Dynamics in the Kuramoto Model with a Discontinuous Bimodal Distribution of Natural Frequencies

We consider a Kuramoto model in which the natural frequencies of oscillators follow a discontinuous bimodal distribution constructed from a Lorentzian one. Different synchronous dynamics （such as different types of travelling wave states, standing wave states, and stationary synchronous states） are identified and the transitions between them are investigated. We find that increasing the asymmetry in frequency distribution brings the critical coupling strength to a low value and that strong as.ymmetry is unfavorable to standing wave states.     

Dynamics of Symmetric Conserved Mass Aggregation Model on Complex Networks

We investigate the dynamical behaviour of the aggregation process in the symmetric conserved mass aggregation model under three different topological structures. The dispersion a（t, L） = （∑i（mi - ρo ） ^2 / L ）1/2 is defined to describe the dynamical behaviour where Po is the density of particle and mi is the particle number on a site. It is found numerically that for a regular lattice and a scale-free network, σ（t, L） follows a power-law scaling σ（ t, L） ~ t^δ1 and σ（ t, L） ~ t^δ4 from a random initial condition to the stationary states, respectively. However, for a small-world network, there are two power-law scaling regimes, σ（t, L） ~ t^δ2 when t 〈 T and 〈（t, L） ~ t^δ3 when t 〉 T. Moreover, it is found numerically that 62 is near to 61 for small rewiring probability q, and 63 hardly changes with varying q and it is almost the same as 64. We speculate that the aggregation of the connection degree accelerates the mass aggregation in the initial relaxation stage and the existence of the long-distance interactions in the complex networks results in the acceleration of the mass aggregation when t 〉 T for the small-world networks. We also show that the relaxation time r follows a power-law scaling τ ~ L^z and σ（t, L） in the stationary state follows a power-law Gs（L） - L^α for three different structures.     

Opinion Dynamics on Complex Networks with Communities

The Ising or Potts models of ferromagnetism have been widely used to describe locally interacting social or economic systems. We consider a related model, introduced by Sznajd to describe the evolution of consensus in the scale-free networks with the tunable strength （noted by Q） of community structure. In the Sznajd model, the opinion or state of any spins can only be changed by the influence of neighbouring pairs of similar connection spins. Such pairs can polarize their neighbours. Using asynchronous updating, it is found that the smaller the community strength Q, the larger the slope of the exponential relaxation time distribution. Then the effect of the initial upspin concentration p as a function of the final all up probability E is investigated by taking different initialization strategies, the random node-chosen initialization strategy has no difference under different community strengths, while the strategies of community node-chosen initialization and hub node-chosen initialization are different in fina/probability under different Q, and the latter one is more effective in reaching final state.     

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.     

Local Events and Dynamics on Weighted Complex Networks

We examine the weighted networks grown and evolved by local events, such as the addition of new vertices and links and we show that depending on frequency of the events, a generalized power-law distribution of strength can emerge. Continuum theory is used to predict the scaling function as well as the exponents, which is in good agreement with the numerical simulation results. Depending on event frequency, power-law distributions of degree and weight can also be expected. Probability saturation phenomena for small strength and degree in many real world networks can be reproduced. Particularly, the non-trivial clustering coefficient, assortativity coefficient and degree-strength correlation in our model are all consistent with empirical evidences.     

Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling

We study the synchronization transition in the Kuramoto model by considering a unidirectional coupling with a chain structure. The microscopic clustering features are characterized in the system. We identify several clustering patterns for the long-time evolution of the effective frequencies and reveal the phase transition between them. Theoretically, the recursive approach is developed in order to obtain analytical insights; the essential bifurcation schemes of the clustering patterns are clarified and the phase diagram is illustrated in order to depict the various phase transitions of the system. Furthermore, these recursive theories can be extended to a larger system. Our theoretical analysis is in agreement with the numerical simulations and can aid in understanding the clustering patterns in the Kuramoto model with a general structure.     

Discontinuity and Complex Dynamics of Neural Networks

We focus on the discontinuity of a neural network model with diluted and clipped synaptic connections (±l only). The exact evolution rule of the average firing rate becomes a discontinuous piece-wise nonlinear map when very simple functions of dynamical threshold are introduced into the network. Complex dynamics is observed.     

Travelling Wave in the Generalized Kuramoto Model with Inertia

We study the dynamics of the generalized Kuramoto model with inertia,in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians.By numerically simulating the model,we find that the model supports a modulated travelling wave state except for already displayed travelling wave states and π state in previous literature.The modulated travelling wave state may be characterized by the phase distributions of oscillators.Finally,the modulated travelling wave state and the travelling wave state of the model in the parameter space are presented.     

Weighted Networks Model Based on Traffic Dynamics with Local Perturbation

In the study of weighted complex networks, the interplay between traffic and topology have been paid much attention. However, the variation of topology and weight brought by new added vertices or edges should also be considered. In this paper, an evolution model of weighted networks driven by traffic dynamics with local perturbation is proposed. The model gives power-law distribution of degree, weight and strength, as confirmed by empirical measurements. By choosing appropriate parameters W and δ, the exponents of various power law distributions can be adjusted to meet real world networks. Nontrivial clustering coefficient C, degree assortativity coefficient r, and strength-degree correlation are also considered. What should be emphasized is that, with the consideration of local perturbation, one can adjust the exponent of strength-degree correlation more effectively. It makes our model more general than previous ones and may help reproducing real world networks more appropriately. PACS numbers： 87.23.Kg, 89.75.Da, 89.75.Fb, 89.75.Hc.     

A Generalized Voter Model on Complex Networks

We study a generalization of the voter model on complex networks, focusing on the scaling of mean exit time. Previous work has defined the voter model in terms of an initially chosen node and a randomly chosen neighbor, which makes it difficult to disentangle the effects of the stochastic process itself relative to the network structure. We introduce a process with two steps, one that selects a pair of interacting nodes and one that determines the direction of interaction as a function of the degrees of the two nodes and a parameter α which sets the likelihood of the higher degree node giving its state to the other node. Traditional voter model behaviors can be recovered within the model, as well as the invasion process. We find that on a complete bipartite network, the voter model is the fastest process. On a random network with power law degree distribution, we observe two regimes. For modest values of α, exit time is dominated by diffusive drift of the system state, but as the high-degree nodes become more influential, the exit time becomes dominated by frustration effects dependent on the exact topology of the network.     

Self-organized Critical Model Based on Complex Brain Networks with Hierarchical Organization

The dynamical behavior in the cortical brain network of macaque is studied by modelling each cortical area with a subnetwork of interacting excitable neurons. We find that the avalanche of our model on different levels exhibits power-law. Furthermore the power-law exponent of the distribution and the average avalanche Size are affected by the topology of the network.     

Self-organized Critical Model Based on Complex Brain Networks with Hierarchical Organization

The dynamical behavior in the cortical brain network of macaque is studied by modelling each cortical area with a subnetwork of interacting excitable neurons. We find that the avalanche of our model on different levels exhibits power-law. Furthermore the power-law exponent of the distribution and the average avalanche size are affected by the topology of the network.     

Synchronization and Pattern Dynamics of Coupled Chaotic Maps on Complex Networks

The synchronization and pattern dynamics of coupled logistic maps on a certain type of complex network, constructed by adding random shortcuts to a regular ring, is investigated. For parameters where an isolated map is fully chaotic, the defect turbulence, which is dominant in the regular network, can be tamed into ordered periodic patterns or synchronized chaotic states when random shortcuts are added, and the patterns formed on the complex network can be grouped into two or three branches depending on the coupling strength.     

Rumor Spreading Model with Trust Mechanism in Complex Social Networks

In this paper, to study rumor spreading, we propose a novel susceptible-infected-removed (SIR) model by introducing the trust mechanism. We derive mean-field equations that describe the dynamics of the SIR model on homogeneous networks and inhomogeneous networks. Then a steady-state analysis is conducted to investigate the critical threshold and the final size of the rumor spreading. We show that the introduction of trust mechanism reduces the final rumor size and the velocity of rumor spreading, but increases the critical thresholds on both networks. Moreover, the trust mechanism not only greatly reduces the maximum rumor influence, but also postpones the rumor terminal time, which provides us with more time to take measures to control the rumor spreading. The theoretical results are confirmed by sufficient numerical simulations.     

Unified Model for Generation Complex Networks with Utility Preferential Attachment

In this paper, based on the utility preferential attachment, we propose a new unified model to generate different network topologies such as scale-free, small-world and random networks. Moreover, a new network structure named super scale network is found, which has monopoly characteristic in our simulation experiments. Finally, the characteristics of this new network are given.     

Unified Model for Generation Complex Networks with Utility Preferential Attachment

In this paper, based on the utility preferential attachment, we propose a new unified model to generate different network topologies such as scale-free, small-world and random networks. Moreover, a new network structure named super scale network is found, which has monopoly characteristic in our simulation experiments. Finally, the characteristics ofthis new network are given.     

A Robustness Model of Complex Networks with Tunable Attack Information Parameter

We introduce a novel model for robustness of complex with a tunable attack information parameter. The random failure and intentional attack known are the two extreme cases of our model. Based on the model, we study the robustness of complex networks under random information and preferential information, respectively. Using the generating function method, we derive the exact value of the critical removal fraction of nodes for the disintegration of networks and the size of the giant component. We show that hiding just a small fraction of nodes randomly can prevent a scale-free network from collapsing and detecting just a small fraction of nodes preferentially can destroy a scale-free network.     

An Improved Heterogeneous Mean-Field Theory for the Ising Model on Complex Networks

Heterogeneous mean-field theory is commonly used methodology to study dynamical processes on complex networks,such as epidemic spreading and phase transitions in spin models.In this paper,we propose an improved heterogeneous mean-field theory for studying the Ising model on complex networks.Our method shows a more accurate prediction in the critical temperature of the Ising model than the previous heterogeneous mean-field theory.The theoretical results are validated by extensive Monte Carlo simulations in various types of networks.