Hanshuang Chen

Explosive synchronization transitions in complex neural networks

It has been recently reported that explosive synchronization transitions can take place in networks of phase oscillators [Gómez-Gardeñes et al. Phys. Rev. Lett. 106, 128701 (2011)] and chaotic oscillators [Leyva et al. Phys. Rev. Lett. 108, 168702 (2012)]. Here, we investigate the effect of a microscopic correlation between the dynamics and the interacting topology of coupled FitzHugh-Nagumo oscillators on phase synchronization transition in Barabási-Albert (BA) scale-free networks and Erdös-Rényi (ER) random networks. We show that, if natural frequencies of the oscillations are positively correlated with node degrees and the width of the frequency distribution is larger than a threshold value, a strong hysteresis loop arises in the synchronization diagram of BA networks, indicating the evidence of an explosive transition towards synchronization of relaxation oscillators system. In contrast to the results in BA networks, in more homogeneous ER networks, the synchronization transition is always of continuous type regardless of the width of the frequency distribution. Moreover, we consider the effect of degree-mixing patterns on the nature of the synchronization transition, and find that the degree assortativity is unfavorable for the occurrence of such an explosive transition.

Strategy to suppress epidemic explosion in heterogeneous metapopulation networks.

We propose an efficient strategy to suppress epidemic explosion in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals and is assigned a curing rate that is proportional to kα with the node degree k and an adjustable parameter α. We perform stochastic simulations of the dynamical reaction-diffusion processes associated with the susceptible-infected-susceptible model in scale-free networks. We find that the epidemic threshold reaches a maximum when α is tuned at αopt≃1.3. This nontrivial phenomenon is robust to the change of the network size and the average degree. In addition, we carry out a mean field analysis to further validate our scheme, which also demonstrates that epidemic explosion follows different routes for α larger or less than αopt. Our work suggests that in order to efficiently suppress epidemic spreading on heterogeneous complex networks, subpopulations with higher degrees should be allocated more resources than just being linearly dependent on k.

First-order phase transition in a majority-vote model with inertia

We generalize the original majority-vote model by incorporating inertia into the microscopic dynamics of the spin flipping, where the spin-flip probability of any individual depends not only on the states of its neighbors, but also on its own state. Surprisingly, the order-disorder phase transition is changed from a usual continuous or second-order type to a discontinuous or first-order one when the inertia is above an appropriate level. A central feature of such an explosive transition is a strong hysteresis behavior as noise intensity goes forward and backward. Within the hysteresis region, a disordered phase and two symmetric ordered phases are coexisting and transition rates between these phases are numerically calculated by a rare-event sampling method. A mean-field theory is developed to analytically reveal the property of this phase transition.

Critical noise of majority-vote model on complex networks.

The majority-vote model with noise is one of the simplest nonequilibrium statistical model that has been extensively studied in the context of complex networks. However, the relationship between the critical noise where the order-disorder phase transition takes place and the topology of the underlying networks is still lacking. In this paper, we use the heterogeneous mean-field theory to derive the rate equation for governing the models dynamics that can analytically determine the critical noise f(c) in the limit of infinite network size N→∞. The result shows that f(c) depends on the ratio of 〈k〉 to 〈k(3/2)〉, where 〈k〉 and 〈k(3/2)〉 are the average degree and the 3/2 order moment of degree distribution, respectively. Furthermore, we consider the finite-size effect where the stochastic fluctuation should be involved. To the end, we derive the Langevin equation and obtain the potential of the corresponding Fokker-Planck equation. This allows us to calculate the effective critical noise f(c)(N) at which the susceptibility is maximal in finite-size networks. We find that the f(c)-f(c)(N) decays with N in a power-law way and vanishes for N→∞. All the theoretical results are confirmed by performing the extensive Monte Carlo simulations in random k-regular networks, Erdös-Rényi random networks, and scale-free networks.

Resonant response of forced complex networks: The role of topological disorder

We investigate the effect of topological disorder on a system of forced threshold elements, where each element is arranged on top of complex heterogeneous networks. Numerical results indicate that the response of the system to a weak signal can be amplified at an intermediate level of topological disorder, thus indicating the occurrence of topological-disorder-induced resonance. Using mean field method, we obtain an analytical understanding of the resonant phenomenon by deriving the effective potential of the system. Our findings might provide further insight into the role of network topology in signal amplification in biological networks.

Impact of asymptomatic infection on coupled disease-behavior dynamics in complex networks

Studies on how to model the interplay between diseases and behavioral responses (so-called coupled disease-behavior interaction) have attracted increasing attention. Owing to the lack of obvious clinical evidence of diseases, or the incomplete information related to the disease, the risks of infection cannot be perceived and may lead to inappropriate behavioral responses. Therefore, how to quantitatively analyze the impacts of asymptomatic infection on the interplay between diseases and behavioral responses is of particular importance. In this Letter, under the complex network framework, we study the coupled disease-behavior interaction model by dividing infectious individuals into two states: U-state (without evident clinical symptoms, labelled as U) and I-state (with evident clinical symptoms, labelled as I). A susceptible individual can be infected by U- or I-nodes, however, since the U-nodes cannot be easily observed, susceptible individuals take behavioral responses \emph{only} when they contact I-nodes. The mechanism is considered in the improved Susceptible-Infected-Susceptible (SIS) model and the improved Susceptible-Infected-Recovered (SIR) model, respectively. Then, one of the most concerned problems in spreading dynamics: the epidemic thresholds for the two models are given by two methods. The analytic results \emph{quantitatively} describe the influence of different factors, such as asymptomatic infection, the awareness rate, the network structure, and so forth, on the epidemic thresholds. Moreover, because of the irreversible process of the SIR model, the suppression effect of the improved SIR model is weaker than the improved SIS model.

Optimal allocation of resources for suppressing epidemic spreading on networks

Efficient allocation of limited medical resources is crucial for controlling epidemic spreading on networks. Based on the susceptible-infected-susceptible model, we solve the optimization problem of how best to allocate the limited resources so as to minimize prevalence, providing that the curing rate of each node is positively correlated to its medical resource. By quenched mean-field theory and heterogeneous mean-field (HMF) theory, we prove that an epidemic outbreak will be suppressed to the greatest extent if the curing rate of each node is directly proportional to its degree, under which the effective infection rate λ has a maximal threshold λ_{c}^{opt}=1/〈k〉, where 〈k〉 is the average degree of the underlying network. For a weak infection region (λ≳λ_{c}^{opt}), we combine perturbation theory with the Lagrange multiplier method (LMM) to derive the analytical expression of optimal allocation of the curing rates and the corresponding minimized prevalence. For a general infection region (λ>λ_{c}^{opt}), the high-dimensional optimization problem is converted into numerically solving low-dimensional nonlinear equations by the HMF theory and LMM. Counterintuitively, in the strong infection region the low-degree nodes should be allocated more medical resources than the high-degree nodes to minimize prevalence. Finally, we use simulated annealing to validate the theoretical results.

Mobility and density induced amplitude death in metapopulation networks of coupled oscillators.

We investigate the effects of mobility and density on the amplitude death of coupled Landau-Stuart oscillators and Brusselators in metapopulation networks, wherein each node represents a subpopulation occupied any number of mobile individuals. By numerical simulations in scale-free topology, we find that the systems undergo phase transitions from incoherent state to amplitude death, and then to frequency synchronization with increasing the mobility rate or density of oscillators. Especially, there exists an extent of intermediate mobility rate and density that can lead to global oscillator death. Furthermore, we show that such nontrivial phenomena are robust to diverse network topologies. Our findings may invoke further efforts and attentions to explore the underlying mechanism of collective behaviors in coupled metapopulation systems.

Noise-induced vortex reversal of self-propelled particles.

We report an interesting phenomenon of noise-induced vortex reversal in a two-dimensional system of self-propelled particles (SPPs) with soft-core interactions. With the aid of forward flux sampling, we analyze the configurations along the reversal pathway and thus identify the mechanism of vortex reversal. We find that the reversal exhibits a hierarchical process: those particles at the periphery first change their motion directions, and then more inner layers of particles reverse later on. Furthermore, we calculate the dependence of the average reversal rate on noise intensity D and the number N of SPPs. We find that the rate decreases exponentially with the reciprocal of D. Interestingly, the rate varies nonmonotonically with N and a local minimal rate exists for an intermediate value of N.

Nucleation in scale-free networks.

We have studied nucleation dynamics of the Ising model in scale-free networks whose degree distribution follows a power law with the exponent γ by using the forward flux sampling method and focusing on how the network topology would influence the nucleation rate and pathway. For homogeneous nucleation, the new phase clusters grow from those nodes with smaller degree, while the cluster sizes follow a power-law distribution. Interestingly, we find that the nucleation rate R{Hom} decays exponentially with network size and, accordingly, the critical nucleus size increases linearly with network size, implying that homogeneous nucleation is not relevant in the thermodynamic limit. These observations are robust to the change of γ and are also present in random networks. In addition, we have also studied the dynamics of heterogeneous nucleation, wherein w impurities are initially added either to randomly selected nodes or to targeted ones with the largest degrees. We find that targeted impurities can enhance the nucleation rate R{Het} much more sharply than random ones. Moreover, ln(R{Het}/R{Hom}) scales as w{(γ-2)/(γ-1)} and w for targeted and random impurities, respectively. A simple mean-field analysis is also present to qualitatively illustrate the above simulation results.