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This paper studies the adaptive fixed-time synchronization issue for convex-delayed neural networks. First, the convex delay is introduced to address the state delay of neural networks in order to reflect the impacts of multiple delay components such as input transition time and switching communication. Then, a new fixed-time control method is presented to adaptively determine multi-control gains with a unified update law. Afterward, some sufficient criteria are figured out by using Lyapunov stability theorem to ensure that the delayed neural networks are fixed-timely stable. Finally, simulated examples are adopted to validate our theoretical results. • The convex delay is introduced to reflect the impacts of multiple delay components. • An adaptive fixed-time control is proposed to uniformly adjust the feedback gains. • Sufficient criteria are derived to ensure the fixed-time stability of neural networks. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of fixed-time cluster lag synchronization for directed heterogeneous community networks (DHCNs), i.e., directed community networks with nonidentical dynamical nodes. Simple state feedback controllers are designed and applied to drive the DHCNs to reach cluster lag synchronization in fixed-time. Through using the Lyapunov stability theory and reduction to absurdity, some sufficient conditions ensuring fixed-time cluster lag synchronization are derived. Moreover, it is theoretically verified that our estimated settling time is more accurate and less conservative in comparison with that given in the existing literature. Finally, the validity of the theoretical analysis is confirmed with numerical simulations. • Fixed-time cluster lag synchronization in directed community networks is analyzed. • A simple state feedback control strategy is proposed. • By reduction to absurdity, some criteria for the synchronization are obtained. • Our estimated settling time is more accurate and less conservative. [ABSTRACT FROM AUTHOR]

In this paper, adaptive exponential synchronization of directed networks with complex-variable systems and distributed delays coupling is investigated. An adaptive nonperiodical intermittent control scheme is adopted to realize exponential synchronization of such complex-variable directed dynamical networks. Based on the complex inequality, piecewise analysis method and Lyapunov stability theory, some sufficient conditions guaranteeing globally exponential synchronization are established. Different from previous works, here the designed adaptive update law for intermittent feedback control gain does not explicitly depend on time, which makes the adaptive nonperiodical intermittent control technique more convenient to implement in realistic applications. Moreover, it is indicated that the established synchronization criteria depend on the control rates rather than the control periods or control widths, and therefore the control periods can be optionally chosen for practical problems. Finally, numerical simulations are given to illustrate the effectiveness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

This paper focuses on the cluster synchronisation problem of coupled complex networks with uncertain disturbances under an adaptive fixed-time control strategy. To begin with, complex dynamical networks with community structure which are subject to uncertain disturbances are taken into account. Then, a novel adaptive control strategy combined with fixed-time techniques is proposed to guarantee the nodes in the communities to desired states in a settling time. In addition, the stability of complex error systems is theoretically proved based on Lyapunov stability theorem. At last, two examples are presented to verify the effectiveness of the proposed adaptive fixed-time control. [ABSTRACT FROM AUTHOR]

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid-coupled dynamical network with time-varying internal delay and time-varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning-control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer-synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned-node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non-fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593-605, 2016 [ABSTRACT FROM AUTHOR]

Fixed-time control allows complex systems to be stable in a settling time independent of initial conditions, which receives extensive attentions in the field of control and engineering. However, the application to complex systems suffers from the issues of chattering effects and multi-parameters. To address these issues, a light fixed-time controller is proposed with a compact formulation by revisiting continuous control paradigm. Sufficient conditions are then obtained by Lyapunov stability theorem to guarantee the nodes in each cluster to desired states in a settling time. At last, numerical examples are given to verify the effectiveness of our proposed control strategy. [ABSTRACT FROM AUTHOR]

The fixed-time stability on uncertain neural networks with adaptive coupling strength is addressed in this paper. To beign with, a new time-varying coupling strength is introduced, which is based on the projective transform of quantized error systems. Next, to address various disturbances in master-slave systems, inhomogeneous uncertainty is taken into consideration. Then, a multi-quantized fixed-time controller is put forward to ensure that the systems reach to a prescribed trajectory in the settling time. Afterward, sufficient synchronization criteria are derived on the strength of the Lyapunov stability theorem. Finally, simulation examples are given to validate the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper is concerned with cluster synchronization in an array of coupled neural networks subject to cyber-attacks, where a random variable is employed to reflect the success ration of the launched cyber-attacks. To save the energy consumption and alleviate the transmission load of the network, a novel adaptive distributed dynamic event-triggered communication scheme is presented based on the local stochastic the state sampling information, compared with some existing results, the different event-triggered matrices and auxiliary variables are introduced for each node to adjust its threshold dynamically, which can further reduce the sampled-data transmission, the proposed event-triggered scheme includes some existing event-triggered schemes as special cases. The cluster synchronization controllers are designed based on the states of neighboring nodes at event-triggered instants, a new stochastic sampled-data dependent error model is constructed, some mean-square cluster synchronization criteria can be derived by the Lyapunov stability theory and algebraic graph theory, and the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the theoretical results. [ABSTRACT FROM AUTHOR]