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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]

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 study addresses the preassigned-time synchronization for complex-valued memristive neural networks with reaction–diffusion terms and Markov parameters. Employing a preassigned-time stable control strategy, two distinct controllers with varying power exponent parameters are designed to ensure that synchronization can be achieved within a predefined time frame. Unlike existing finite/fixed-time results, a priori specification of the settling time is addressed. Furthermore, Green's formula and boundary conditions are efficiently applied to overcome potential symmetry loss. Additionally, the activation function's constraint range is more lenient compared to existing constraints. Finally, the effectiveness of the presented methods are demonstrated through two examples. [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]

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete Mittag–Leffler functions. In order to guarantee the global asymptotic stability, adequate criteria are determined using Lyapunov's direct technique, the Lyapunov approach, and some novel analysis techniques of fractional calculation. Thus, some sufficient conditions are obtained to guarantee the global stability. The validity of the theoretical results are finally shown using numerical examples. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of Mittag-Leffler synchronization of T–S fuzzy fractional-order discrete-time complex-valued molecular models of mRNA and protein in regulatory mechanisms with two kinds of regulation functions, respectively. A novel approach is proposed to effectively deal with the joint effects from leakage delay and time varying delay for the class of T–S fuzzy fractional-order discrete-time complex-valued genetic regulatory networks (FDTCVGRNs). By employing Lyapunov stability method and Caputo fractional difference inequalities, several effective conditions according to algebraic inequality and complex-valued linear matrix inequalities are deduced to guarantee the synchronization of the addressed FDTCVGRNs. Moreover, Mittag-Leffler synchronization problem of the nonlinear regulation function in complex-valued molecular models on the basis of general regulation function and linear threshold one. Compared with existing results in the literature, our results are less conservative than existing ones. Finally, simulation results with two numerical examples are demonstrated, which proves the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the quasi-synchronization and global asymptotic synchronization of memristor-based complex-valued neural networks with time-varying delays are studied respectively. Two suitable controllers are designed to achieve the control objective. To get the corresponding conclusion, the method of vector ordering is employed, which can be used to compare the size of two different complex numbers, as a result, the closed convex hull derived by the complex-valued connections can be derived. Finally, the effectiveness of the proposed method is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete Mittag–Leffler functions. In order to guarantee the global asymptotic stability, adequate criteria are determined using Lyapunov’s direct technique, the Lyapunov approach, and some novel analysis techniques of fractional calculation. Thus, some sufficient conditions are obtained to guarantee the global stability. The validity of the theoretical results are finally shown using numerical examples.

In this paper, without dividing the fractional-order complex-valued coupled neural networks (FCVCNNs) into two real-valued systems, the problem of synchronization is investigated for FCVCNNs with time-varying coupling strength. To achieve synchronization, by updating coupling strength, two feasible adaptive protocols are designed, 1) a fractional-order adaptive strategy depending on global information; 2) a fractional-order adaptive law relying on the local information based on the connected dominating set theory. Additionally, instead of making the weighted average technique or the solution of the isolated node equation as synchronization reference value, direct error method is adopted to realize synchronization, which offers a flexible way in analysis of FCVCNNs. At last, a numerical simulation is provided to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

Finite-time synchronization is concerned for the fractional-order complex-valued fuzzy cellular neural networks (FOCVFCNNs) with leakage delay and time-varying delays. Without using the usual complex-valued system decomposition method, this paper designs the different forms of the controllers by using 2-norm. And we construct the appropriate Lyapunov functional and apply inequality analytical techniques, some new sufficient conditions are obtained to ensure finite-time synchronization of the FOCVFCNNs. The upper bound of setting-time function is obtained. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. [ABSTRACT FROM AUTHOR]

This paper discusses synchronization problem of two delayed stochastic neural networks. By constructing the Lyapunov functions, using stochastic analysis technique, some sufficient conditions guaranteeing the synchronization in mean square for the drive system with the response system have been derived in terms of linear matrix inequalities (LMIs) approach. Moreover, the main feature of this paper lies in that the present results are applicable for the drive system and the response system which all are considered not only in complex-valued domain but also with stochastic noise case. Two numerical examples are given to illustrate the effectiveness and merits of the present results.

This paper is concerned with finite-time and fixed-time synchronization of complex-valued recurrent neural networks with discontinuous activations and time-varying delays. First, by separating the complex-valued recurrent neural networks into real and imaginary parts, we get subsystems with real values covered by the framework of differential inclusions, and novel time-delays feedback controllers are constructed to understand the synchronization problem in finite time and fixed time of error system. Second, by creating Lyapunov functions and applying some differential inequalities, several new criteria are derived to get the synchronization in finite time and fixed time of the studied neural networks. Finally, two numerical examples are presented to justify the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, the fixed-time synchronization of complex-valued memristor-based neural networks with impulsive effects is investigated. We first separate these complex-valued networks into real and imaginary parts, and design the appropriate controllers. Then apply the set-valued map and the differential inclusion theorem to handle the discontinuity problems at the right-hand side of the drive-response systems. By constructing the comparison systems together with the Lyapunov function, we get the fixed-time synchronization conditions. Moreover, the estimate of the settling time is also explicitly obtained. Finally, two examples and their numerical simulations are presented to show the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates exponential synchronization of complex-valued memristor-based delayed neural networks (CVMDNNs). Firstly, the CVMDNNs are divided into two real-valued systems: the real and the imaginary part. These two parts are not isolated, they are interrelated. Secondly, integrating the theory of differential inclusion with the definition of Filippov solution, the interval parameter system is established, and the synchronization problem of CVMDNNs is studied. Thirdly, an innovative quantized intermittent controller is designed that takes full advantage of the networks' transmission capacity and reduces control costs. Moreover, the exponential synchronization sufficient condition of CVMDNNs can be obtained via applying the Lyapunov function technique and quantized intermittent control. Finally, an explanatory illustration is offered to certify the validity of the theoretical outcomes. [ABSTRACT FROM AUTHOR]

This paper is devoted to the global exponential stability (GES) and synchronization control of delayed complex-valued memristive neural networks (CVMNNs). The criterion on the existence, uniqueness and GES of the equilibrium point (EP) for delayed CVMNNs is established by constructing a suitable Lyapunov functional and using the homeomorphism theory as well as linear matrix inequality. Meanwhile, a sampled-data controller is designed to synchronize the master and slave systems under the framework of inequality techniques and Lyapunov method. Finally, two examples are presented to show the validity of the obtained results. [ABSTRACT FROM AUTHOR]

Compared with real-valued complex networks, complex-valued dynamic networks have a wider application space. In addition, considering the existence of time delay and uncertainty in the actual system, the synchronization problem of fractional-order complex-valued dynamic networks with uncertain parameter and coupled delay is studied in this paper. In particular, the uncertain parameter is correlated with time delay. By using fractional derivative inequalities and linear delay fractional order equations, the synchronization of uncertainty complex networks with coupling delay is realized. Sufficient conditions for global asymptotic synchronization are obtained. The obtained synchronization results are applicable to most complex network systems with or without delay. Finally, numerical simulations verify the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

• This is the first time to investigate the master-slave synchronization for complex-valued delayed chaotic Lure systems. • The model and results in this paper are more general which treat real valued chaotic Lure systems as special cases. • A novel LKF is constructed and new sampled-data synchronization criteria of CVCLSs are exported. The master-slave synchronization of a type of the complex-valued chaotic Lur'e systems (CVCLSs) with time delay is addressed for the first time, with decomposing complex-valued dynamic systems into two real-valued systems. The complex-valued state variables are introduced in the chaotic Lur'e systems, which expand the application in image processing and remote operation control, and improve the confidentiality in secure communication. Firstly, on the basis of the Lyapunov principle, a Lyapunov-Krasovkii functional (LKF) is established by using certain novel augmented terms, which can take full advantage of the usable information on the sampled-data and the characteristics of the system. Secondly, in the case of a complex-valued delayed chaotic Lur'e system, a more general synchronization criterion is constructed to expand certain current conclusions in the real domain. What's more, the required gain matrices can be designed according to the solution of the linear matrix inequalities (LMIs). In contrast, the conclusions of this paper are more extensive than some existing studies. At last, the validity of the conclusions of this paper is proved by numerical simulations. [ABSTRACT FROM AUTHOR]