Potentiality of mathematical models in complex systems.

A long time has passed after receiving many expectations for mathematical theories and applications in real world complex systems. Unfortunately potentiality for theory and modeling of complex systems is not properly advocated. In this paper potentiality of mathematical models in complex systems is discussed in conjunction with real world examples. First, it is described "what mathematical model is" in complex systems. The mathematical model of complex system is not for describing the spatio-temporal features in real world objects, but for idealizing the reality of them. Successful statistical models based on Bayes theorem in complex systems are exemplified, and discussed with the problems of "Big Data". Further, feasibility and availability of mathematical models in complex systems are remarked. [ABSTRACT FROM AUTHOR]