Flux Fluctuation In Complex System And Self-organization Of Resource Allocation

Real system is composed of plenty of agents with complex interaction. Comparing with simple system (such as ideal gas), a striking difference is that the collective behavior of the system can be completely different with the expected behavior of agent; consequently, analytical methods beyond reductionism should be proposed. Although the interactions of agents should be different in different systems, there are two impressive simple facts. First, some universal emerged collective behaviors are observed in different complex system. Second, complex system seems to exhibit critical phenomena such as power law and fractal structure. This thesis gives a summary of our research in routing strategy, flux fluctuation in transport system and self-organization of resource allocation. The brief content follows.Traffic is essential for many dynamical processes on real-world networks, such as internet or urban traffic systems. The transport efficiency of the traffic system can be improved by taking full advantage of the resources in the system. In this paper, we propose a hybrid routing strategy model for network traffic system, to realize the plenary utility of the whole network. The packets are delivered according to different "efficient routing strategies"(Yan G. et al., Phys. Rev. E,73(2006)046108). We introduce the accumulating rate of packets, η, to measure the performance of traffic system in the congested phase, and propose the so-called equivalent generation rate of packet to analyze the jamming processes. From analytical and numerical results, we find that, for proper selection of strategies, the hybrid routing strategy system performs better than the single-strategy system in a broad region of strategy mixing ratio. The analytical solution to the jamming processes is verified by estimating the number of jammed nodes, which agrees well with the result from simulation.A fundamental relation characterizing complex physical systems is the flux-fluctuation law. A recently obtained formula for this law predicts monotonous enhancement of the fluctuations as the average flux is increased, which in principle is valid but only for infinite systems. Here we demonstrate the failure of the formula using both real data and model complex systems of finite size, and obtain analytically a more general formula for the flux-fluctuation law. The law is validated by extensive computations of a variety of complex networked systems. Our finding leads to new insights into finite-size complex systems, and this can have significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.Complex systems arising in a modern society typically have many resources and strategies available for their dynamical evolutions. To explore quantitatively the behaviors of such systems, we propose a class of models to investigate Minority Game (MG) dynamics with multiple strategies. In particular, agents tend to choose the least used strategies based on available local information. A striking finding is the emergence of grouping states defined in terms of distinct strategies. We develop an analytic theory based on the mean-field framework to understand the "bifurcations" of the grouping states. The grouping phenomenon has also been identified in the Shanghai Stock-Market system, and we discuss its prevalence in other real-world systems. Our work demonstrates that complex systems obeying the MG rules can spontaneously self-organize themselves into certain divided states, and our model represents a basic and general mathematical framework to address this kind of phenomena in social, economical and political systems.Period three is specific dynamic phenomenon. When the average number of neighbors of agent is more than the number of strategies, it is possible collective behavior of period three emerges. It is different with grouping phenomenon mentioned above, grouping two can’t keep stable period three, and grouping three is accompany period three. Here we analyze the orbit of period three grouping three and the boundary of basin of attraction. Furthermore, the life time near critical point and the condition of higher grouping existing are discussed. Recently, Zhou et al report grouping three phenomena in U.S. house market. This work gives a prospect of self-organization of resource allocation, and it also indicates why stock system does not emerge grouping three.