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It is well known that weighted sum of node states plays an essential role in function implementation of neural networks. Therefore, this paper proposes a new weighted sum synchronization model for memristive neural networks. Unlike the existing synchronization models of memristive neural networks which control each network node to reach synchronization, the proposed model treats the networks as dynamic entireties by weighted sum of node states and makes the entireties instead of each node reach expected synchronization. In this paper, weighted sum complete synchronization and quasi-synchronization are both investigated by designing feedback controller and aperiodically intermittent controller, respectively. Meanwhile, a flexible control scheme is designed for the proposed model by utilizing some switching parameters and can improve anti-interference ability of control system. By applying Lyapunov method and some differential inequalities, some effective criteria are derived to ensure the synchronizations of memristive neural networks. Moreover, the error level of the quasi-synchronization is given. Finally, numerical simulation examples are used to certify the effectiveness of the derived results.

In this paper, we focus on synchronization issue of coupled multistable memristive neural networks (CMMNNs) with time delay under multiple stable equilibrium states. First, we build delayed CMMNNs consisting of one master subnetwork without controller and N−1 identical slave subnetworks with controllers, and every subnetwork has n nodes. Moreover, this paper investigates multistability of delayed CMMNNs with continuous nonmonotonic piecewise linear activation function (PLAF) owning 2 r + 2 corner points. By using the theorems of differential inclusion and fixed point, sufficient conditions are derived such that master subnetwork of CMMNNs can acquire ( r + 2 ) n exponentially stable equilibrium points, stable periodic orbits or hybrid stable equilibrium states. Then, this paper proposes hybrid multisynchronization of delayed CMMNNs related with various external inputs under multiple stable equilibrium states for the first time. There exist ( r + 2 ) n hybrid multisynchronization manifolds in CMMNNs with different initial conditions and external inputs. Finally, two numerical simulations are given to illustrate the effectiveness of the obtained results.

This paper investigates the finite-time H∞ sampled-data synchronization problem for a class of dynamical complex networks with Markovian jump and time-varying delays. Based on a modified Lyapunov–Krasovskii function (LKF), which is fully considered the characteristics of sampled-data, a sampled-data controller are obtained. By introducing the free weighting matrices, some novel auxiliary function-based integral inequalities are applied to have less conservative than other existing results. Finally, three examples are given to show the effectiveness and superiority of the proposed methods.

This paper addresses the problem of finite-time synchronization for a class of multi-layer nonlinear coupled complex networks via intermittent feedback control. Firstly, based on finite-time stability theory, some novel criteria are given to guarantee that the error system of drive-response systems is still finite-time stable under an inherently discontinuous controller. Then, by proposing two kinds of intermittent feedback control laws, sufficient conditions of finite-time synchronization of two kinds of multi-layer complex networks are derived, respectively. The time delay between different layers is also taken into consideration. Finally, a numerical example is provided to verify the effectiveness of the proposed methods.

This paper investigated the finite-time H ∞ synchronization control for complex dynamical networks with mixed mode-dependent time delays. The complex dynamical networks system contains the general coupling term and the time-delay coupling term. The state feedback control is designed to ensure that the complex dynamical networks system is finite time H ∞ synchronized. The sufficient conditions are established in the form of linear matrix inequalities by constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and using Kronecker product. In the last, a numerical example is given to demonstrate the effectiveness of proposed approach.

The fast synchronization problem for a class of complex dynamical networks with time varying delay by means of periodically intermittent control is studied. Based on the finite-time stability theory and periodically intermittent control technique, some sufficient synchronization criteria are obtained to guarantee the fast synchronization. Furthermore, the essential condition for guaranteeing periodically intermittent control realized in finite time is given in this paper. Finally, two examples are illustrated to verify the proposed theoretical results. HighlightsFast synchronization between two complex networks is studied.Two types of periodically intermittent controller to guarantee the finite-time synchronization are obtained.A necessary condition of fast synchronization for periodically intermittent control is given.Numerical simulations are given to show the effectiveness of theoretical results.

In this paper, we investigate the global synchronization problem for a class of nonlinearly-coupled complex networks (NCCNs) with mixed time-varying delays by using an M-matrix approach. The M-matrix strategy allows many synchronization problems with much relaxed conditions to be considered and can be used to derive sufficient conditions for this new class of NCCNs by pinning control. We also propose an effective way of adapting the coupling strengths of complex networks and give numerical examples to illustrate the effectiveness of our theoretical results. HighlightsThe global synchronization problem for a class of nonlinearly-coupled complex networks (NCCNs) with mixed time-varying delays are investigated.Sufficient conditions are derived for this new class of NCCNs via pinning control by using the M-matrix strategy.An effective way proposed to adapt the coupling strengths of complex networks.Numerical examples are given to illustrate the effectiveness of our theoretical results.

In this paper we present a novel approach to model perceptual grouping based on phase and frequency synchronization in a network of coupled Kuramoto oscillators. Transferring the grouping concept from the Competitive Layer Model (CLM) to a network of Kuramoto oscillators, we preserve the excellent grouping capabilities of the CLM, while dramatically improving the convergence rate, robustness to noise, and computational performance, which is verified in a series of artificial grouping experiments and with real-world data.

The Fast Spiking interneurons are coupled by both inhibitory and electrical synapses and the experimental findings suggest they operate as clockworks affecting the neural information processing. At present, the functional role of the electrical synapses in a network of inhibitory interneurons is not well understood. In this paper, this issue is investigated by using a single compartment biophysical interneuron model of a Fast Spiking cell. In particular, the parameter values leading to the emergence of synchronous regimes in a network model of inhibitory interneurons coupled by chemical and electrical synapses are determined theoretically in the weak-coupling limit. Moreover, the effects on the firing coherence, arising from heterogeneity and noise, are studied by means of numerical simulations, both for a pair of Fast Spiking cells and for larger size networks.