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In this work, an adaptive controller, formulated as linear feedback controls plus nonlinear parts, is synthesized to achieve bipartite leader-following synchronization of delayed incommensurate fractional-order memristor-based neural networks (FMNNs), in which follower FMNNs are linearly coupled under a signed digraph. The salient features of this research lie in two aspects: (1) the assumption on time-varying delays is very weak, since it neither requires boundedness of delays nor restricts the differentiation of time delay functions; (2) the adaptive controller contains no delay term, and it is feasible for both bounded and unbounded activation functions. As the preparatory work for stability analysis of the controlled synchronization error system, the ready-made results on delayed incommensurate fractional-order linear positive systems, especially stability condition and comparison principle, are perfected by relaxing premises of time-varying delays. Besides, a group of differential inclusion inequalities are established as a powerful aid in scaling the bipartite synchronization error system. More relevantly, an algebraic synchronization criterion, formulated in terms of coupling strength, inner coupling matrix, Laplacian matrix and FMNN system parameters, is proved with the benefit of vector Lyapunov function and positive system theory. With the controller utilized, linear feedback controls can be exerted merely on partial neurons of some selected FMNNs, which is exemplified by numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, the adaptive finite-time passivity (FTP) and finite-time synchronization (FTS) of coupled fractional-order memristive neural networks with multi-state couplings (CFMNNMCs) are investigated. Firstly, a sufficient condition for guaranteeing the FTP of CFMNNMCs is obtained by developing an edge-based adaptive strategy and a state-feedback controller. Furthermore, a node-based adaptive controller is designed to ensure the FTP of CFMNNMCs. Additionally, with the help of properties of Gamma function and some inequality techniques, the adaptive FTS problem for the considered network model is addressed. Finally, two numerical examples are given to demonstrate the validity of the adaptive FTP and FTS criteria. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problem of pinning synchronization for delayed complex directed networks via generalized intermittent adaptive control strategy is considered. First, a dynamical mode of delayed network is investigated. Second, a generalized intermittent adaptive control strategy which unified the traditional periodic intermittent control and the aperiodic case is introduced. Additionally, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria to ensure the global synchronization of delayed complex networks based on the designed control protocols are obtained. Finally, an example with numerical simulations is provided to demonstrate the validness of the theoretical results proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problem of exponential lag synchronization for a class of neural networks with mixed delays including discrete and distributed delays is investigated via adaptive intermittent control. Based on piecewise analytic method, some sufficient conditions for globally exponential lag synchronization are established through constructing a piecewise continuous auxiliary function. It is noted that both the control periods and the control widths in our adaptive intermittent control strategy are allowed to be nonidentical, which extends the scope of application of periodically intermittent control with fixed both control period and control width employed widely in previous works. Moreover, it is shown that the derived globally exponential lag synchronization criteria are related to the control rates rather than the control periods, which facilitates the choice of the control periods for practical problems. Finally, a numerical example is given to illustrate the correctness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: This Letter investigates cluster synchronization in the adaptive complex dynamical networks with nonidentical nodes by a local control method and a novel adaptive strategy for the coupling strengths of the networks. In this approach, the coupling strength of each node adjusts adaptively only based on the state information of its neighborhood. By means of the proposed scheme, the sufficient conditions for achieving cluster synchronization are derived analytically by utilizing Lyapunov stability theory. It is demonstrated that the synchronization performance is sensitively affected by the control gain, the inner-coupling matrix and the network topological structure. The numerical simulations are performed to verify the effectiveness of the theoretical results. [Copyright &y& Elsevier]