The concept of diffusion entropy(DE) was used to estimate the scaling behavior.With this method,the scaling value of Dow Jones industrial average index was obtained.Then,the log-probability distribution function log_(10)(P(x,t)) of the diffusion process was obtained by time series with different t.It obeys the centered Levy distribution and displays fat-tail property,which means that the estimating methods on the basis of moments are unavailable.However,the scaling value given by the method of fractional derivative analysis(FDA) appreciably deviates from the genuine value given by diffusion entropy.
In the past decade, synchronization on complex networks has attracted increasing attentions from various research disciplines. Most previous works, however, focus only on the dynamic behaviors of synchronization process in the stable region, i.e., global synchronization. In this letter, we demonstrate that synchronization process on complex networks can efficiently reveal the substructures of networks when the coupling strength of chaotic oscillators is under the lower boundary of stable region. Both analytic and numerical results show that the nodes belonging to the same component in the hierarchical network are tightly clustered according to the Euclidean distances between the state vectors of the corresponding oscillators, and different levels of hierarchy can be systematically unfolded by gradually tuning the coupling strength. When the coupling strengths exceed the upper boundary of stable region, the hierarchy of the network cannot be recognized by this approach. Extensive simulations suggest that our method may provide a powerful tool to detect the hierarchical community structure of complex systems and deep insight into the relationship between structure and dynamics of complex systems.
We investigate a set of complex heart rate time series from healthy human in different behaviour states with the detrended fluctuation analysis and diffusion entropy (DE) method. It is proposed that the scaling properties are influenced by behaviour states. The memory detected by DE exhibits an approximately same pattern after a detrending procedure. Both of them demonstrate the long-range strong correlations in heart rate. These findings may be helpful to understand the underlying dynamical evolution process in the heart rate control system, as well as to model the cardiac dynamic process.
Recent studies have demonstrated that the allocation of individual resources has a significant influence on the dynamics of epidemic spreading. In the real scenario, individuals have a different level of awareness for self-protection when facing the outbreak of an epidemic. To investigate the effects of the heterogeneous self-awareness distribution on the epidemic dynamics, we propose a resource-epidemic coevolution model in this paper. We first study the effects of the heterogeneous distributions of node degree and self-awareness on the epidemic dynamics on artificial networks. Through extensive simulations, we find that the heterogeneity of self-awareness distribution suppresses the outbreak of an epidemic, and the heterogeneity of degree distribution enhances the epidemic spreading. Next, we study how the correlation between node degree and self-awareness affects the epidemic dynamics. The results reveal that when the correlation is positive, the heterogeneity of self-awareness restrains the epidemic spreading. While, when there is a significant negative correlation, strong heterogeneous or strong homogeneous distribution of the self-awareness is not conducive for disease suppression. We find an optimal heterogeneity of self-awareness, at which the disease can be suppressed to the most extent. Further research shows that the epidemic threshold increases monotonously when the correlation changes from most negative to most positive, and a critical value of the correlation coefficient is found. When the coefficient is below the critical value, an optimal heterogeneity of self-awareness exists; otherwise, the epidemic threshold decreases monotonously with the decline of the self-awareness heterogeneity. At last, we verify the results on four typical real-world networks and find that the results on the real-world networks are consistent with those on the artificial network.
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