Study Of Coupled Signals Dynamics In Complex Networks

The weak coupling dynamics and the signals transmission on the complex networks are significant issues of the complex-system studies, which are well studied in many fields, such as the weak synchronization of the coupled systems,the signals interaction and amplification in their transmission process, etc.. In this thesis, we study the weak coupling dynamics and the signals transmission based on three aspects:the discrete maps of chaotic systems,the epidemic spreading and the stochastic resonance. We obtain the following results:Firstly, the abnormal phase order of coupled logistic maps, i.e., the ratio of two sequential "up phases" in the total iterations, can be characterized by the direction phase [Phys. Rev. Lett.,84 (2000) 2610]. We here consider the case of coupled logistic maps on complex networks and study how the network topology influences the abnormal phase order. Our numerical simulations reveal that the critical point for the appearance of abnormal phase order increases with the coupling strength but decreases with the degree of heterogeneity of complex networks. Moreover, we find that unlike in the case of normal phase order, it is possible for the system to show a periodic window in the case of abnormal phase order, but only within an appropriate range of coupling strengths, and finally, that the heterogeneity can reduce the maximum number of the phase clusters in a given periodic window.Secondly, it is known that for chaotic flows, a weak coupling does not always make the coupled systems approach synchronization but sometimes make them become more complicated [PRE 67,045203(R)]. We here report that a similar situation also occurs in the coupled chaotic maps, where a weak coupling will make the number of direction-phase clusters increase. We find a double resonance effect on the coupling strength where the first resonance comes from the coupling induced periodic behaviors and the second one owing to the disappearance of disorder phase. The mechanism of the second resonance is revealed through the out-of-phase links. Moreover, we show that the critical coupling strength of the maximum of the number of direction-phase clusters will increase rapidly with the bifurcation parameter but slowly with the range of the distribution of non-identical oscillators.Thirdly, It is reported in Nature (London) 427,344(2004) that there are periodic waves in the spatiotemporal data of epidemic. For understanding its mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.Finally, we proposed a method to amplify the signal in a double well system by adaptively adjusting the weight of the connections between the objective and its neighbors. This method is to increase the weights of the connections which link the objective with its neighbors in the different well while to decrease the weights of the connections which link the objective with its neighbors in the same well. This method is proved to be quite effective and could be utilized to a wide range of nodes while only local information of the system is needed. Our theoretical analysis provides the explanation of the mechanism of this method.All the results show that topological structure and the dynamical process can interact each other, i.e., the topological structure of complex networks may influence the dynamics on it; and the coupled signals dynamics may, in contrast, also influence the topology of complex networks. Hence, the dynamics of the coupled signals on the complex networks is a significant issue in the nonlinear physics.This thesis mainly consists of four parts. Firstly, we introduce the influence of network topology on the abnormal phase order. Secondly, we discuss the resonance effect of direction-phase clusters in a scale-free network. Thirdly, we introduce the periodic wave of epidemic spreading in community networks. At last, we discuss the signal amplification by adaption on weighted network.