Complexity And The Complexity Of Network And Some Research

It has been an important research subject to search for an even more convenient definition of complexity, and then to describe quantitatively how a real world system is complex. All the existing definition of complexity have attempted to suggest a quantitative description of complexity, which gradually changed from the minimum values of the simplest systems such as complete order systems (e.g., a stable periodic motion or a perfect crystals) or complete disorder systems (e.g., isolated ideal gas) to the maximum values of the most complex systems such as society or living animals. The authors of the precious researches are trying to propose a definition with which a clear boundary between simple and complex systems could be described. In this article, we are attempting to propose such a definition and call it"information measure".We assume that many systems in our nature are evolving via a transient state, longer or shorter, to a final state, stable or unstable. Its information measure depends on the abundance of both the final state and the transient state. We suggest depict the abundance of the transient state by the reaction abundance to the perturbation. Simultaneously, we suggest, based on the current understanding, divide the system evolution final state into six kinds, and"equivalently"describe them by periodic motions. It is our hope that this description method can set up a clear boundary between simple systems and complex systems by showing that all the simple systems have zero information measure, and all the complex systems have positive information measure. The information measure values of some example simple systems are analytically discussed. All the results show zero values. As examples for complex systems, numerically we discuss the complexity values of logistic map, and also discuss Bak-Sneppen model partly analytically and partly numerically. The results of logistic map show information measure values beyond zero in chaotic states. All the maximal values locate at the edges of chaos. The information measure of Bak-Sneppen model is rather large due to the large value of the transient state information measure.The third chapter reports a pilot study on the avalanche processes in a complex self-adaptive system model. Our model is on the assumption that: 1) there are two kinds of nodes in the fixed topological networks; 2) the nodes transmit a message with the symmetrical mechanism; 3) the transfer processes is dynamical, the same message can transmitted to the same node for several times which are very from time to time. This model will be placed on the small-world network and scale-free network. While the nodes transmit the message, we statistics the avalanche size of the positive and the negative nodes and theΔ(t) (which means the proportion of the positive node of the total nodes) variation of the time.For small-world network, there are both positive and negative avalanches, while the positive's avalanche's distribution is power-law, and the negative's is exponential. The distribution doesn't change whenΔ(0) changes, when (the model parameter) is small. TheΔ(t) has nothing to do with the initial moment. Once there is a message transmits in the network, the negative nodes occupy the absolute supremacy immediately. But the positive rebounds more formidable when is greater.For the scale-free network, there are both positive and negative avalanches, whenε<0.05 , and the positive's avalanche's distribution is power-law, the negative's is exponential. Whenε≥0.05 , the negative nodes would not exist, and the positive nodes'avalanche distribution began to approach random. The negative nodes occupy the absolute supremacy immediately whenε<0.05 , the positive nodes occupy the absolute supremacy immediately whenε≥0.05 . So, we suppose that there might be a threshold with the range0.03<ε<0.05 , making the positive and the negative nodes turns occupy the supremacy. For the same set of parameters (when is small), scale-free network is more available to the avalanche of self-organized criticality than the small-world network. This model could be applied on the dissemination of ideas and thoughts that may be used to predict the consequences of the proliferation. It is possible to do some aspects of decision-making reference.In the end, we report a network description and empirical investigation on human acupuncture point network. Chinese medical theory is ancient and profound, however is confined by qualitative and faint understanding. The effect of Chinese acupuncture in clinical practice is unique and effective, and the human acupuncture point plays a mysterious and special role, however there is no modern scientific understanding on human acupuncture point until today. For this reason, we attend to use complex network theory, one of the frontiers in the statistical physics, for describing the human acupuncture points and their connections. It is our wish that we could create a new research direction in the searching for the explanation on human acupuncture points by using modern physics. We have defined the network of human acupuncture points and made statistical analysis. The results certify that the degree distribution and other statistical properties of this network obey SPL distribution function. In addition, we have made statistical investigation on the weight of nodes and their assortativity, and analyzed some characteristics of the weighted network.