Synchronization in Complex Networks with Multiple Connections

In this paper a class of networks with multiple connections are discussed. The multiple connections include two different types of links between nodes in complex networks. For this new model, we give a simple generating procedure. Furthermore, we investigate dynamical synchronization behavior in a delayed two-layer network, giving corresponding theoretical analysis and numerical examples.     

Pattern Synchronization in a Two-Layer Neuronal Network

Pattern synchronization in a two-layer neuronal network is studied. For a single-layer network of Rulkov map neurons, there are three kinds of patterns induced by noise. Additive noise can induce ordered patterns at some intermediate noise intensities in a resonant way; however, for small and large noise intensities there exist excitable patterns and disordered patterns, respectively. For a neuronal network coupled by two single-layer networks with noise intensity differences between layers, we find that the two-layer network can achieve synchrony as the interlayer coupling strength increases. The synchronous states strongly depend on the interlayer coupling strength and the noise intensity difference between layers.     

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper,by the help of evolutionary algorithm and using Hindmarsh–Rose(HR)neuron model,we investigate the efect of topology structures on synchronization transition between diferent states in coupled neuron cells system.First,we build diferent coupling structure with N cells,and found the efect of synchronized transition contact not only closely with the topology of the system,but also with whether there exist the ring structures in the system.In particular,both the size and the number of rings have greater efects on such transition behavior.Secondly,we introduce synchronization error to qualitative analyze the efect of the topology structure.Furthermore,by fitting the simulation results,we find that with the increment of the neurons number,there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems.Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system.Biological system may gradually acquire such efcient topology structures through the long-term evolution,thus the systems’information process may be optimized by this scheme.     

Effect of Topology Structures on Synchronization Transition in Coupled Neuron Cells System

In this paper, by the help of evolutionary algorithm and using Hindmarsh-Rose (HR) neuron model, we investigate the effect of topology structures on synchronization transition between different states in coupled neuron cells system. First, we build different coupling structure with N cells, and found the effect of synchronized transition contact not only closely with the topology of the system, but also with whether there exist the ring structures in the system. In particular, both the size and the number of rings have greater effects on such transition behavior. Secondly, we introduce synchronization error to qualitative analyze the effect of the topology structure. Furthermore, by fitting the simulation results, we find that with the increment of the neurons number, there always exist the optimization structures which have the minimum number of connecting edges in the coupling systems. Above results show that the topology structures have a very crucial role on synchronization transition in coupled neuron system. Biological system may gradually acquire such efficient topology structures through the long-term evolution, thus the systems' information process may be optimized by this scheme.     

Fixed-Time Outer Synchronization of Complex Networks with Noise Coupling

In this paper,the fixed-time outer synchronization of complex networks with noise coupling is investigated.Based on the theory of fixed-time stability and matrix inequalities,sufficient conditions for fixed-time outer synchronization are established and the estimation of the upper bound of the setting time is obtained.The result shows that the setting time can be adjusted to a desired value regardless of the initial states.Numerical simulations are performed to verify the effectiveness of the theoretical results.The effects of control parameters and the density of controlled nodes on the converging time are studied.     

Transition to complete synchronization via near-synchronization in two coupled chaotic neurons

The synchronization transition in two coupled chaotic Morris-Lecar （ML） neurons with gap junction is studied with the coupling strength increasing. The conditional Lyapunov exponents, along with the synchronization errors are calculated to diagnose synchronization of two coupled chaotic ML neurons. As a result, it is shown that the increase in the coupling strength leads to incoherence, then induces a transition process consisting of three different synchronization states in succession, namely, burst synchronization, near-synchronization and embedded burst synchronization, and achieves complete synchronization of two coupled neurons finally. These sequential transitions to synchronization reveal a new transition route from incoherence to complete synchronization in coupled systems with multi-time scales.     

Synchronization in Triangled Complex Networks

Using a tunable clustering coefficient model without changing the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.     

Synchronization in Oscillator Networks with Nonlinear Coupling

Synchronization in coupled oscillator networks has attracted much attention from many fields of science and engineering. In this paper, it is firstly proved that the oscifiator network with nonlinear coupling is also eventually dissipative under the hypothesis of eventual dissipation of the uncoupled oscillators. And the dynamics of the network is analyzed in its absorbing domain by combining two methods developed recently. Suufficient conditions for synchronization in the oscillator networks with nonlinear coupling are obtained. The two methods are combined effectively and the results embody the respective merits of the two methods. Numerical simulations confirm the validity of the results.     

Synchronization Stability in Weighted Complex Networks with Coupling Delays

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.     

Effects of Correlation between Network Structure and Dynamics of Oscillators on Synchronization Transition in a Kuramoto Model on Scale-Free Networks

A recent study has found an explosive synchronization in a Kurammoto model on scale-free networks when the natural frequencies of oscillators are equal to their degrees. In this work, we introduce a quantity to characterize the correlation between the structural and the dynamical properties and investigate the impacts of the correlation on the synchronization transition in the Kuramoto model on scale-free networks. We find that the synchronization transition may be either a continuous one or a discontinuous one depending on the correlation and that strong correlation always postpones both the transitions from the incoherent state to a synchronous one and the transition from a synchronous state to the incoherent one. We find that the dependence of the synchronization transition on the correlation is also valid for other types of distributions of natural frequency.     

单向耦合神经元网络中螺旋波的自发形成机制

构造一个具有单向耦合的二维神经元网络,引入信息传输熵来描述定向信息传输,采用Hindmarsh-Rose神经元模型研究网络中螺旋波等有序波自发产生的机制.数值模拟表明：适当选取耦合的强度和单向耦合的距离,网络可自发出现螺旋波、行波、靶波和平面波.各种有序波的产生与网络中出现信息间歇定向传输有关,网络出现单或多螺旋波时发生熵共振现象.噪声、抑制性耦合和排斥性耦合诱发螺旋波时网络中也存在信息间歇定向传输.首次发现自维持长平面波,其存在是由于网络存在持续的强信息定向传输.     

New Approach to Cluster Synchronization in Complex Dynamical Networks

In this paper, a distributed control strategy is proposed to make a complex dynamical network achieve cluster synchronization, which means that nodes in the same group achieve the same synchronization state, while nodes in different groups achieve different synchronization states. The local and global stability of the cluster synchronization state are analyzed. Moreover, simulation results verify the effectiveness of the new approach.     

Outer Synchronization of Complex Networks by Impulse

This paper investigates outer synchronization of complex networks, especially, outer complete synchronization and outer anti-synchronization between the driving network and the response network. Employing the impulsive control method which is uncontinuous, simple, efficient, low-cost and easy to implement in practical applications, we obtain some sufficient conditions of outer complete synchronization and outer anti-synchronization between two complex networks. Numerical simulations demonstrate the effectiveness of the proposed impulsive control scheme.     

Adaptive Impulsive Outer Synchronization Between Drive-Response Dynamical Networks

In this paper, outer synchronization between drive-response dynamical networks is investigated. Impulsive control combining with adaptive strategy is adopted to design controllers for achieving the goal. Based on the Lyapunov function method and mathematical analysis technique, a synchronization criterion with respect to the impulsive gains and intervals is analytically derived. From the criterion, the impulsive gains can adjust themselves to proper values when the impulsive intervals and some constants are fixed, and vice versa. Finally, two numerical examples are provided to verify the effectiveness of the derived result.     

Exponential Synchronization of Uncertain Complex Dynamical Networks with Delay Coupling

This paper studies the global exponential synchronization of uncertain complex delayed dynamical networks. The network model considered is general dynamical delay networks with unknown network structure and unknown coupling functions but bounded. Novel delay-dependent linear controllers are designed via the Lyapunov stability theory. Especially, it is shown that the controlled networks are globally exponentially synchronized with a given convergence rate. An example of typical dynamical network of this class, having the Lorenz system at each node, has been used to demonstrate and verify the novel design proposed. And, the numerical simulation results show the effectiveness of proposed synchronization approaches.     

Global Synchronization of Directed Networks with Fast Switching Topologies

Global synchronization of a class of directed dynamical networks with switching topologies is investigated. It is found that if there is a directed spanning tree in the fixed time-average of network topology and the time-average is achieved sufficiently fast, then the network will reach global synchronization for sufficiently large coupling strength.     

Global Synchronization of Directed Networks with Fast Switching Topologies

Global synchronization of a class of directed dynamical networks with switching topologies is investigated. It is found that if there is a directed spanning tree in the fixed time-average of network topology and the time-average is achieved sufficiently fast, then the network will reach global synchronization for sufficiently large coupling strength.     

Finite-Time Generalized Outer Synchronization Between Two Different Complex Networks

This paper investigates the finite-time generalized outer synchronization between two complex dynamical networks with different dynamical behaviors. The two networks can be undirected or directed, and they may also contain isolated nodes and clusters. By using suitable controllers, sufficient conditions for finite-time generalized outer synchronization are derived based on the finite-time stability theory. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the synchronization time is also numerically demonstrated.