Deterministic Chaos

One of the most considerable discoveries of last decades is discovery of the deterministic chaos in dynamical systems. The essence of this discovery consists that completely determined dynamical system, in the absence of any random excitations on it, starts to behave an unpredictable (chaotically) manner. But at this unpredictability (chaotically) at more close examination it is possible to find a number of regularities in behaviour of system that distinguishes the given phenomenon from classical random processes. Unlike classical random processes, the phenomenon of the deterministic chaos can be repeatedly reiterated in natural and laboratory experiments.

The most powerful is that the deterministic chaos is not any exclusive regime of behaviour of dynamical systems, on the contrary, such regimes are observed in many dynamical systems which are considered in mathematics, physics, chemistry, biology, medicine and economy.
Such deterministic chaotic regimes sometimes are more typical regimes, than completely predicted (regular) regimes. It is possible to tell, that the material world surrounding us "completely is deeping in chaos". As it was found out, the phenomenon of the deterministic chaos is peculiar not only to a material world. Last time such phenomena are even more often featured in examinations on sociology, philosophy, history. Therefore investigation of chaotic dynamics is one of the main trajectories of development of the up-to-date natural sciences.

The phenomena of the deterministic chaos are possible only in non-linear systems. Therefore, with opening of the deterministic chaos, earlier existing illusions about however-is necessary adequate description of real processes by means of the linear mathematical models have completely vanished. A sight at non-linear systems as on some "cosmetic" betterment of the linear models, leaves in the past.

The mathematical images of the deterministic chaos is so-called strange attractors -very complicated boundary sets in phase spaces of dynamic systems. The first strange attractor has been constructed by american researcher E.N. Lorenz in 1963 at studying of processes of heat exchange in a fluid.

On this site results of investigations of the deterministic chaos by participants of scientific group are presented.

Краснопольская Т.С., Швец А.Ю. Регулярная и хаотическая динамика систем с ограниченным возбуждением

ISBN 978-5-93972-619-1
2008 г.
280 стр.


В книге исследовано возникновение, развитие и исчезновение детерминированного хаоса в некоторых маятниковых, электроупругих и гидродинамических системах с ограниченным возбуждением. Выявлено существование большого разнообразия типов хаотических аттракторов и сценариев перехода к хаосу в рассмотренных системах. Построены и тщательно проанализированы фазовые портреты, сечения и отображения Пуанкаре, распределения спектральных плотностей и инвариантных мер регулярных и хаотических аттракторов. Изучено влияние различных факторов запаздывания на динамическую стабилизацию маятниковых систем.
Предназначена для студентов, аспирантов, преподавателей университетов и специалистов по нелинейной динамике.