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.