Study On The Dynamic Properties Of The Collective Behaviour And Critical Phenomenon In Complex System

Complex system is a very broad domain, including social organizations, economic systems, information diffusion, industrial technology, human beings, etc, on which various knowledge systems and methodologies have been established. However, classical theories are facing a great challenge due to the emergence of huge amount of data. We are confronting many unknown questions when knowledge is transferred from intuition to data:whether our cognition of the environment can achieve a qualitative leap? Whether this leap and can lead to discovery of deep universal law? Whether the foundation of new theory improves our ability to control the nature?The core issues of complex system:how the emergence appears in a new non-equilibrium open-structure system self-organized by the large number of subsystems? The objectives of complex system science:to generate new technologies (including new software) and the deeper understanding about the basic problems of complex system.Statistical mechanics is a theory bridge micro and macro many-body system. It can play a important role in organizing all kinds of measurement data systematically, establishing appropriate kinetic model to obtain its properties and finding the law of movement and other aspects of the system. The studies of complex networks have shown that the organizational structure in different areas can have surprisingly similarity in recent years, which suggests the common underlying in complex system. Statistical mechanics is an important way to reveal the universal law. In this paper, we study a number of critical phenomena and collective behaviors in complex systems by various means of statistical mechanics and find some interesting results.We propose a effective routing strategy on the basis of the so-called nearest neighbor search strategy by introducing a preferential delivering exponent a and a waiting time exponentβ. We assume that the handling capacity of one vertex is proportional to its degree when the degree is smaller than a cut-off value K, and is infinite otherwise. Traffic dynamics both near and far away from the critical generating rate Rc are discussed. Simulation results demonstrate that the optimal a,βand K. Our strategy may be useful and reasonable for the protocol designing of modern communication networks.We study the traffic dynamics in two-dimensional Biham-Middleton-Levine(BML) traffic flow model based on the irregular lattice. It is found that a phase separation phenomenon, in which the system separates into coexistence of free flow and jam, could be observed in intermediate vehicle density range.We investigate the prisoner's dilemma game based on a new rule:players will change their current strategies to opposite strategies with some probability if their neighbors'average payoffs are higher than theirs. Compared with the cases on regular lattices (RL) and Newman-Watts small world network (NW), cooperation can be best enhanced on the scale-free Barabasi-Albert network (BA). It is found that cooperators are dispersive on RL network, which is different from previously reported results that cooperators will form large clusters to resist the invasion of defectors. Cooperative behaviors on the BA network are discussed in detail.We generalize a majority-rule model on the opinion dynamics, where all mobile agents update their status based on Vicsek model. We find the existence of an optimal preferential rule for which the convergence to global consensus can be achieved much more rapidly than under other rules. Qualitative insights are obtained by examining the spatiotemporal evolution of the opinion clusters.The three-dimensional Vicsek model is introduced to investigate the collective motion of self-propelled particles. In this model each particle has a limited view angle. We find that there exists an optimal value of view angle, leading to the quickest direction consensus. Our work shows that the optimal view angle is just a function of the absolute velocity and the particles density in the limit of large boundary size. We present a series of special results demonstrating more fundamental and practical rules in the daily-life pragmatic collective phenomena, which is of significance to the low-cost communication.We generalize the Eden model to take into account of the screening effect, i.e., the end point grows much faster than the interior points do. Highly anisotropic clusters are obtained in our generalized Eden model. It is found that the length in the long direction scales differently than that in the short direction does as the number of site increases.