Nonlinear dynamics. Approaches, results, hopes. Malinetsky G.G., Potapov A.B., Podlazov A.V.

The book discusses some key problems of modern nonlinear dynamics. The concept of the authors boils down to the fact that the fundamental difficulties that this interdisciplinary approach encountered a new paradigm. The book makes an attempt to outline its possible contours. The era of dissipative structures and the era of dynamic chaos should be replaced by a new era. If earlier many concepts and basic mathematical models came to synergetics from physics, chemistry, hydrodynamics, now neuronac, risk theory, biology, theoretical history, psychology and other areas related to the analysis of complex irreversibly developing systems are becoming their main suppliers. A number of original results are discussed regarding the mathematical modeling of nonlinear phenomena and the analysis of time series. Much attention is paid to such violently developing in synergetics as the theory of inertial diversity, reconstruction of the attractions, the theory of self -organizational criticism, and reshet gases.

This makes the book interesting for specialists in nonlinear dynamics and related areas. More than twenty -year development of synergetics makes us summarize the preliminary results and re -evaluate the main ideas, models, concepts, edited during the large path traveled, to comprehend the “language” of nonlinear science. A significant part of the book is devoted to this, which makes it useful to everyone who wants to get acquainted with the specific mathematical content of nonlinear dynamics.

The book is of independent interest, but can be considered as a continuation of the book by G.G. Malinetsky and A.B. Potapov “Non -linear dynamics and chaos: basic concepts” (URSS, 2009).

The publication will be useful to a wide range of students, graduate students and scientists, as well as all readers who want to get acquainted with the specific mathematical content of nonlinear dynamics.