The work is devoted to the analysis of ways of development of the theory of self-organization for the world of complex systems. This is due to the fact that the modern world understanding is based on the concepts of complex world and correspondingly on interactions of complex systems, such as nonlinearity, imbalance and chaotic state in the process of evolution. The paper summarizes not only all types of self-organization known to date, but also the degree of participation of authors in the topic. In addition, a new type of cumulative self-organization is considered separately.
The role of bifurcation or structural-phase transitions in the evolution of complex systems is analyzed using a phenomenological algorithm and formalized concepts of adaptability and stability. It is shown that the algorithm makes it possible to estimate the degree of transition harmonicity and the stability of the new state. Knowledge of the features of the most critical zones of structural-phase transitions makes it possible to change the trajectory, pace and ultimate goal of the evolution of various dangerous natural processes by small energy impacts, preventing their development to extreme states. The knowledge of the functional significance of such “acupuncture” points of evolutionary processes makes it possible to control them with minimal energy costs for the purpose of preventive protection.