Adaptability And Sensitivity In The Complex Systems

In the famous Santa Fe institute in early1980s, a group of famous scientistsdevoted themselves to researching and exploring a new scientific fields–science of com-plexity. However, there is yet no unified strict definition of complex systems.Generally, there are two kinds of systems–simple systems and complex systems.And complex systems have both the characteristics of determinacy and randomness.A large number of scientific problems in life science, physical science, and informationscience etc theoretically belong to complex systems. These issues are hard to put upwith in the traditional scientific theory framework which is dominated by linear andrestore theory, so the theory of complexity is honored as " the21st century science"a Inrecent years, the research on complex systems have attracted more and more attention.The famous Santa Fe institute has always persisted the research on the complexity inthe past decades. Its research has gradually developed from the behavior of complexsystems by qualitative methods and computer simulations to the basic mechanism ofcomplexity. Not only does the complexity research have prominent academic signifi-cance but also possess great practical meanings.Due to the opening of complex systems, they must interact with the externalenvironment. It is natural to suggest a new concept to describe their reaction toexternal stimulus. This concept is called the sensitivity of a system. On the other hand,adaptability of a system refers to the ability of restoring the system to its previous stateafter being afected by external stimulus. In this paper, we analyze these concepts fromthe viewpoint of dynamical systems. This paper includes the following two aspects:1. From the viewpoint of dynamical systems, we give the descriptive mathematicaldefinition of adaptability and sensitivity. When the attractor of the system is fixedpoint case, we give the exactly mathematical definition. We also proposed an adaptivecontrol method to improve both the adaptability and sensitivity.2. By using the adaptive control method to40widely exist three-note and three-link motifs in real biological networks, we improve both the adaptability and sensitivitysuccessfully of these motifs. In addition, we illustrate the method is robustness to theparameters by varying the parameters. Last but not the least, we summarize the whole dissertation and point out somenew research fields.