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This article addresses the exponential bipartite synchronization (EBS) of multilayer signed networks with time-varying coupling (MSNs) under aperiodic intermittent-based adaptive dynamic event-triggered control (AAIDETC). Firstly, to increase the elasticity, a novel AAIDETC strategy is presented, whose superiority is that the control gains and the triggering parameters can vary with the evolution of the considered networks. Meanwhile, concerning the aperiodic intermittent control, a new definition of average control ratio (ACR) is put forward, which is more rigorous compared with the relevant results. Then, by the method of ACR, graph theory and Lyapunov approach, the simpler synchronization criterion is gained, which avoids the topology structure of MSNs. Moreover, the EBS issues of Chua's circuits and neural networks established on MSNs are studied, which are two practical applications of our theoretical results. Finally, corresponding numerical simulations are presented to verify the availability of the obtained results. • A new MSN model with time-varying coupling is proposed. • A novel AAIDETC is developed. • An improved definition of average control ratio is presented. [ABSTRACT FROM AUTHOR]

This article is concerned with fixed-time synchronization and preassigned-time synchronization of Cohen–Grossberg quaternion-valued neural networks with discontinuous activation functions and generalized time-varying delays. Firstly, a dynamic model of Cohen–Grossberg neural networks is introduced in the quaternion field, where the time delay successfully integrates discrete-time delay and proportional delay. Secondly, two types of discontinuous controllers employing the quaternion-valued signum function are designed. Without utilizing the conventional separation technique, by developing a direct analytical approach and using the theory of non-smooth analysis, several adequate criteria are derived to achieve fixed-time synchronization of Cohen–Grossberg neural networks and some more precise convergence times are estimated. To cater to practical requirements, preassigned-time synchronization is also addressed, which shows that the drive-slave networks reach synchronization within a specified time. Finally, two numerical simulations are presented to validate the effectiveness of the designed controllers and criteria. [ABSTRACT FROM AUTHOR]

In this paper, synchronization issue of discrete-time fractional fuzzy neural networks (DFFNNs) with delays is solved via quantized control, and is applied in image encryption. Firstly, a novel fractional-order h -difference inequality which makes Lyapunov method more flexible and practical is strictly proved based on the properties of convex functions and theory of discrete fractional calculus. Secondly, by using compression mapping theorem and mathematical induction, we obtain two sufficient conditions to ensure the existence and uniqueness of solutions for DFFNNs. Whereafter, we design a suitable quantized controller, which not only saves channel resources but also reduces control costs. By utilizing our inequality and some analytical techniques, several conservative synchronization criteria for DFFNNs are acquired. Finally, two examples are arranged to illustrate the validity and practicability of our results. • An important fractional difference inequality is strictly proved, which contributes to constructing more flexible Lyapunov functions in the study of discrete-time fractional systems. • Two sufficient conditions are derived to guarantee the existence and uniqueness of the solution for DFFNN with delay by utilizing the compression mapping and mathematical induction. • Discrete-time fractional Halanay inequality is employed to explore synchronization of DFFNNs for the first time. • Under the quantized controller, some easily verifiable synchronization criteria related to step h are acquired. • Based on synchronization of DFFNNs, an image encryption algorithm is designed, and an example is given to verify the encryption effect of our designed algorithm. [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 is concentrated on the fixed/preassigned-time (FXT/PAT) synchronization of multilayered networks, in which the self-dynamics of nodes are heterogeneous and the synchronized state can be an arbitrary prescribed smooth orbit. Above all, the original network is augmented by involving the synchronized state as a virtual node, it is allowed to remove the topological connectivity limitations and reduce the conservatism of the synchronization conditions. Subsequently, several continuous control protocols have been developed to achieve FXT synchronization and some effective criteria are established by utilizing the theorem of FXT stability. Additionally, the relationship is revealed between the estimation of the synchronized time and the layer parameter. Moreover, the PAT synchronization is investigated for a preassigned synchronized time by proposing two control schemes with finite control gains. Eventually, the developed control designs and criteria are validated by some numerical simulations. • FXT/PT synchronization is considered for multilayer networks with a specified state. • The conservatism on topology and criteria is reduced by augmenting original network. • The relationship is revealed between the synchronized time and the layer parameter. [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]

In this paper, synchronization analysis and parameters identification issues are explored for uncertain delayed fractional-order BAM neural networks. By designing pertinent state feedback control strategies and parameters updated laws, some ample criteria are procured for ensuring the finite-time synchronization and the Mittag-Leffler synchronization of the considered networks via exploiting the Lyapunov function theory, fractional calculus theory and inequality analysis techniques, meanwhile, the settling time of finite-time synchronization is given, which relates to the initial values. Moreover, parameters identification is actualized triumphantly for uncertain or unknown parameters. Finally, numerical examples are provided to show the availability of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates quasi-synchronization (QS) and complete synchronization(CS) for fractional-order fuzzy bidirectional associative memory neural networks. To realize QS and CS, two kinds of novel nonlinear controllers are designed, which are more general and effective compared to the existing results. By using Lyapunov function method, fractional calculation and some inequality techniques, some sufficient synchronization criteria are derived for the considered networks. Moreover, the error level of QS is estimated. Finally, two illustrative examples are presented to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This study addresses the fixed/preset-time bipartite synchronization (FTBS/PTBS) of memristor-based discontinuous multi-layer signed networks via quantized dynamic event-triggered control (ETC). Firstly, a memristor-based neural network model incorporating multi-layer coupling structures, signed networks and discontinuous activations is built. Subsequently, by designing two quantized dynamic ETC strategies without the linear feedback term, the FTBS and PTBS of the considered networks are discussed, and it is proved that Zeno behavior can be ruled out. In contrast to the previous static ETC mechanism, the introduced internal dynamic variable can significantly decrease the triggering times and further save communication resources. Lastly, three numerical examples are offered to verify the correctness and practicability of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this article, we considered the fixed‐time stability (FXT) of a type of discontinuous dynamical system. First, we introduced some new FXT stability results via variable substitutions and using inequality techniques, which are more accurately estimate the upper bound of settling time (ST). Then, based on the established results and using the differential inclusion theory, we investigated the FXT synchronization of a type of general neural networks (NNs) with state‐dependent switching coefficients and discontinuous neuron activation functions via introducing a type of discontinuous controller which is more simple compared to existing results. In addition, the estimated upper bound of ST shown to be independent to the initial values of considered drive‐response networks, and it is much smaller and nearer to the real synchronization time than those given in the previously published works. Lastly, two numerical examples are given to demonstrate the feasibility of our derived theoretical results. We believe that the results of this article can give some new insights for the FXT stabilization and FXT synchronization analysis of state‐dependent switching dynamics with or without discontinuous right‐hand sides. [ABSTRACT FROM AUTHOR]

This article concerns the fixed-time (FET) and prescribed-time (PET) synchronization of quaternion-valued fuzzy BAM neural networks via aperiodic intermittent pinning control. First of all, two improved inequalities for FET and PET stability are proposed to reduce the conservatism of existing results in theoretical analysis. Subsequently, by excluding the control input of the rest interval in previous semi-intermittent design, two novel quaternion-valued aperiodic intermittent pinning controllers are developed. Furthermore, regarding the original quaternion-valued networks as an entirety instead of decomposing it into four real-valued subnetworks, several sufficient criteria that ensure the FET and PET synchronization of quaternion-valued fuzzy BAM neural networks are obtained by means of the improved stability inequalities and the designed controllers. Finally, the validity of the theoretical results is verified by three numerical examples. [ABSTRACT FROM AUTHOR]

This article aims to address the exponential bipartite synchronization (EBS) issue of multilayer signed stochastic coupled neural networks under the fully aperiodic intermittent pinning control (FAIPC) strategy. At first, a network model incorporating stochastic perturbations, multilayer signed graphs and multiple time-varying delays is built. Subsequently, instead of the maximum rest rate condition, by means of the average control rate of aperiodically intermittent control, an improved differential inequality is established to reduce the conservatism of existing results. Furthermore, by employing the presented differential inequality and stochastic analysis technique, some sufficient conditions for ensuring mean square EBS are obtained based on FAIPC with constant control gains and FAIPC with adaptive control gains, respectively. Finally, the availability of the theoretical results is verified by some numerical simulations. [ABSTRACT FROM AUTHOR]

This paper is concerned with the global asymptotic stability and global robust stability of inertial neural networks with proportional delays. First, by using linear matrix inequality and constructing appropriate Lyapunov functional, several sufficient conditions are obtained for the global asymptotic stability of inertial neural networks with proportional delays. Furthermore, the problem of global robust stability of the network under the assumptions that the network parameters are uncertain and bounded is studied. Finally, some simulation examples are presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a class of fuzzy cellular neural networks (FCNNs) with distributed delays and variable coefficients is discussed. By applying the matrix theory and the inequality analysis technique, some sufficient conditions on the existence, global exponential stability and weak global exponential stability of periodic solutions are established. Particularly, differently from some previous works, in this paper we do not require the activation functions in the system are bounded and . [Copyright &y& Elsevier]

Abstract: This Letter studies the Cohen–Grossberg networks dynamical systems with variable coefficients and time-varying delays. By applying the Young inequality technique, Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the boundedness, global exponential stability are established. The results obtained in this Letter extend and generalize the corresponding results existing in previous literature. [Copyright &y& Elsevier]

Abstract: This paper studies the general neural networks dynamical systems with variable coefficients and time-varying delays. By applying the Young inequality technique, Dini derivative and introducing many real parameters, and estimating the upper bound of solutions of the system, a series of new and useful criteria on the boundedness, global exponential stability and the existence and global exponential stability of the periodic solutions are established. Particularly, when the system degenerates into the autonomous case, the new criteria on the existence, uniqueness and global exponential stability of the equilibrium points are obtained. The results obtained in this paper extend and generalize the corresponding results existing in previous literature. [Copyright &y& Elsevier]

This paper is concerned with complete synchronization for discrete-time fractional-order fuzzy neural networks (DFFNNs) with time-varying delays. First, three original equalities and two Caputo σ -difference inequalities are established based on theory of discrete-time fractional Calculus. Next, a novel discrete-time adaptive controller with time-varying delay is designed, by virtue of 1-norm Lyapunov function and newly established lemmas herein as well as inequality techniques and contradiction method, some judgement conditions are derived to guarantee complete synchronization for the explored DFFNNs. Benefitting from discrete-time adaptive control strategy and our analysis method, the conservatism of the derived synchronization criteria is reduced. Ultimately, the effectiveness of our theoretical results and secure communication scheme are demonstrated through two numerical examples. • We establish three original equalities, which enrich theory of discrete-time fractional Calculus. • Two Caputo σ -difference inequalities are introduced and proved herein. The first one is b c ∇ σ μ (f (t) − ϱ) 2 ⩽ 2 (f (t) − ϱ) b c ∇ σ μ f (t) , which can be applied to adaptive control-based asymptotic synchronization of nonlinear systems depicted by Caputo σ -difference equations. The second inequality is b c ∇ σ μ | f (t) | ⩽ s i g n (f (t)) b c ∇ σ μ f (t) , which plays a central role in building the relationship between 1-norm Lyapunov function and Caputo σ -difference of state variable. • A universal theoretical framework analyzing adaptive control-based complete synchronization for DFNNs is developed for the first time. • Our results are more general, which can be extended to DFNNs without fuzzy logic or DFNNs without delay. • A secure communication scheme for DFFNNTDs is proposed based on complete synchronization method. [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]

• The fixed/predefined-time lag synchronization issue of complex-valued BAM neural networks with stochastic effects is studied by utilizing the non-separation approach. • The designed controller does not contain a linear term − λ i e i (t) and is only composed of two nonlinear terms, which reduce the control cost and provide more accurate settling time estimations. • The feasibility of the proposed synchronization scheme is verified by two numerical examples and their MATLAB simulations. • Compared with the previous corresponding works, the complexity of analyzing the fixed/predefined-time synchronization behaviour of original complex-valued master-slave systems is reduced thanks to the simplicity of non-separation method. This paper studies the fixed-time and predefined-time lag synchronization of a class of complex-valued BAM neural networks with random disturbances. Firstly, based on the non-separation method, some basic properties of sign function in complex domain are introduced. Then, two simple complex-valued controllers are designed to achieve the fixed/predefined-time lag synchronization of considered stochastic systems. Compared with the results of existing works, the designed complex-valued controllers do not contain the linear term − λ i e i (t) , which makes the controller more simpler and efficient. Finally, two numerical examples are provided to verify the feasibility of our results through MATLAB simulation. [ABSTRACT FROM AUTHOR]

In this article, the fixed-time (FIT) and preassigned-time (PRT) stability of nonlinear models and the FIT/PRT synchronization of discontinuous delayed fuzzy Cohen–Grossberg neural networks (DFCGNNs) are explored, respectively. Firstly, by means of hyperbolic-cosine function and Gudermannian function, a novel FIT stability theorem is established by utilizing Lyapunov method. Then, based on the developed stability theorem, several new discontinuous control schemes with hyperbolic-cosine function are developed to discuss the FIT synchronization of DFCGNNs. Furthermore, the PRT synchronization is also explored by slightly modifying FIT control schemes, where the synchronization time is predetermined. Eventually, two numerical examples are provided to validate the theoretical research. [ABSTRACT FROM AUTHOR]

This paper is committed to explore synchronization issues for a class of nabla fractional-order fuzzy neural networks with time delays. First, we establish two useful nabla fractional inequalities by feat of the theory of nabla fractional calculus and N -transform together with nabla convolution. Next, we design two distinctive controllers including nonlinear delay feedback controller and hybrid nonlinear delay controller, some easily verified quasi-synchronization (QS) criteria and complete synchronization (CS) criteria are derived by virtue of newly proposed inequalities therein and some inequality techniques. Finally, the correctness of theoretical results is indicated finally through numerical simulations. What is more important, theoretical results therein can offer some new avenues about QS and CS analysis for nabla fractional dynamical networks. [ABSTRACT FROM AUTHOR]

In this paper, under the framework of Filippov solutions, quasi-synchronization issue of fractional-order complex-valued neural networks (FCNNs) with discontinuous activations and uncertainties is investigated. Firstly, using Laplace transform and the property of Mittag-Leffler function, a novel fractional differential inequality is derived. Then combining the newly constructed inequality with delay feedback control scheme, several quasi-synchronization conditions are obtained for the considered FCNNs by means of non-decomposable method. Eventually, a numerical example is provided to substantiate validation of the proposed results. [ABSTRACT FROM AUTHOR]

• Based on quaternion theory, Mittag-Leffler function and nabla h -Laplace transform, two new inequalities are obtained. • In order to realize synchronization more conveniently, we design a quaternion controller with time delay. • Under the direct quaternion framework, quasi-synchronization criteria of DTFQMNNs are obtained by utilizing our lemmas and some analysis techniques. Besides, the error bound for quasi-synchronization is evaluated. In this paper, quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks (DTFQMNNs) with time delays and uncertain parameters is investigated. Firstly, some related preliminaries are introduced and two new inequalities are obtained based on nabla fractional difference, quaternion theory and nabla h -Laplace transform. Then, a quaternion-valued controller with time delay is designed to realize quasi-synchronization goal, and some sufficient criteria are derived to guarantee quasi-synchronization of DTFQMNNs by using our created inequalities and some analysis techniques. Finally, a numerical example is provided to verify the correctness of our theoretical results. [ABSTRACT FROM AUTHOR]