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From the perspective of large-scale system, a directed complex dynamic network (DCDN) may be considered as a coupling system of the node subsystem (NS) and the link subsystem (LS). In this paper, by using the outgoing link vector and incoming link vector for DCDN, the dynamics of LS is described by employing the vector differential equation instead of the matrix differential equation. Since the outgoing and incoming link vectors have the stronger geometric intuition, the results in this paper show that this kind model of links can not only reflect the direction of links but also find the dynamic tracking goal of links more easily when the state synchronization of NS emerges. Furthermore, by employing the simple mathematical conditions, the nonlinear controller of NS and the coupling term of LS are proposed to ensure achieving the asymptotical state synchronization for DCDN. Finally, the numerical simulations are given to demonstrate the validity of the results in this paper. [ABSTRACT FROM AUTHOR]

This paper is concerned with the issue of fixed-time (FT) and preassigned-time (PT) synchronization of impulsive complex networks (ICNs) with mismatched parameters. Firstly, several more succinct conditions are established to achieve FT stability of impulsive systems and an improved estimation for the stable time is given. Subsequently, based on the improved FT stability results, the FT synchronization criteria for ICNs with mismatched parameters are proposed by designing fixed-time controllers without the linear part. Correspondingly, the PT synchronization problem is also considered by developing several innovative control protocols, where the synchronized time can be arbitrary predefined according to task demands and the control gains are bounded. Ultimately, the presented synchronization criteria are verified by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper deals with global exponential stabilization (GES) and exponential lag synchronization (ELS) for impulsive complex-valued inertial neural networks (ICVINNs) with proportional delays, without employing the standard order-reduction transformation and the general separation approach of the real and imaginary part of the ICVINNs. Several algebraic criteria involving multi-parameters for examining the GES and ELS of the ICVINNs are built, via establishing an appropriate Lyapunov functional, and utilizing inequality techniques, which can be achieved by the novel design of the adaptive controller. Numerical simulations are shown to sustain the availability and efficiency of the proposed criteria. [ABSTRACT FROM AUTHOR]

In this paper, without dividing the fractional-order complex-valued coupled neural networks (FCVCNNs) into two real-valued systems, the problem of synchronization is investigated for FCVCNNs with time-varying coupling strength. To achieve synchronization, by updating coupling strength, two feasible adaptive protocols are designed, 1) a fractional-order adaptive strategy depending on global information; 2) a fractional-order adaptive law relying on the local information based on the connected dominating set theory. Additionally, instead of making the weighted average technique or the solution of the isolated node equation as synchronization reference value, direct error method is adopted to realize synchronization, which offers a flexible way in analysis of FCVCNNs. At last, a numerical simulation is provided to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

This paper discusses the finite-time synchronization of memristor-based Cohen–Grossberg neural networks with time-varying delays. By using nonlinear transformation, an equivalent system is obtained from the discussed neural network. By investigating the finite-time synchronization of the alternative system, some finite-time synchronization criteria of the considered memristor-based Cohen–Grossberg neural network can be obtained. In the whole process, the error state | e (t)| are divided into two procedures: | e (t)| moving from initial value to 1, next, | e (t)| from 1 to 0. Especially, the error state variables e (t) move to 1 in a finite time, and move to 0 in a fixed time. Compared to the classical Lyapunov asymptotic convergence, the finite-time convergence of this paper is a new way to study the synchronization problems. Finally, numerical simulations are presented to display the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the globally exponential synchronization (GES) of a class of complex dynamical networks (CDNs) with switching topology involving impulse action. A novel state-dependent switching (SDS) approach to tune the switching topology of CDNs is designed based on the information of the node dynamics with impulses. Different from the traditional SDS results which are based on continuous state space, some sufficient conditions for network synchronization based on SDS are proposed in the framework of impulse action. A relationship between impulse action, the network structure, and switching topology is established, which is crucial to design the SDS law. Two different impulse actions on the network dynamics are fully considered in this paper, namely, stabilizing continuous dynamics with desynchronizing impulses and destabilizing continuous dynamics with synchronizing impulses. Finally, two numerical simulations are given to demonstrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper respectively discusses the passivity of fractional-order coupled neural networks with multiple state couplings (FOCNNMSCs) or multiple derivative couplings (FOCNNMDCs). In light of fractional-order system theory, several sufficient conditions for ensuring the passivity of the FOCNNMSCs are established. Moreover, a synchronization criterion for the FOCNNMSCs is obtained under the condition that the FOCNNMSCs is output-strictly passive. Similarly, we also investigate the passivity of the FOCNNMDCs by resorting to the Lyapunov functional method, and the output-strict passivity is used to deal with the synchronization for the FOCNNMDCs. Finally, the effectiveness of the obtained criteria is verified by two numerical examples with simulations. [ABSTRACT FROM AUTHOR]

Bipartite networks, which comprise two classes of nonoverlapping nodes with links existing only between nodes in different classes, are natural models for many practical systems. Currently, most researches on network synchronization have been focusing on unipartite networks, and relatively few works have been done on bipartite networks. This paper aims to investigate the impulsive pinning control problem for synchronization of directed delayed bipartite networks with node delays and hybrid coupling. By using the methods of average impulsive interval and mathematical induction, some sufficient conditions ensuring global exponential synchronization of the addressed networks are derived. Here, a more flexible impulsive pinning scheme is proposed, which allows the set of pinned nodes as well as the corresponding number of pinned nodes to be different at distinct impulsive instants. Furthermore, an index called impulse pinned proportion is introduced, and the lower bound of impulse pinned proportions is determined, based on which a simple guide to picking what kind of nodes as pinned candidates is given. Some numerical simulations are finally presented to verify the correctness of the derived theoretical results. [ABSTRACT FROM AUTHOR]

• A duplex network model with different intralayer coupling delay and interlayer transmission delay has been constructed. • The intralayer network topologies are independent each other, and the nodal dynamics in different layers are different as well. • A few pinning impulsive strategies guaranteeing interlayer synchronization are obtained. • The relatively small intralayer coupling delay and interlayer transmission delay can enlarge the stable region. This paper mainly focuses on interlayer synchronization in a duplex network setting with the intralayer coupling delay and the interlayer transmission delay via pinning impulsive control. Firstly, based on Lyapunov stability theory, a general pinning impulsive strategy guaranteeing interlayer synchronization is obtained. Then, the minimum number of pinned nodes and the maximum impulse interval needed theoretically for interlayer synchronization are obtained. Moreover, when some parameters, including the impulse strengths, the ratio of pinned nodes and the impulse interval, are fixed certain values, their influences on the stable region are further discussed. It is found that the stable region becomes smaller as the ratio of pinned nodes decreases, and gets larger as the impulse strength with no delay is closer to −1 and that with delay is closer to 0. At the same time, the small intralayer coupling delay and interlayer transmission delay can enlarge the stable region. Finally, numerical simulations are provided to verify the effectiveness and correctness of our results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of synchronization for a class of fractional-order delayed spatio-temporal neural networks with Dirichlet boundary conditions is investigated. Firstly, based on the L'Hopital law, a Caputo fractional partial differential inequality with p -norm is established to improve the previous results. Besides, a generalized fractional-order Halanay inequality is introduced by rigorous theoretical deduction. Additionally, to realize synchronization, two different control schemes are designed for the networks, respectively, and several criteria are derived based on the developed fractional inequalities. Finally, numerical examples and simulations are provided to verify the correctness of the results. [ABSTRACT FROM AUTHOR]

In this paper, periodic dynamics and periodic synchronization of a class of delayed neural networks with discontinuous neuron activations and impulsive perturbations are investigated. Firstly, based on Filippov's functional differential inclusion and impulsive differential inclusions theory, the existence of solutions of the considered neural network system is studied. Secondly, according to Krasnoselskii's fixed point theorem on cones of set-valued analysis, sufficient conditions are provided for the existence of at least one periodic solution and at least two periodic solutions for the neural network systems. Furthermore, we also use Kakutani's fixed point theorem to give sufficient criteria for the existence of at least one periodic solution of the neural network systems. These results shown that there are still one or more periodic solutions for the neural networks with discontinuous activations under the impulsive effects. Moreover, sufficient criteria are given to the exponential periodic synchronization under the switching state-feedback control strategy with or without delay. Finally, two numerical simulation examples are presented to verify the correctness and validity of our main conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we proposed an iterative learning control (ILC) update rule to synchronize an array of non-identical time-varying delayed neural network systems in a repetitive environment. Under the identical initial conditions, we employed a distributed D -type ILC update rule that guaranteed synchronization by choosing the appropriate inner coupling matrix. Besides, to accommodate non-identical initial conditions, we proposed another adaptive ILC update rule that also could synchronize the systems. Two numerical simulations are presented to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronized stationary distribution of stochastic coupled networks with Markovian switching (CNMS) and the exponential synchronization of CNMS. Except for the Lyapunov method, the periodically intermittent control strategy and the technique of graph theory are applied to the study of synchronized stationary distribution and exponential synchronization. Some sufficient conditions to achieve synchronized stationary distribution and exponential synchronization are presented. The results show that the existing domain of synchronized stationary distribution is affected by control rate and the realization of exponential synchronization is also influenced by intensity of control, control rate. In addition, the theoretical results are applied to stochastic coupled oscillators and coupled Chua's circuits with Markovian switching. Finally, two examples with numerical simulations are provided to illustrate the effectiveness of the results developed. [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite time impulsive synchronization problem of fractional order memristive BAM neural networks (MBAMNNs) with switching jumps mismatch. By utilizing the properties of fractional calculus and comparison principle, a novel fractional order result about finite time impulsive stability is obtained. In the light of the double layer structure of fractional order MBAMNNs, two impulsive controllers are designed for the response fractional order MBAMNNs. By combing properties of Gamma functions and some analysis techniques of impulsive interval, several sufficient conditions are given which ensure finite time synchronization of fractional order MBAMNNs, and the upper bound of the setting time for synchronization is estimated, which is related to the fractional order of the system. Finally, numerical simulation is provided to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization problem of the Kuramoto-oscillator network with non-identical oscillators. The fixed-time event-triggered synchronization control strategies are developed for phase agreement and frequency synchronization under both continuous and intermittent communication. With the developed fixed-time controller, the synchronization can be achieved within a pre-defined time for any initial phase of each oscillator. The event-triggered mechanism avoids continuous controller update and data transmission, which significantly saves the computation and communication resources. Furthermore, theoretical analysis shows that the fixed-time convergence can be guaranteed and the Zeno behavior is avoided by the proposed methods. The numerical simulations of each situation also verify the effectiveness of the proposed synchronization control strategies. [ABSTRACT FROM AUTHOR]

In this paper, the impulsive synchronization of fractional order chaotic systems with time-delay is investigated. Based on Lyapunov stability theory and linear matrix inequalities, the impulsive synchronization of same structure and different structure fractional order chaotic systems with time-delay is discussed respectively. Some sufficient conditions for synchronization of the above systems are obtained. Numerical simulation is presented to illustrate the effectiveness of the results obtained in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new fixed-time stability theorem. Numerical simulations show that our upper bound estimate for the settling time is much smaller than those in the existing fixed-time stability theorems. Based on the new fixed-time stability theorem, we investigate the fixed-time synchronization of memristive neural networks (MNNs) by adopting a delay-dependent feedback controller. Numerical simulations are provided to demonstrate the correctness of our theoretical results and the superiority of the new fixed-time stability theorem. [ABSTRACT FROM AUTHOR]

This paper considers the synchronization problem of coupled harmonic oscillators via event- and self-triggered control. In the presence of periodic event detection, an event-detecting algorithm is provided to determine the update times of each controller. Then, two self-triggered synchronization algorithms are designed to further decrease resource consumption. In the considered system, time-invariant delays appear in all edge information channels, and the design of control protocol and triggering conditions is only based on quantized relative state information, termed e dge information. Numerical simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the cluster synchronization problem of complex networks via pinning control. Nodes in the same cluster are governed by the same dynamical function, while the functions for different clusters are different. For the coupling scheme, the effects of the coupling are assumed to be only cooperative, i.e., the coupling matrix is a Metzler matrix with zero row sums, and the connections between the same cluster can be few. For this type of coupling, the main difference of this paper with previous works is that the cluster synchronization is realized by pinning control technique. A simple pinning control strategy is proposed and some sufficient criteria to realize cluster synchronization with both static and adaptive control strength are given. Finally, numerical simulations are presented to verify our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a modified sliding mode control scheme is proposed to realize complete synchronization of a class of three-dimensional fractional-order chaotic systems. By constructing the suitable sliding mode surface with fractional-order derivative, a single-state sliding mode controller is designed to realize the asymptotical stability of synchronization error system. Compared with the existing results, the main results in this paper are more reasonable and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a finite-time lag synchronization of coupled neural networks with time delay is investigated. By means of the Lyapunov stability theory, a feedback controller is designed for achieving lag synchronization between two delayed neural networks systems in finite time. Paper extends some basic results from the area of finite time to time-delay systems. Numerical simulations on coupled Lu neural systems illustrate the effectiveness of the results. [Copyright &y& Elsevier]

This paper aims to study the finite-time synchronization (i.e., synchronization in finite-time sense) of Cohen–Grossberg neural networks with mixed time delays (both time-varying discrete delay and infinite-time distributed delay). By constructing Lyapunov–Krasovskii functional candidates and using inequality techniques, some new sufficient conditions are derived to design the discontinuous state feedback controllers such that the addressed neural networks can be synchronized in a finite settling time, where the upper bounds of the settling time of synchronization are estimated. The effects of unknown or known time-delay are seriously taken into account, respectively, which lead to two different delay-independent discontinuous state feedback controllers. Thus our results can be applied to the finite-time synchronization of neural networks whether the time delay can be measured or not. As some special cases, our results also improve some recent works. Simulation results show the applicability and the advantages of the proposed finite-time controllers. [ABSTRACT FROM AUTHOR]

In this paper, quasi-synchronization is investigated for heterogeneous complex networks. All nodes of complex networks are nonlinear and have different dynamics. When topology is switching and disconnected, some sufficient criteria that guaranteeing the quasi-synchronization of heterogeneous complex networks are obtained based on the theory of sequential connectivity and joint connectivity. Even if the complex networks are heterogeneous, without any external control, and the topology is not connected at any moment, the errors between any pair of nodes will not exceed the upper bound, which is derived by calculating the maximal distance between any pair of nodes. Finally, some numerical simulations are provided to demonstrate the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, two coupled reaction-diffusion neural networks (CRDNNs) with spatial diffusion coupling are studied. In the first one, the single reaction-diffusion neural network (RDNN) is coupled by their current states. The single RDNN is coupled by their current states and delayed states in the second one. Combined with some inequality techniques and Lyapunov functional approach, a synchronization criterion for the first network model is established via adding controllers to the first l nodes. In addition, a sufficient condition is derived to make sure that the considered network can achieve synchronization by designing pinning adaptive feedback controllers. Similarly, the pinning synchronization for the second network model is also considered. Finally, the correctness of the obtained results are confirmed by numerical simulation in two illustrated examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the pinning adaptive synchronization control problem for a class of complex networks of networks. The complex networks of networks under consideration are composed of both leaders' network and followers' networks (also called “subnetworks”), where the leaders' network and subnetworks are regarded as the nodes of the networks of networks, each subnetwork can receive the information from leaders' network, but not the reverse. In order to achieve the synchronization for the networks of networks, pinning control strategy is adopted, and adaptive controllers are designed for the controlled nodes. By utilizing the stability theory of dynamical systems and some analysis techniques such as the Barbalat lemma, several sufficient criteria are obtained to ensure global exponential synchronization for the controlled complex networks of networks. Finally, a numerical simulation example is given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an aperiodically adaptive intermittent control scheme combined with pinning strategy is proposed for outer synchronization between two general complex delayed dynamical networks. Through constructing a novel piecewise auxiliary function, some sufficient conditions for outer synchronization are derived based on the reduction to absurdity and piecewise analytic method. Different from the periodically intermittent pinning control, here the adaptive intermittent pinning control can be aperiodic. Additionally, an effective pinned-node selection scheme is provided to guide what kinds of nodes should be pinned first. Numerical simulations are finally given to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the author investigates the global synchronization problem for linearly coupled neural networks with reaction–diffusion terms and unbounded time delays. The main difference of this paper from previous works in literature is that the time delay can be unbounded and non-differential. Moreover, the pinning control problem of such neural networks is also investigated. Some sufficient criteria for synchronization are given by means of the linear matrix inequality (LMI). Finally, numerical simulations are also given to show the validity of the obtained criteria. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, synchronization control of switched linearly coupled delayed neural networks is investigated by using the Lyapunov functional method, synchronization manifold and linear matrix inequality (LMI) approach. A sufficient condition is derived to ensure the global synchronization of switched linearly coupled complex neural networks, which are controlled by some designed controllers. A globally convergent algorithm involving convex optimization is also presented to construct such controllers effectively. In many cases, it is desirable to control the whole network by changing the connections of some nodes in the complex network, and this paper provides an applicable approach. It is even applicable to the case when the derivative of the time-varying delay takes arbitrary. Finally, some simulations are constructed to justify the theoretical analysis. [Copyright &y& Elsevier]

This paper concerns the problem of global and local finite-time synchronization for a class of memristor-based Cohen–Grossberg neural networks with time-varying delays by designing an appropriate feedback controller. Through a nonlinear transformation, we derive an alternative system from the considered memristor-based Cohen–Grossberg neural networks. Then, by considering the finite-time synchronization of the alternative system, we obtain some novel and effective finite-time synchronization criteria for the considered memristor-based Cohen–Grossberg neural networks. These results generalize and extend some previous known works on conventional Cohen–Grossberg neural networks. Finally, numerical simulations are given to present the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive learning algorithm is proposed for an interval type-2 fuzzy fractional order controller. The use of fractional order controller adds more degrees of freedom which makes it possible to obtain superior performance in comparison with ordinary differential controllers. A fractional order reference model is used to define the desired trajectory of the nonlinear dynamic system. The structure of the system is based on the feedback error learning method. The stability of the adaptation laws is proved using Lyapunov theory. In order to test the efficiency and efficacy of the proposed learning and the control algorithm, the trajectory tracking problem of a magnetic rigid spacecraft is studied. The simulation results show that the proposed control algorithm outperforms the case when ordinary differential fuzzy controller is used. Furthermore, it is shown that it is possible to define a master chaotic system as a reference model and obtain synchronization between the two chaotic systems using the proposed approach. In the simulation part the synchronization between two Duffing–Holmes system is also achieved. In order to show the implementability of the proposed method, it is used to control a real time laboratory setup 2-DOF helicopter. It is shown that the proposed fractional order controller can be implemented in a low cost embedded system and can successfully control a highly nonlinear dynamic system. [ABSTRACT FROM AUTHOR]

This paper studies synchronization problems of complex dynamical network with mixed coupling via impulsive control. The model involves both advanced and delayed arguments, and the problem of the existence of the model is analyzed. Based on the stability theory for impulsive differential equations, an effective impulsive control scheme is proposed to achieve synchronization for complex dynamical networks. Finally, an example with numerical simulations is given to illustrate our results. [ABSTRACT FROM AUTHOR]

This paper explores the complete synchronization of chaotic neural networks with time delays by intermittent control with two switches in a control period. Some sufficient conditions for complete synchronization are derived by using Lyapunov stability theory. Numerical simulations are also presented to show their good agreements with the theoretical analysis. [ABSTRACT FROM AUTHOR]

This paper focuses on the hybrid effects of coupling, time-varying delay, intermittent controller on memristor-based neural networks. Firstly, we constructed an array of linearly coupled memristor-based neural networks with time-varying delay. Secondly, our sufficient conditions, ensuring the stability and synchronization, are dependent on coupling and intermittent control and show coupling and intermittent control on the stability and synchronization of memristor-based neural networks. Finally, numerical simulations were given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the projective synchronization between two delayed networks of different sizes with nonidentical nodes and unknown parameters. The two complex networks are of diverse dynamical nodes, different topological structures and different sizes. Both networks contain unknown parameters and coupling delay. Based on stability theory, the bidirectional coupling control condition is proposed to ensure the realization of projective synchronization between the two delayed networks. During synchronization, the unknown parameters are successful estimated by adaptive updated laws. Furthermore, in numerical simulations, the Small-World network and Scale-Free network based on well-known Lorenz system and Chen system are constructed. The results verified the effectiveness of the proposed synchronization method. [ABSTRACT FROM AUTHOR]

This paper attempts to probe into the calcium oscillation behavior in a biological mathematical model, from which the conditions of complete synchronization are derived based on gap-junction. And thus the ranges of coupling strength g are obtained under the ring coupling and the global one for identical cells. It is observed that bigger synchronization threshold is needed for the ring coupling than the global one. In particular, we point out that the unidentical cells require stronger coupling to make the system reach nearly complete synchronization by means of numeric simulation. [ABSTRACT FROM AUTHOR]

This paper investigates the hybrid synchronization problem of two coupled complex networks with fractional-order dynamical nodes. Based on the fractional-order Lyapunov stability theorem, some sufficient conditions are derived to realize the hybrid synchronization of two coupled fractional-order networks. Under suitable condition, two coupled networks can reach the hybrid synchronization, i.e., the outer synchronization between the drive and response networks, and the inner synchronization in each networks. Numerical simulations demonstrate the effectiveness and feasility of the proposed synchronization protocol. [ABSTRACT FROM AUTHOR]

In the present paper, two kinds of adaptive output synchronization problems for a complex delayed dynamical network with output coupling are investigated, that is, the cases with positive definite output matrix and with semi-positive definite output matrix. For the former, by using adaptive control method, a sufficient condition is obtained to guarantee the output synchronization of the complex dynamical network. In addition, a pinning adaptive output synchronization criterion is also derived for such network model. Then we extend these results to the case when the output matrix is semi-positive definite. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the problem of steering a group of marine surface vehicles along given spatial paths, while holding a desired formation pattern subject to dynamical uncertainty and ocean disturbances induced by unknown wind, waves and ocean currents. The control design is categorized into two envelopes. One is to steer individual marine surface vehicle to track a given spatial path. The other is to synchronize the speed of each vehicle along its path and path variables under the constraints of an underlying communication network in order to holding a desired formation pattern. The key features of the developed controllers are that, first, the neural network adaptive technique allows one to handle the dynamical uncertainty and ocean disturbances, without the need for explicit knowledge of the model; second, the proposed dynamic surface control technique simplifies the controller design by introducing the first-order filters and avoids the calculation of derivatives of virtual control signals. Further, this result is extended to the output feedback case, where a high-gain observer based cooperative path following controller is developed without measuring the velocity of each vehicle. Under the proposed controllers, all signals in the closed-loop system are guaranteed to be uniformly ultimately bounded for both state and output feedback cases. Simulation results validate the performance and robustness improvement of the proposed strategy. [Copyright &y& Elsevier]

Abstract: In this paper, an integral sliding mode control (SMC) approach is presented to investigate the projective synchronization of nonidentical chaotic neural networks with mixed time delays. By considering a proper sliding surface and constructing Lyapunov–Krasovskii functional, as well as using the linear matrix inequality (LMI) technique, a sliding mode controller is designed to achieve the projective synchronization of the different neural networks. Finally, numerical simulations are carried out to illustrate the effectiveness of the main results. [Copyright &y& Elsevier]

Abstract: This paper focuses on the exponential synchronization problem of coupled fuzzy neural networks with disturbances and mixed time-delays. For the network under study, the effects of both random and vague factors are considered. By stochastic analysis techniques, we establish sufficient conditions for the coupled fuzzy neural networks to be exponentially synchronized in the mean square. It is demonstrated that the network synchronizability is largely dependent on the coupling structure of such network. Moreover, the information exchange network needs not to be undirected or strongly connected. Finally, numerical simulations are given to verify the usefulness and effectiveness of our results. [Copyright &y& Elsevier]

Abstract: The synchronization of two Ghostburster neurons under different external electrical stimulations is considered. First, Ghostburster neuron model under external electrical stimulation is introduced. Then, the synchronization of general master-slave chaotic systems is formulated and an adaptive controller based on dynamic compensation is designed to drive the slave neuron to track the behaviors of the master neuron. The construction of synchronization controller is easy to achieve and the exact knowledge of the systems is not necessarily required. Asymptotic synchronization can be achieved by choosing proper controller parameters. Simulation results confirm that the adaptive control approach employed in this paper is valid in the synchronization of two Ghostburster neurons. As a promising synchronization approach, it is expected to realize the synchronization of other neural systems effectively. [Copyright &y& Elsevier]

Abstract: This paper investigates the hybrid synchronization problem of two coupled complex dynamical networks with non-delayed and delayed coupling by the pinning control strategy. Based on the LaSalle invariance principle and linear matrix inequality technique, we obtain some sufficient conditions for the hybrid synchronization by applying the simple linear feedback and adaptive controllers to a part of nodes. Under suitable conditions, two coupled networks can reach the hybrid synchronization, i.e., the outer synchronization between the drive and response networks, and the inner synchronization in each network simultaneously. Numerical simulations show the effectiveness of the proposed synchronization scheme. [Copyright &y& Elsevier]

Abstract: Burst phase response properties of the leach heart interneuron are analyzed in this paper. By numerical simulation, we find some inherent laws for the burst phase response curve (BPRC) of the interneuron. The onto Poincaré return mapping combined with the phase portrait analysis can be used to explain the inherent properties of the BPRC effectively. For understanding the relationship between phase response curve and synchronization, we compare the synchronization properties of the interneuron with the Hindmarsh–Rose (HR) neuron which has the almost opposite shapes of BPRC to that of the interneuron, and find perfect phase synchronization exists in the interneuron model, but cannot be observed in the HR model under excitatory weak synaptic connectivity. [Copyright &y& Elsevier]

Abstract: This paper investigates the problem of lag synchronization for a kind of chaotic neural networks with discrete and distributed delays (mixed delays). The driver system has uncertain parameters and uncertain nonlinear external perturbations, while the response system has channel noises. A simple but all-powerful robust adaptive controller is designed to circumvent the effects of uncertain external perturbations such that the response system synchronize with the driver system. Based on the invariance principle of stochastic differential equations and some suitable Lyapunov functions, several sufficient conditions are developed to solve this problem. Moreover, under certain conditions, parameters of the uncertain master system can be estimated. Numerical simulations are exploited to show the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: A delay-differential equation, modeling a bidirectional associative memory (BAM) neural network with five neurons, is considered. Some results of synchronization and bifurcation are exhibited. By Lyapunov functional methods, some sufficient conditions for the absolute synchronization of the system and global attractivity of the trivial solution are established. This synchronization is independent of the size of time delay. Furthermore, delay-induced synchronized periodic solution is given analytically, as well as necessary and sufficient conditions for the synchronized periodic solution by perturbation-incremental scheme (PIS). The main difference in this paper from previous works in the literatures is that delay-induced synchronization is studied quantitatively. Theoretical results are illustrated with numerical simulations. [Copyright &y& Elsevier]

Abstract: A simulation study has been done to address how the connectivity structure of the brain complex network relates to its dynamics and its behavioral properties. In this study, we intend to find plausible candidates of structural organization for an epileptic network capable of exhibiting its characteristic dynamics/behavior. For this purpose, a network of hippocampus CA3 neuronal population was implemented and evolved structurally with a constrained genetic algorithm (CGA). This optimization technique was favored by maximizing synchronization among excitable neurons, simulating seizure focus. On the other hand it was constrained to conserve some prescribed characteristics by penalizing infeasible structures in search space. Meanwhile some structural and dynamical aspects of the network were investigated to characterize the evolution path as well as the structure/dynamic to which the network ultimately reaches. The results of our simulations show the following: (1) a network with this evolutionary rewiring process is convergent to a synchronized state where seizures can arise. (2) Numerical analysis of the dynamical origin of seizures, calculated in each generation of CGA, indicates a critical point where global synchrony among multiple neuronal clusters may occur. (3) Different graph topologies more or less have similar endings. Indeed, the search for optimal patterns of connectivity in physiological or pathological models of brain activity may shed light on some of issues that must be dealt with in real neuronal systems; e.g. the control of seizures in epileptogenesis. The present paper tries to step forward this aim. [Copyright &y& Elsevier]

Abstract: Under the premise of analysis on the dynamic characteristics of the transmission mechanism among the synapses, this paper has modified the coupling term in the Tass’s stochastic evolution model of neuronal oscillator population, introduced the variable higher-order coupling term. Then, we have performed the numerical simulation on the modified model. The simulation result shows that the variable coupling mechanism can induce the transition between different cluster states of the neuronal oscillator population, without the external stimulation. Another result from the numerical simulation is that, in the transient process between two different synchronization states caused by the variable coupling mechanism, it is allowed to have a full desynchronization state for a period. However, after the period of desynchronization state, the neuronal oscillator population can still reenter a new synchronization state under the action of the coupling term with the order different from initial condition. [ABSTRACT FROM AUTHOR]

Abstract: Biological systems have facility to capture salient object(s) in a given scene, but it is still a difficult task to be accomplished by artificial vision systems. In this paper a visual selection mechanism based on the integrate and fire neural network is proposed. The model not only can discriminate objects in a given visual scene, but also can deliver focus of attention to the salient object. Moreover, it processes a combination of relevant features of an input scene, such as intensity, color, orientation, and the contrast of them. In comparison to other visual selection approaches, this model presents several interesting features. It is able to capture attention of objects in complex forms, including those linearly non-separable. Moreover, computer simulations show that the model produces results similar to those observed in natural vision systems. [Copyright &y& Elsevier]