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Conference publicationsAbstractsXXII conferenceDeterministic chaos without mysticismMoscow, 117570 , st. Krasnogo Mayaka, 11 , 3, 200 1 pp. (accepted)Deterministic chaos without mysticism
Half a century ago in mathematics was opened deterministic (or dynamic) chaos. This event had a profound influence on the development of the nonlinear theory and research on the world as a whole, as mathematicians and scientists, and representatives of the humanities. Over the past from now been published great number of studies chaotic behavior of solutions to nonlinear differential equations used in modeling a wide variety of systems: from physico-chemical and biological to the socio-economic. And today, such studies have not lost relevance. What is deterministic chaos, what caused the high sensitivity of solutions of dynamical systems to initial conditions, whether the chaos typical feature large, including biological dynamic systems or whether it is a consequence of computational errors, whether related complexity of the chaotic attractor with complexity, with the dimension of the dynamical system ? In this paper, the author focuses on the issues to which the stockade theories raised to explain the nature of deterministic chaos, has been neglected - it is a numerical experiment. In an effort to understand the nature of dynamic chaos theorists often avoided by the fact that the discovery of this phenomenon was made in the numerical experiment with all the ensuing consequences associated primarily with errors. Did not decrease the value, beauty and originality of the mathematical theories of dynamical chaos, it must be admitted that no theory can not, must not exceed the accuracy of the experiment. Based on a thorough computational experiments by the author shows that the nature of deterministic chaos caused by the ultra-high density of trajectories in phase space. This high density is created bifurcation mechanism of the birth of an infinite number of periodic (and, in certain cases, quasi-periodic) trajectories, during which period some multiple of the original decision. This mechanism is universal and occurs in all types of non-linear dissipative differential equations, including partial differential equations and equations with retarded argument. The theoretical justification for establishing a single mechanism for the transition to dynamic chaos in these systems of differential equations, set conditions for the formation of dynamic chaos.
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