the practical effectiveness of our theoretical findings. [ABSTRACT FROM AUTHOR]

This paper examines the issue of almost periodic quasi-projective synchronization of delayed fractional-order quaternion-valued neural networks. First, using a direct method rather than decomposing the fractional quaternion-valued system into four equivalent fractional real-valued systems, using Banach's fixed point theorem, according to the basic properties of fractional calculus and some inequality methods, we obtain that there is a unique almost periodic solution for this class of neural network with some sufficient conditions. Next, by constructing a suitable Lyapunov functional, using the characteristic of the Mittag-Leffler function and the scaling idea of the inequality, the adequate conditions for the quasi-projective synchronization of the established model are derived, and the upper bound of the systematic error is estimated. Finally, further use Matlab is used to carry out two numerical simulations to prove the results of theoretical analysis. [ABSTRACT FROM AUTHOR]

This article analyzes the quasi-projective synchronization (QPS) issues of delayed Caputo-type BAM neural networks in the complex field. In order to facilitate calculation and realize QPS, the non-decomposition method is adopted. Moreover, a novel lemma in the form of algebraic inequality is established based on the Laplace transform, which makes it more convenient to deal with the delay term. Applying the proposed lemma, inequality techniques and Lyapunov method, some criteria of QPS are obtained via the designed different controllers. Meanwhile, the error bound is effectively derived. Eventually, the rationality of the gained criteria is tested by two simulations. [ABSTRACT FROM AUTHOR]

The quasi‐projective synchronization problems for Caputo inertial neural networks (INNs) with delays are analyzed in this article. The considered model is transformed into two subsystems by selecting a suitable variable substitution. To realize synchronization, a novel fractional differential inequality is established, and the new lemma is derived via Laplace transform. Applying the given lemmas and inequality techniques, the synchronization conditions are inferred through different nonlinear feedback controllers. From the derivation of the theorems, it can be seen that the designed controllers are more extensive and efficacious. Furthermore, the error bound is validly estimated, and the validity of obtained theorems is illustrated by the numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a type of discrete-time fractional-order complex-valued fuzzy neural networks. First, based on symbolic functions and complex-valued theory, two new inequalities are established to study synchronization problems of networks. Secondly, two simple and original control strategies including linear feedback controller and adaptive controller which can better reduce the control cost, are designed to guarantee quasi-projective synchronization and Mittag-Leffler synchronization of the considered networks, then sufficient synchronization criteria with simplified algebraic conditions are established on the basis of our established lemmas and some inequality techniques. Finally, numerical simulations are given to check effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper presents new theoretical results on quasi-projective synchronization (Q-PS) and complete synchronization (CS) of one kind of discrete-time fractional-order delayed neural networks (DFDNNs). At first, three new fractional difference inequalities for exploring the upper bound of quasi-synchronization error and adaptive synchronization are established by dint of Laplace transform and properties of discrete Mittag-Leffler function, which vastly expand a number of available results. Furthermore, two controllers are designed including nonlinear controller and adaptive controller. And on the basis of Lyapunov method, the aforementioned inequalities and properties of fractional-order difference operators, some sufficient synchronization criteria of DFDNNs are derived. Because of the above controllers, synchronization criteria in this paper are less conservative. At last, numerical examples are carried out to illustrate the usefulness of theoretical upshots. • The neoteric fractional-order difference inequality is established by Laplace transform and some characters of discrete Mittag–Leffler function. Compare the variable substitution method adopted in Gu et al. (2020), Zhao et al. (2023), Xu et al. (2023), the new difference inequality is more simple to get the error upper bound of quasi-projective synchronization due to the existence of constant. • An original nonlinear state feedback controller is designed to attain Q-PS of DFDNNs. Compared with the linear feedback controller used in Zhao et al. (2023), Xu et al. (2023), it is not difficult to find that the nonlinear controller in this paper degenerates into a linear controller when ω = 0 , so the results in this paper are more general. • Some sufficient synchronization criteria in regard to Q-PS and CS of DFDNNs are yielded by dint of Lyapunov direct method and the proposed difference inequalities. Compared with synchronization criteria in Gu et al. (2020), Li et al. (2021), Zhao et al. (2023), Xu et al. (2023), the establishment of fractional difference inequality in this paper makes the calculation simpler, so synchronization criteria obtained are less conservative. [ABSTRACT FROM AUTHOR]

This paper deals with the problems of quasi‐projective synchronization (QPS) and finite‐time synchronization (FTS) for a kind of delayed fractional‐order BAM neural networks (DFOBAMNNs). In order to reach the goals of synchronization and more accurately gauge of settling time and error level, several fresh quantized controllers are structured to make the utmost of confined communication resources. Then, based on the finite‐time theorem, quantized control strategy, Lyapunov function theory and properties of Mittag–Leffler function as well as inequality analysis techniques, some plentiful criteria are formed to set up a relation between control gains and quantization parameters. In addition, the corresponding error bound of QPS and guages of the settling time on FTS are also given. Finally, a few numerical examples are introduced to validate the effectiveness of the presented control protocols. [ABSTRACT FROM AUTHOR]

This article investigates the quasi-projective synchronization (QPS) of non-identical quaternion-valued neural networks (QVNNs) with time-varying delays and interaction terms. Due to parameter mismatches between the drive and response systems, complete projective synchronization is not possible. As a result, a novel idea, known as QPS, is explored up to a small error bound. The direct method is used to derive several general criteria to achieve QPS. The Lyapunov stability theory is employed to estimate the error bound. The numerical simulation results are presented graphically for various special cases to demonstrate the synchronization of time-varying delayed QVNNs with mismatched parameters and interaction terms, which confirm the efficiency of the presented research results. The second example showcases the application of QVNNs coupled with associative memory to illustrate its efficacy in accurately restoring the original color image patterns. [ABSTRACT FROM AUTHOR]

In this paper, the quasi-projective synchronization of distributed-order recurrent neural networks is investigated. Firstly, based on the definition of the distributed-order derivative and metric space theory, two distributed-order differential inequalities are obtained. Then, by employing the Lyapunov method, Laplace transform, Laplace final value theorem, and some inequality techniques, the quasi-projective synchronization sufficient conditions for distributed-order recurrent neural networks are established in cases of feedback control and hybrid control schemes, respectively. Finally, two numerical examples are given to verify the effectiveness of the theoretical results.

This paper studies quasi-projective synchronization (QPS) and complete synchronization (CS) for a class of fractional-order complex-valued neural networks with time delays by designing suitable controllers. To realize QPS and CS, linear feedback controller and adaptive controller are designed, and a novel fractional-order differential inequality is built by means of Laplace transform and properties of Mittag-Leffler function. By utilizing Lyapunov method, our proposed inequality, fractional-order Razumikhin theorem and some complex analysis techniques, some effective criteria are derived to ensure QPS and CS of the considered networks. Furthermore, the error bound of QPS is obtained. Finally, some numerical results are given to demonstrate the effectiveness of the presented theoretical results. [ABSTRACT FROM AUTHOR]

This article focuses on the quasi-projective synchronization for a class of non-identical memristor-based complex-valued recurrent neural networks (MCVRNNs) with time-varying delays and parameters' mismatched. Here, the quasi-projective synchronization is presented in two ways based on the Halanay inequality and some useful techniques. Some novel sufficient conditions are firstly derived for quasi-projective synchronization criteria of non-identical memristor-based CVRNNs with time-varying delays and parameters' mismatched by using the matrix measure method. And then, by using the Lyapunov-Krasovskii functional, another sufficient stabilization condition for quasi-projective synchronization of the concerned model is presented. Finally, two numerical simulation results are given to demonstrate the usefulness and persistence of the proposed methods under some conditions. [ABSTRACT FROM AUTHOR]

In this paper, without separating the complex-valued neural networks into two real-valued systems, the quasi-projective synchronization of fractional-order complex-valued neural networks is investigated. First, two new fractional-order inequalities are established by using the theory of complex functions, Laplace transform and Mittag-Leffler functions, which generalize traditional inequalities with the first-order derivative in the real domain. Additionally, different from hybrid control schemes given in the previous work concerning the projective synchronization, a simple and linear control strategy is designed in this paper and several criteria are derived to ensure quasi-projective synchronization of the complex-valued neural networks with fractional-order based on the established fractional-order inequalities and the theory of complex functions. Moreover, the error bounds of quasi-projective synchronization are estimated. Especially, some conditions are also presented for the Mittag-Leffler synchronization of the addressed neural networks. Finally, some numerical examples with simulations are provided to show the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the quasi-projective synchronization of distributed-order recurrent neural networks is investigated. Firstly, based on the definition of the distributed-order derivative and metric space theory, two distributed-order differential inequalities are obtained. Then, by employing the Lyapunov method, Laplace transform, Laplace final value theorem, and some inequality techniques, the quasi-projective synchronization sufficient conditions for distributed-order recurrent neural networks are established in cases of feedback control and hybrid control schemes, respectively. Finally, two numerical examples are given to verify the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the quasi-projective synchronization problem of fractional order chaotic systems subject to input saturation. Based on the sector-bounded condition and fractional order Lyapunov theorem, some matrix inequalities based sufficient criteria are derived to guarantee the quasi-projective synchronization between the master system and slave system. Then, an algorithm for estimating the synchronization region is given. Moreover, the quasi-synchronization and quasi-anti-synchronization are also discussed as special cases. Finally, the results of the proposed methodologies are verified through some numerical simulations. • The quasi-projective synchronization criteria have been derived. • The saturation constraint has been taken into account in the control input. • An algorithm has been provided to estimate the stable region. [ABSTRACT FROM AUTHOR]