ABSTRACT

Chapter 1 introduced the theoretical foundation of the systemic yoyo model. In this chapter, let us glance at the blown-up theory and related main results.

2.1 The Concept of Blown-Ups When developments and changes naturally existing in the surrounding environment are seen as a whole, we have the concept of whole evolutions. And in whole evolutions, other than continuities, as well studied in modern mathematics, what seems to be more important and more common is discontinuity, with which transitional changes (or blown-ups) occur. These blown-ups reflect not only the singular transitional characteristics of the whole evolutions of nonlinear equations, but also the changes of old structures being replaced by new structures.