Explosive synchronization transitions in scale-free networks

Explosive collective phenomena have attracted much attention since the discovery of an explosive percolation transition. In this Letter, we demonstrate how an explosive transition shows up in the synchronization of scale-free networks by incorporating a microscopic correlation between the structural and the dynamical properties of the system. The characteristics of the explosive transition are analytically studied in a star graph reproducing the results obtained in synthetic networks. Our findings represent the first abrupt synchronization transition in complex networks and provide a deeper understanding of the microscopic roots of explosive critical phenomena.     

Explosive synchronization of multi-layer complex networks based on inter-layer star network connection

Explosive synchronization (ES) is a first-order transition phenomenon that is ubiquitous in various physical and biological systems. In recent years, researchers have focused on explosive synchronization in a single-layer network, but few in multi-layer networks. This paper proposes a frequency-weighted Kuramoto model in multi-layer complex networks with star connection between layers and analyzes the factors affecting the backward critical coupling strength by both theoretical analysis and numerical validation. Our results show that the backward critical coupling strength of each layer network is influenced by the inter-layer interaction strength and the average degree. The number of network layers, the number of nodes, and the network topology can not directly affect the synchronization of the network. Enhancing the inter-layer interaction strength can prevent the emergence of explosive synchronization and increasing the average degree can promote the generation of explosive synchronization.     

Explosive transitions to synchronization in weighted static scale-free networks

We present a systemical study on the thermodynamic and physical properties of Ti₂CoIn and Ti₂NiIn by using first-principles calculations. Both alloys are found to be half-metallic ferromagnets with a total spin magnetic moment per formula unit of 2.00 and 3.00μ _B . The stability is evaluated from the physical, chemical and mechanical points of view. The Curie temperature is estimated to be 553.16 K for Ti₂CoIn and 1008.59 K for Ti₂NiIn, which is well-above the room temperature. In addition, the half-metallicity of Ti₂CoIn and Ti₂NiIn is retained when the lattice constants are changed by ?12.58% to 6.76% and ?13.08% to 4.36%, respectively. Finally, using a quasiharmonic Debye model which exhibits Ti₂CoIn has a higher thermal stability than Ti₂CoIn within a limited temperature (0–500 K). Thus, the present calculations show that Ti₂CoIn and Ti₂NiIn have a great application potential in the spin valve and magnetic tunnel junction.     

Complex transitions to synchronization in delay-coupled networks of logistic maps

A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a time-dependent state [F.M. Atay, J. Jost, A. Wende, Phys. Rev. Lett. 92, 144101 (2004)], which may be periodic or chaotic depending on the delay; when the delays are sufficiently heterogeneous, the synchronization proceeds to a steady-state, which is unstable for the uncoupled map [C. Masoller, A.C. Marti, Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from time-dependent to steady-state synchronization as the width of the delay distribution increases. We also compare the two transitions to synchronization as the coupling strength increases. We use transition probabilities calculated via symbolic analysis and ordinal patterns. We find that, as the coupling strength increases, before the onset of steady-state synchronization the network splits into two clusters which are in anti-phase relation with each other. On the other hand, with increasing delay heterogeneity, no cluster formation is seen at the onset of steady-state synchronization; however, a rather complex unsynchronized state is detected, revealed by a diversity of transition probabilities in the network nodes.     

Channel noise-induced temporal coherence transitions and synchronization transitions in adaptive neuronal networks with time delay

Using spike-timing-dependent plasticity (STDP), we study the effect of channel noise on temporal coherence and synchronization of adaptive scale-free Hodgkin-Huxley neuronal networks with time delay. It is found that the spiking regularity and spatial synchronization of the neurons intermittently increase and decrease as channel noise intensity is varied, exhibiting transitions of temporal coherence and synchronization. Moreover, this phenomenon depends on time delay, STDP, and network average degree. As time delay increases, the phenomenon is weakened, however, there are optimal STDP and network average degree by which the phenomenon becomes strongest. These results show that channel noise can intermittently enhance the temporal coherence and synchronization of the delayed adaptive neuronal networks. These findings provide a new insight into channel noise for the information processing and transmission in neural systems.     

Finite-time analysis of global projective synchronization on coloured networks

A novel finite-time analysis is given to investigate the global projective synchronization on coloured networks. Some less conservative conditions are derived by utilizing finite-time control techniques and Lyapunov stability theorem. In addition, two illustrative numerical simulations are provided to verify the effectiveness of the proposed theoretical results.     

Delay-induced synchronization transitions in small-world neuronal networks with hybrid electrical and chemical synapses

We study the dependence of synchronization transitions in small-world networks of bursting neurons with hybrid electrical–chemical synapses on the information transmission delay, the probability of electrical synapses, and the rewiring probability. It is shown that, irrespective of the probability of electrical synapses, the information transmission delay can always induce synchronization transitions in small-world neuronal networks, i.e., regions of synchronization and nonsynchronization appear intermittently as the delay increases. In particular, all these transitions to burst synchronization occur approximately at integer multiples of the bursting period of individual neurons. In addition, for larger probability of electrical synapses, the intermittent synchronization transition is more profound, due to the stronger synchronization ability of electrical synapses compared with chemical ones. More importantly, chemical and electrical synapses can perform complementary roles in the synchronization of hybrid small-world neuronal networks: the larger the electrical synapse strength is, the smaller the chemical synapse strength needed to achieve burst synchronization. Furthermore, the small-world topology has a significant effect on the synchronization transition in hybrid neuronal networks. It is found that increasing the rewiring probability can always enhance the synchronization of neuronal activity. The results obtained are instructive for understanding the synchronous behavior of neural systems.     

一类不确定延迟神经网络的自适应投影同步

研究了一类参数不确定的延迟神经网络的投影同步,基于Lyapunov稳定性理论,设计了一种新型的自适应控制方法.该方法能同时实现一类参数不确定延迟神经网络的参数识别和投影同步.数值模拟证明了该方法的有效性. 关键词： 延迟神经网络 Lyapunov稳定性理论 参数识别 投影同步     

Effect of spike-timing-dependent plasticity on coherence resonance and synchronization transitions by time delay in adaptive neuronal networks

In this paper, we numerically study how time delay induces multiple coherence resonance (MCR) and synchronization transitions (ST) in adaptive Hodgkin-Huxley neuronal networks with spike-timing dependent plasticity (STDP). It is found that MCR induced by time delay STDP can be either enhanced or suppressed as the adjusting rate A_p of STDP changes, and ST by time delay varies with the increase of A_p, and there is optimal A_p by which the ST becomes strongest. It is also found that there are optimal network randomness and network size by which ST by time delay becomes strongest, and when A_p increases, the optimal network randomness and optimal network size increase and related ST is enhanced. These results show that STDP can either enhance or suppress MCR and optimal STDP can enhance ST induced by time delay in the adaptive neuronal networks. These findings provide a new insight into STDP’s role for the information processing and transmission in neural systems.     

Noise-induced phase synchronization and synchronization transitions in chaotic oscillators

Whether common noise can induce complete synchronization in chaotic systems has been a topic of great relevance and long-standing controversy. We first clarify the mechanism of this phenomenon and show that the existence of a significant contraction region, where nearby trajectories converge, plays a decisive role. Second, we demonstrate that, more generally, common noise can induce phase synchronization in nonidentical chaotic systems. Such a noise-induced synchronization and synchronization transitions are of special significance for understanding neuron encoding in neurobiology.     

Order parameter analysis of seismicity of the Mexican Pacific coast

The natural time domain has shown to be an important tool to obtain relevant information hidden in time series of complex systems not easily obtainable by means of standard analysis methods. By assuming that tectonism is a complex system and that earthquakes are similar to a phase transition, it is possible to define an order parameter for seismicity in the context of the natural time domain. In this work we analyze the statistical features of the order parameter (OP) computed for the seismic Mexican catalog spanning from 1974 to 2012. We found that in four out of the six regions the pdf of the order parameter fluctuations is similar with that earlier reported by other authors, but in two of these regions noticeable differences are identified. Also, except for Michoacán, the scaled pdfs analysis of all regions collapse on a universal curve with non-Gaussian tails.     

New synchronization analysis for complex networks with variable delays

This paper deals with the issue of synchronization of delayed complex networks. Differing from previous results,the delay interval [0,d(t)] is divided into some variable subintervals by employing a new method of weighting delays. Thus,new synchronization criteria for complex networks with time-varying delays are derived by applying this weighting-delay method and introducing some free weighting matrices. The obtained results have proved to be less conservative than previous results. The sufficient conditions of asymptotical synchronization are derived in the form of linear matrix inequality,which are easy to verify. Finally,several simulation examples are provided to show the effectiveness of the proposed results.     

Paths to synchronization on complex networks

The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this Letter, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena.     

Mutual and intermittent enhancements of synchronization transitions by autaptic and synaptic delay in scale-free neuron networks

In neural networks, there exist both synaptic delays among different neurons and autaptic self-feedback delays in a neuron itself. In this paper, we study synchronization transitions induced by synaptic and autaptic delays in scale-free neuron networks, mainly exploring how these two time delays affect synchronization transitions induced by each other. It is found that the synchronization transitions induced by synaptic (autaptic) delay are intermittently enhanced when autaptic (synaptic) delay is varied. There are optimal autaptic strength and synaptic coupling strength by which the synchronization transitions induced by autaptic and synaptic delays become strongest. The underlying mechanisms are briefly discussed in terms of the relationships of autaptic delay, synaptic delay, and inter-burst interval. These results show that synaptic and autaptic delays could contribute to each other and enhance synchronization transitions in the neuronal networks. This implies that autaptic and synaptic delays could play a vital role for the information transmission in neural systems.     

Order parameter of inhomogeneous superconductors

The configuration-averaged thermodynamic free-energy 〈f〉 of an inhomogeneous superconductor is calculated within a Gaussian approximation of the Ginzburg-Landau formalism. The equilibrium order parameter $\text{gy}$ (T) shows a systematic depression below the predicted BCS values, whereas the critical exponent β remains unchanged. These predictions are supported by recent tunneling measurements in A?—A?₂O₃)—Pb junctions done by Gray and Schuller. The small tails observed in these experiments are explained by the existing Josephson coupling between A? and Pb order parameters.     

Optimal synchronization on strongly connected directed networks

In this paper we construct and analyse strongly connected sparse directed networks with an enhanced propensity for synchronization (PFS). Two types of PFS-enhanced networks are considered: (i) an eigenratio minimizing ensemble with non-vanishing complex parts of the spectrum and (ii) a class of networks with real spectrum but slightly larger eigenratios than (i). We relate the superior PFSs to a strongly skewed out-degree distribution, the density of double links and a hierarchical periphery-core organization. Ensembles (i) and (ii) are found to differ in the density of double links and the particular organization of the core and the periphery-core linkage.     

Performance analysis and improvement of loss recovery mechanisms in star OBS networks

In OBS networks, burst loss affects negatively the performance of the higher layers. Proactive loss recovery mechanisms, such as burst cloning, have the advantage of low burst delay but it suffers from low bandwidth utilization. However, reactive loss recovery mechanisms, such as burst retransmission, have the advantage of high bandwidth utilization but at the cost of high burst delay. In this paper, we present an analysis of this trade-off and we propose two new schemes to improve bandwidth utilization while keeping burst delay as low as possible in star OBS networks. The first scheme controls the retransmissions. The second scheme combines burst cloning and burst retransmission mechanisms. Analytical and simulation results show that the both schemes achieve high bandwidth utilization. The results confirm also that compared to basic burst retransmission scheme, the first scheme reduces burst delay only at moderate and high load, however, the second scheme reduce delay at every load.     

Adaptive synchronization of dynamics on evolving complex networks

We study the problem of synchronizing a general complex network by means of an adaptive strategy in the case where the network topology is slowly time varying and every node receives at each time only one aggregate signal from the set of its neighbors. We introduce an appropriately defined potential that each node seeks to minimize in order to reach or maintain synchronization. We show that our strategy is effective in tracking synchronization as well as in achieving synchronization when appropriate conditions are met.     

具有双重时滞的时变耦合复杂网络的牵制外同步研究

针对同时具有节点时滞和耦合时滞的时变耦合复杂网络的外同步问题, 提出一种简单有效的自适应牵制控制方法. 首先构建一种贴近实际的驱动-响应复杂网络模型, 在模型中引入双重时滞和时变不对称外部耦合矩阵. 进一步设计易于实现的自适应牵制控制器, 对网络中的一部分关键节点进行控制. 构造适当的Lyapunov泛函, 利用 LaSalle不变集原理和线性矩阵不等式, 给出两个复杂网络实现外同步的充分条件. 最后, 仿真结果表明所提同步方法的有效性, 同时揭示耦合时滞对同步收敛速度的影响.     

Stochastic theory of synchronization transitions in extended systems

We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits, depending on parameter values: (i) a continuous transition in the bounded Kardar-Parisi-Zhang universality class, with a zero largest Lyapunov exponent at the critical point; (ii) a continuous transition in the directed percolation class, with a negative Lyapunov exponent, or (iii) a discontinuous transition (that is argued to be possibly just a transient effect). Cases (ii) and (iii) exhibit coexistence of synchronized and unsynchronized phases in a broad (fuzzy) region. This reproduces almost all of the reported features of synchronization transitions, providing a unified theoretical framework for the analysis of synchronization transitions in extended systems.