A novel approach is presented to measure the synchronization of two time series. Based on the consistent changing tendency of temporal permutation entropies, we introduce an order parameter to characterize the synchronization between two coupled systems. The value of the order parameter can be used as an indicator of the degree of synchronization, which has been confirmed by numerical simulations and analytically illustrated through an example. Our method is effective and can be easily used in practical situations.

Social networks have the structure of communities. To understand how the community structure affects epidemic spreading, we present a simplified model of community network, and investigate the epidemic propagation in this model. We find that, compared to the random network, the community network has a broader degree distribution, a smaller threshold of epidemic outbreak, and more prevalence to keep the outbreak endemic. The formulae of epidemic threshold are given and confirmed by numerical simulations.

Motivated by the problem of ozone production in atmospheres of urban areas, we consider chemical reactions of the general type: A+B→2C, in idealized two-dimensional nonlinear flows that can generate Lagrangian chaos. Our aims differ from those in the existing work in that we address the role of transient chaos versus sustained chaos and, more importantly, we investigate the influence of noise. We find that noise can significantly enhance the chemical reaction in a resonancelike manner where the product of the reaction becomes maximum at some optimal noise level.We also argue that chaos may not be a necessary condition for the observed resonances. A physical theory is formulated to understand the resonant behavior.

The detection of the interrelation between non-stationary time series is a key problem unsolved in the analysis of practical data. Here we present a novel approach to detect the phase locking of time series in non-stationary status, which does not need the reconstruction of the attractor but gets information from the consistence of local rotation speeds. This method can be conveniently used for practical situations, such as the epileptic seizure.

We propose and study the collective behavior of a model of networked signaling objects that incorporates several ingredients of real-life systems. These ingredients include spatial inhomogeneity with grouping of signaling objects, signal attenuation with distance, and delayed and impulsive coupling between non-identical signaling objects. Depending on the coupling strength and/or time-delay effect, the model exhibits completely, partially, and locally collective signaling behavior. In particular, a correlated signaling (CS) behavior is observed in which there exist time durations when nearly a constant fraction of oscillators in the system are in the signaling state. These time durations are much longer than the duration of a spike when a single oscillator signals, and they are separated by regular intervals in which nearly all oscillators are silent. Such CS behavior is similar to that observed in biological systems such as fireflies, cicadas, crickets, and frogs. The robustness of the CS behavior against noise is also studied. It is found that properly adjusting the coupling strength and noise level could enhance the correlated behavior.

Recently, it has been found that noise can induce chaos and destruct the zero Lyapunov exponent in the situation where a nonchaotic attractor coexists with a nonattracting chaotic saddle, as in a periodic window [Phys. Rev. Lett. 88 (2002) 124101]. Here we report that noise can also destruct the zero Lyapunov exponent in coupled chaotic systems where there is only one attractor. Moreover, the zero Lyapunov exponent in noise free will become positive when adding noise and be proportional to the average frequency of bursting induced by noise. A physical theory and numerical simulations are presented to explain how the average frequency of bursting depends on the coupling and noise strength.

A general class of growing networks is constructed with both preferential and random attachments, which includes random and scale-free networks as limiting cases when a physical parameter is tuned. Formulas are derived characterizing the evolution and distribution of the connectivity, which are verified by numerical computations. Study of the effect of random failures and intentional attacks on the performance of network suggests that general networks which are neither completely random nor scale-free are desirable.

We consider situations where, in a continuous-time dynamical system, a nonchaotic attractor coexists with a nonattracting chaotic saddle, as in a periodic window. Under the influence of noise, chaos can arise. We investigate the fundamental dynamical mechanism responsible for the transition and obtain a general scaling law for the largest Lyapunov exponent. A striking finding is that the topology of the flow is fundamentally disturbed after the onset of noisy chaos, and we point out that such a disturbance is due to changes in the number of unstable eigendirections along a continuous trajectory under the influence of noise.

We study the condensation phenomenon in a zero range process on weighted scale-free networks in order to show how the weighted transport influences the particle condensation. Instead of the approach of grand canonical ensemble which is generally used in a zero range process, we introduce an alternate approach of the mean-field equations to study the dynamics of particle transport. We find that the condensation on the scalefree network is easier to occur in the case of weighted transport than in the case of weight-free networks. In the weighted transport, especially, a dynamical condensation is even possible for the case of no interaction among particles, which is impossible in the case of weight-free networks.

We discuss a general approach for chaotic synchronization of dynamical systems that is based on adjusting the response-system parameter. Numerical simulation shows that this method is robust against external noise.