The huge role of a non-linear language in the formation of a new non-linear worldview, which created a new non-linear-synergetic paradigm of modern science, is shown. First, the development of this language induced the development of nonlinear dynamics and its formation as a new science. Secondly, this language has enriched many sciences with such concepts as “deterministic chaos”, “strange attractor”, “dissipative structures”, “fractal”, “bifurcation”, which have now become general scientific. Thirdly, this language formed the basis of a new “non-linear” thinking. Fourth, the non-linear language, which is especially attractive to young scientists, has contributed to the influx of new talented scientists into non-linear dynamics. All of the above played a decisive role in the formation of a new general scientific non-linear paradigm, impossible and inconceivable without a new language. It is thanks to this language that modern scientists look at the world with a “nonlinear vision”, not imagining a linear reality, incomparably enriching their ideas about everything that exists and develops. So, eidetically varying the concept of “chaos”, outlined the range of systems that allow chaotic behavior, found out the methodological principles for the study of such systems, determined the characteristic features of chaotic development, and thus passed the “second stage” of the phenomenological analysis of deterministic chaos.
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.
They outlined briefly the basic concepts of nonlinear dynamics, such as evolution, bifurcations, autowaves, instability, fractals, chaos, and dynamic chaos.
The paper considers a new method for finding patterns in a chaotic system and an algorithm implementing it that automatically computes geometric, physical, and other possible interactions based on preferences between objects in a chaotic system in a reasonable computational time, selecting the only possible solution from the whole population. The algorithm has P-class simplicity in solving NP-class problems, bringing machine intelligence as close as possible to human intelligence. Descriptions of original solutions to a number of technical and creative problems are presented.