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This study sets out to solve the synchronization problem of complex-valued multi-layer coupled systems (CVMLCSs) under two asynchronous intermittent event-triggered mechanisms (IETMs). Unlike the existing works on IETM, two kinds of novel IETMs including static IETM and dynamic IETM are developed, where the asynchronous nature is mainly reflected in the fact that each node in each layer possesses its own control and rest intervals. Remarkably, under two control schemes, the choice of control time sequence is based on corresponding event-triggered condition rather than being preset artificially. Moreover, by utilizing graph theory and Lyapunov approach, two synchronization conditions for CVMLCSs are given, respectively. In the end, as an application, a complex-valued multi-layer neural network model is established and some numerical examples are provided to validate the feasibility of the theoretical results. • A new model of time-varying complex-valued multi-layer coupled systems is built. • Two novel asynchronous intermittent event-triggered mechanisms are proposed. • Two controllers remove the limitation on artificial selection of control time sequence. [ABSTRACT FROM AUTHOR]

In this paper, an I2S2R rumor spreading model in complex networks is established and analyzed. Firstly, the threshold value is acquired to identify the existence and stability of rumor-free equilibria state and rumor equilibria state by using the next generation matrix method. Secondly, based on Routh–Hurwitz judgment, Lyapunov stability theory and LaSalle's invariance principle, the local and global stability of rumor-free/rumor equilibrium points are discussed. Thirdly, the sensitivity analysis about the threshold value is given to analyze the impact of model parameters on rumor propagation. Finally, some numerical simulations are presented to illustrate the validity and feasibility of corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, the guaranteed cost consensus problem for second-order multi-agent systems with directed topology is considered, in which each agent has a heterogeneous inertia and control gain. The distributed control protocols with the absolute and relative velocity dampings are proposed, respectively. In each kind of protocol, both the communications with and without the input time delay are also considered. By introducing the auxiliary variables and using Lyapunov stability theory, some sufficient conditions are given to achieve the consensus. Moreover, the upper bounds of the guaranteed cost functions are obtained. Finally, some simulation examples are presented to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper studies the general decay synchronization of a class of bidirectional associative memory neural networks with time-varying delays. First, a useful lemma which generalizes the classical exponential synchronization and polynomial synchronization is introduced. Then by using this lemma, some simple sufficient criteria ensuring the general decay synchronization of considered bidirectional associative memory neural networks are obtained via designing a novel nonlinear feedback controller and using some inequality techniques. Finally, two numerical examples are provided to demonstrate the feasibility of the established theoretical results. The results of this paper are general since the classical polynomial synchronization and exponential synchronization can be seen the special cases of general decay synchronization. [ABSTRACT FROM AUTHOR]

• For describing the influence of higher-order interactions in the rumor propagation, hypergraph theory is introduced in this paper. • The spreading rate in Hyper-SIR model based on higher-order group interactions is related to the size of groups, and the rumor propagation is not just spread by the point-to-point form. Besides, some new properties are founded. • Uniform immunization and targeted immunization strategies are proposed to control rumor propagation process. These strategies have a significant application in rumor spreading model. In this paper, a hyper susceptible-infected-recovered (Hyper-SIR) rumor propagation model is proposed based on hypergraph, which can describe the higher-order information interactions among nodes in the networks. Notably, hyperdegree is substitute for degree to model rumor spreading, and some reasonable results are obtained. Firstly, the threshold of Hyper-SIR rumor propagation model is acquired. Then, the stability of rumor-free/prevailing equilibrium is discussed by employing Lyapunov stability theory and LaSalle's invariance principle. Moreover, uniform immunization and targeted immunization strategies are introduced to control the propagation of rumors. Besides, sensitivity analysis shows the different effects of parameters between Hyper-SIR model and SIR model. Finally, the numerical simulations are displayed and the results show Hyper-SIR model reaches equilibrium faster than general SIR model. [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]

• 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]

• By virtue of integration by parts, Young inequality, and some properties about fractional-order difference, an original power law inequality for fractional-order difference is established. • A neoteric adaptive controller is firstly applied to DFNNs. • Delayed feedback controller is designed to eliminate the impact of time delays on synchronization. • Other than the traditional Lyapunov function with 2-norm form, a more general Lyapunov function based on j-norm is constructed, which expands Lyapunov function with 2-norm considered in [29], [33] and [35]. In this article, the problem of the global Mittag-Leffler synchronization is proposed for a sort of discrete-time fractional-order neural networks (DFNNs) with delays. In the first place, a flesh power law inequality pertaining to fractional difference is constructed by means of integration by parts, Young inequality, and some properties about fractional-order difference. In addition, based on aforesaid inequalities, Lyapunov function theory and properties of nabla Mittag-Leffler function as well as inequality techniques, some plentiful criteria are formed to achieve the global Mittag-Leffler synchronization for the delayed DFNNs via devising novel adaptive controller and delay feedback controller. In the end, numerical modeling is given to demonstrate effectiveness of theoretical verdicts. [ABSTRACT FROM AUTHOR]

Inspired by Lemma 1 in [36], a new fractional differential inequality is derived by means of inequality techniques and reduction to absurdity. • Without the participation of sign function, two kinds of finite-time control strategies are designed. • Non-separation method is first employed to explore the robust F-TS for the uncertain F-OQ-VNNs. • Easily-verified robust F-TS criteria are derived, and settling time is explicitly reckoned. In this paper, robust finite-time synchronization (F-TS) issue is addressed for a class of uncertain fractional-order quaternion-valued neural networks by employing non-separation method instead of separation method. First, a general fractional differential inequality is developed to provide new insight into the research about finite-time stability and synchronization of fractional-order systems. Next, quaternion-valued feedback controller and quaternion-valued adaptive controller are designed. On the basis of the newly developed inequality, quaternion inequality techniques, together with the properties of fractional calculus and reduction to absurdity, some easily-verified algebraic criteria for robust F-TS are established, and the settling time for robust F-TS is explicitly reckoned, which depends on not only the controller parameters but also the initial values and order of the considered systems. Eventually, numerical results are provided to substantiate our robust F-TS criteria. [ABSTRACT FROM AUTHOR]

This paper investigates the global Mittag-Leffler synchronization (GMLS) issue for fractional-order delayed quaternion-valued neural networks, which include leakage delays and transmission delays. First, a new lemma is established to estimate the Caputo fractional derivative for quaternion self-conjugate quadratic Lyapunov function, and a novel quaternion-valued linear feedback controller is designed. Then by utilizing quaternion matrix theory and our proposed lemma, some succinct GMLS criteria are derived respectively in quaternion-valued linear matrix inequality (LMI) form and complex-valued LMI form, which simplify and extend some previous work on the synchronization control for quaternion-value neural networks. Finally, a numerical example is given to validate our theoretical results. [ABSTRACT FROM AUTHOR]