Synchronization Behavior Of Two Classes Of Systems Using Detrended Fluctuation Analvsis

In this paper, the approach of detrended fluctuation analysis (DFA) is taken to analyze synchronization of various complex networks and seismic response of natural draught cooling tower. First of all, the DFA method and its application especially in the long-range correlations is presented briefly, which permits the detection of long-range correlations in data series characterized by a scaling exponent according to DFA method.Next, this DFA method is adopted in the studies of network synchronization for two typical cases, i.e., the classic Kuramoto model, and the linearly and diffusively coupled networks with each node being a Van der Pol oscillator subject to parametric excitation. By comparing with other index parameters of network synchronization, it is found that the DFA scaling exponent can be applied to determine the synchronization behavior of these two complex networks. Moreover, with the increase of the coupling strength and the random connection probability of complex networks, the DFA scaling exponent increase to [0.5,1]. So the DFA scaling exponent can be better than other index parameters of network synchronization under certain conditions.Finally, we go in for applying DFA method in the synchronization behavior of practical complex engineering structure. We make a preliminary exploration on characteristics of shell structural response of natural draft cooling tower applied by seismic load using DFA. It is found that the DFA scaling exponent can be applied to determine that the shell structural response is non-synchronous, with certain periodic.