Dynamics and synchronization in a memristor-coupled discrete heterogeneous neuron network considering noise

Research on discrete memristor-based neural networks has received much attention.However,current research mainly focuses on memristor–based discrete homogeneous neuron networks,while memristor-coupled discrete heterogeneous neuron networks are rarely reported.In this study,a new four-stable discrete locally active memristor is proposed and its nonvolatile and locally active properties are verified by its power-off plot and DC V–I diagram.Based on two-dimensional(2D)discrete Izhikevich neuron and 2D discrete Chialvo neuron,a heterogeneous discrete neuron network is constructed by using the proposed discrete memristor as a coupling synapse connecting the two heterogeneous neurons.Considering the coupling strength as the control parameter,chaotic firing,periodic firing,and hyperchaotic firing patterns are revealed.In particular,multiple coexisting firing patterns are observed,which are induced by different initial values of the memristor.Phase synchronization between the two heterogeneous neurons is discussed and it is found that they can achieve perfect synchronous at large coupling strength.Furthermore,the effect of Gaussian white noise on synchronization behaviors is also explored.We demonstrate that the presence of noise not only leads to the transition of firing patterns,but also achieves the phase synchronization between two heterogeneous neurons under low coupling strength.

RL and AHP-Based Multi-Timescale Multi-Clock Source Time Synchronization for Distribution Power Internet of Things

Time synchronization(TS)is crucial for ensuring the secure and reliable functioning of the distribution power Internet of Things(IoT).Multi-clock source time synchronization(MTS)has significant advantages of high reliability and accuracy but still faces challenges such as optimization of the multi-clock source selection and the clock source weight calculation at different timescales,and the coupling of synchronization latency jitter and pulse phase difference.In this paper,the multi-timescale MTS model is conducted,and the reinforcement learning(RL)and analytic hierarchy process(AHP)-based multi-timescale MTS algorithm is designed to improve the weighted summation of synchronization latency jitter standard deviation and average pulse phase difference.Specifically,the multi-clock source selection is optimized based on Softmax in the large timescale,and the clock source weight calculation is optimized based on lower confidence bound-assisted AHP in the small timescale.Simulation shows that the proposed algorithm can effectively reduce time synchronization delay standard deviation and average pulse phase difference.

General Decay Synchronization of Competitive Fuzzy Neural Networks Involving Time Delays and Right-Hand Discontinuous Activation

This paper discusses the general decay synchronization problem for a class of fuzzy competitive neural networks with time-varying delays and discontinuous activation functions. Firstly, based on the concept of Filippov solutions for right-hand discontinuous systems, some sufficient conditions for general decay synchronization of the considered system are obtained via designing a nonlinear feedback controller and applying discontinuous differential equation theory, Lyapunov functional methods and some inequality techniques. Finally, one numerical example is given to verify the effectiveness of the proposed theoretical results. The general decay synchronization considered in this article can better estimate the convergence rate of the system, and the exponential synchronization and polynomial synchronization can be seen as its special cases.

Improved results on synchronization in arrays of coupled delayed neural networks with hybrid coupling

In order to investigate the influence of hybrid coupling on the synchronization of delayed neural networks, by choosing an improved delay-dependent Lyapunov-Krasovskii functional, one less conservative asymptotical criterion based on linear matrix inequality （LMI） is established. The Kronecker product and convex combination techniques are employed. Also the bounds of time-varying delays and delay derivatives are fully considered. By adjusting the inner coupling matrix parameters and using the Matlab LMI toolbox, the design and applications of addressed coupled networks can be realized. Finally, the efficiency and applicability of the proposed results are illustrated by a numerical example with simulations.

A step to the decentralized real-time timekeeping network

The composite time scale(CTS) provides an accurate and stable time-frequency reference for modern science and technology. Conventional CTS always features a centralized network topology, which means that the CTS is accompanied by a local master clock. This largely restricts the stability and reliability of the CTS. We simulate the restriction and analyze the influence of the master clock on the CTS. It proves that the CTS's long-term stability is also positively related to that of the master clock, until the region dominated by the frequency drift of the H-maser(averaging time longer than ~10~5s).Aiming at this restriction, a real-time clock network is utilized. Based on the network, a real-time CTS referenced by a stable remote master clock is achieved. The experiment comparing two real-time CTSs referenced by a local and a remote master clock respectively reveals that under open-loop steering, the stability of the CTS is improved by referencing to a remote and more stable master clock instead of a local and less stable master clock. In this way, with the help of the proposed scheme, the CTS can be referenced to the most stable master clock within the network in real time, no matter whether it is local or remote, making democratic polycentric timekeeping possible.

Generalized chaos synchronization of a weighted complex network with different nodes

This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, RSssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.

Synchronization and Control of Halo-Chaos in Beam Transport Network with Small World Topology

The synchronous conditions of two kinds of the small-world （SW） network are studied. The small world topology can affect on dynamical behaviors of the beam transport network （BTN） largely, if the BTN is constructed with the SW topology, the global linear coupling and special linear feedback can realize the synchronization control of beam halo-chaos as well as periodic state in the BTN with the SW topology, respectively. This important result can provide an effective way for the experimental study and the engineering design of the BTN in the high-current accelerator driven radioactive clean nuclear power systems, and may have potential use in prospective applications for halo-chaos secure communication.

Simsync: A Time Synchronization Simulator for Sensor Networks

Time synchronization is a critical middleware service of wireless sensor networks. Researchers have already proposed some time synchronization algorithms. However, due to the demands for various synchronization precision, existing time synchronization algorithms often need to be adapted. So it is necessary to evaluate these adapted algorithms before use. Software simulation is a valid and quick way to do it. In this paper, we present a time synchronization simulator, Simsync, for wireless sensor networks. We decompose the packet delay into 6 delay components and model them separately. The frequency of crystal oscillator is modeled as Gaussian. To testify its effectiveness, we simulate the reference broadcast synchronization algorithm (RBS) and the timing-sync synchronization algorithm (TPSN) on Simsync. Simulated results are also presented and analyzed.

Complete and phase synchronization in a heterogeneous small-world neuronal network

Synchronous firing of neurons is thought to be important for information communication in neuronal networks. This paper investigates the complete and phase synchronization in a heterogeneous small-world chaotic Hindmarsh Rose neuronal network. The effects of various network parameters on synchronization behaviour are discussed with some biological explanations. Complete synchronization of small-world neuronal networks is studied theoretically by the master stability function method. It is shown that the coupling strength necessary for complete or phase synchronization decreases with the neuron number, the node degree and the connection density are increased. The effect of heterogeneity of neuronal networks is also considered and it is found that the network heterogeneity has an adverse effect on synchrony.

Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions

This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N＋1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.

ADAPTIVE PINNING SYNCHRONIZATION OF COUPLED NEURAL NETWORKS WITH MIXED DELAYS AND VECTOR-FORM STOCHASTIC PERTURBATIONS

In this article, we consider the global chaotic synchronization of general cou- pled neural networks, in which subsystems have both discrete and distributed delays. Stochastic perturbations between subsystems are also considered. On the basis of two sim- ple adaptive pinning feedback control schemes, Lyapunov functional method, and stochas- tic analysis approach, several sufficient conditions are developed to guarantee global syn- chronization of the coupled neural networks with two kinds of delay couplings, even if only partial states of the nodes are coupled. The outer-coupling matrices may be symmetric or asymmetric. Unlike existing results that an isolate node is introduced as the pinning target, we pin to help the network realizing synchronization without introducing any iso- late node when the network is not synchronized. As a by product, sufficient conditions under which the network realizes synchronization without control are derived. Numerical simulations confirm the effectiveness of the obtained results.

Projective synchronization of a complex network with different fractional order chaos nodes

Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lu system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.

Controlled synchronization of complex network with different kinds of nodes

In this paper, a new dynamical network model is introduced, in which the nodes of the network are different. It is shown that by the designed controllers, the state of the network can exponentially synchronize onto a homogeneous stationary state. Some criteria are derived and some examples are presented. The numerical simulations coincide with theoretical analysis.

Synchronization of complex switched delay dynamical networks with simultaneously diagonalizable coupling matrices

This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.

Synchronization and coherence resonance in chaotic neural networks

Synchronization and coherence of chaotic Morris-Lecar （ML） neural networks have been investigated by numerical methods. The synchronization of the neurons can be enhanced by increasing the number of the shortcuts, even though all neurons are chaotic when uncoupled. Moreover, the coherence of the neurons exhibits a non-monotonic dependence on the density of shortcuts. There is an optimal number of shortcuts at which the neurons＇ motion is most ordered, i.e. the order parameter （the characteristic correlation time） that is introduced to measure the coherence of the neurons has a maximum. These phenomena imply that stochastic shortcuts can tame spatiotemporal chaos. The effects of the coupling strength have also been studied. The value of the optimal number of shortcuts goes down as the coupling strength increases.

Adaptive synchronization of chaos in permanent magnet synchronous motors based on passivity theory

An adaptive synchronization control method is proposed for chaotic permanent magnet synchronous motors based on the property of a passive system. We prove that the controller makes the synchronization error system between the driving and the response systems not only passive but also asymptotically stable. The simulation results show that the proposed method is effective and robust against uncertainties in the systemic parameters.

Successive lag synchronization on dynamical networks with communication delay

In this paper, successive lag synchronization （SLS） on a dynamical network with communication delay is investigated. In order to achieve SLS on the dynamical network with communication delay, we design linear feedback control and adaptive control, respectively. By using the Lyapunov function method, we obtain some sufficient conditions for global stability of SLS. To verify these results, some numerical examples are further presented. This work may find potential applications in consensus of multi-agent systems.

Coherence Resonance and Noise-Induced Synchronization in Hindmarsh-Rose Neural Network with Different Topologies

In this paper, we investigate coherence resonance （CR） and noise-induced synchronization in Hindmarsh- Rose （HR） neural network with three different types of topologies： regular, random, and small-world. It is found that the additive noise can induce CR in HR neural network with different topologies and its coherence is optimized by a proper noise level. It is also found that as coupling strength increases the plateau in the measure of coherence curve becomes broadened and the effects of network topology is more pronounced simultaneously. Moreover, we find that increasing the probability p of the network topology leads to an enhancement of noise-induced synchronization in HR neurons network.

Research on Time Synchronization Method Under Arbitrary Network Delay in Wireless Sensor Networks

To cope with the arbitrariness of the network delays,a novel method,referred to as the composite particle filter approach based on variational Bayesian(VB-CPF),is proposed herein to estimate the clock skew and clock offset in wireless sensor networks.VB-CPF is an improvement of the Gaussian mixture kalman particle filter(GMKPF)algorithm.In GMKPF,Expectation-Maximization(EM)algorithm needs to determine the number of mixture components in advance,and it is easy to generate overfitting and underfitting.Variational Bayesian EM(VB-EM)algorithm is introduced in this paper to determine the number of mixture components adaptively according to the observations.Moreover,to solve the problem of data packet loss caused by unreliable links,we propose a robust time synchronization(RTS)method in this paper.RTS establishes an autoregressive model for clock skew,and calculates the clock parameters based on the established autoregressive model in case of packet loss.The final simulation results illustrate that VB-CPF yields much more accurate results relative to GMKPF when the network delays are modeled in terms of an asymmetric Gaussian distribution.Moreover,RTS shows good robustness to the continuous and random dropout of time messages.

Pinning Synchronization Between Two General Fractional Complex Dynamical Networks With External Disturbances

In this paper, the pinning synchronization between two fractional complex dynamical networks with nonlinear coupling, time delays and external disturbances is investigated. A Lyapunov-like theorem for the fractional system with time delays is obtained. A class of novel controllers is designed for the pinning synchronization of fractional complex networks with disturbances. By using this technique, fractional calculus theory and linear matrix inequalities, all nodes of the fractional complex networks reach complete synchronization. In the above framework, the coupling-configuration matrix and the innercoupling matrix are not necessarily symmetric. All involved numerical simulations verify the effectiveness of the proposed scheme. © 2017 Chinese Association of Automation.