Information Propagation And Emergence Of Collective Behaviors In Complex Networks

The study of complex networks has gotten an increasing interest in recent years. One of the key problems is to study how the network structure influences the dynamical behaviors on the network. The studies in complex networks focus mainly on signal transmission, networked dynamics and collective behaviors. This thesis focus on the dynamical behaviors of oscillators in complex networks from the following aspects: signal transmission, synchronization of mobile oscillators, and two state oscillators such as the fireflies and cicadas.Firstly, for the signal transmission on network, the previous studies show that the output of the signal will be amplified in scale-free network without noise, and there is a resonance on the coupling strength. And with noise, there will be a double resonance, i.e, a resonance on coupling strength and a stochastic resonance on noise strength. We consider the case with noise and study the relationship between the collective behaviors and external signal. We find that the oscillators will be synchronized, and the synchronization depends on the frequency of the external signal on scale free networks. There is a frequencyω_c. Whenω<ω_c, the degree of synchronization will decrease with the increase of the signal frequency.Secondly, for the synchronization of the networked oscillators, the previous works focus on how to enhance the synchronizability of networks. We consider the situation that the individual oscillators move on network with a probability p . The value of p denotes the speed of oscillators. The number of oscillators is smaller than the number of nodes, such that the oscillators can move frequently between the nodes. We find that the mobility can seriously influence the collective behaviors and there is a optimal mobile speed.Thirdly, for the collective behaviors on network, it is generally investigated by a large number of oscillators. There are many kinds of two-state animals in the world such as the fireflies, cicadas and so on. We let each node in network represent an agent and the links among the nodes be the interactions. Through this model we find that there are completely synchronization, partially synchronization and asynchronous behavior in the networked agents. The results show the collective behaviors of real world and is useful for us to recognize and understand the real biological interactions.From the investigation of the above three levels, we find that the network topology influences significantly its dynamics. Signal transmission is the basic and direct way of transferring interaction between static oscillators on networks, and can be regarded as the primary level. Our result show that scale free topology can induce the synchronization of two state systems, and the degree of synchronization is related to the frequency of external signal. The mobile model of oscillators is more close to the real world than the static oscillator model, and belongs to the secondary level. We find that the mobile oscillators will be synchronized on scale free network, and the synchronized behavior is related to the moving speed. The senior level is to use network to model the real biological systems. We use networked model to study the interactions of two state animals and find that the results can reflect the collective behaviors of two-state biological systems.