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.

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.

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.

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.

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.