Study Of Information Propagation In Complex Systems

Information propagation of complex systems is a significant issue in non-linear physics,which has been well studied so far,such as the explanations of various synchronized behaviors and the applications in epileptic signal spreading of human brain,etc.Previous works mainly focus on the transmission of signals induced by coupling.Recently,the interests have been turned to another model because of the increasing interesting in complex networks,i.e., the instantaneous transmission model,such as epidemic spreading and rumor propagation,etc.In this thesis,we have studied the information propagation from both the chaotic dynamics and the complex networks,and obtained the following results:Firstly,we study the epidemic spreading in dynamical community networks. We propose a model of mobile agents to study the epidemic spreading in dynamical community networks,which is formed by communities with different densities of agents and allows the traveling among them.The model addresses the epidemic process from an infected community to a safe community through both direct and indirect contacts.By both theoretic analysis and numerical simulations we find that it is possible to sustain the epidemic spreading in a safe community through contacting with another safe community, provided that the latter is connected with an infected community.Secondly,we study analytically and numerically the rumor propagation in complex networks by using the SIR model.Analytically,a mean-field theory is worked out by considering the influence of network topological structure and the unequal footings of neighbors of an infected node in propagating the rumor. And it is found that the final infected density of population with degreeκisρ(κ)=1-e^ακ,whereαis a parameter related to network structure.The number of the total final infected nodes depends on the network topological structure and will decrease when the structure changes from random to scale-free network.Thirdly,we study the signal propagation in coupled systems.Considering the fact that the distances between coupled oscillators may delay the receiving of signals,we here study the influence of the range of distributed delays in an array of coupled pendula,instead of studying the influence of coupling strength. We find that with the increase of the range of distributed delays,the chaotic behaviors of the coupled array may be controlled and different synchronized patterns can be induced.An analytic solution is given to confirm the numerical results.This finding may provide new insight to the information processing in neurons.Finally,we study the characterization of high-dimensional curves.We have introduced a new concept,spatial phase,to directly characterize the rotation of a spatial curve without using the projections in 2D subspaces.Compared with the plane phase defined for a 2D projected trajectory,the spatial phase uniquely defined for an original nD trajectory reflects the accumulation of spatial angles connected to small arcs of trajectory and turns out to be useful to analyze synchronization of coupled systems.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 information propagation may,in contrast, also influence the formation/growing of complex networks.Besides,even the very simple systems can show complicated behaviors,while the systems with large degree of freedom may also show coherent and simple behavior.Hence, complex systems may have rules,while simple system may not be easy to solve.This thesis mainly consists of four parts.Firstly,we introduce the epidemic spreading in dynamical community networks.Secondly,we discuss the influence of network structure on rumor propagation.Thirdly,we study the synchronized patterns induced by distributed time-delays.At last,we introduce a new concept,spatial phase.