Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Podchukaev V. A. Mathematical model of dynamic chaos. Izv. Sarat. Univ. Math. Mech. Inform., 2012, vol. 12, iss. 4, pp. 27-31. DOI: 10.18500/1816-9791-2012-12-4-27-31

Published online: 
15.11.2012
Full text:
(downloads: 42)
Language: 
Russian
Heading: 
UDC: 
519.71
DOI: 
10.18500/1816-9791-2012-12-4-27-31

Mathematical model of dynamic chaos

Autors: 
Podchukaev Vladimir Anatolyevich, Saratov State Academy of Law
Abstract: 

The problem of analytical designing on the set mathematical model of dynamic system in space of states of mathematical model accompanying it in phase space is put and solved. It is shown, that the representing point of any decision of dynamic system of a general view in space of states conditions belongs to hypersphere with the displaced centre in phase space (or to central hypersphere of variable radius equivalent to it). Analytical representation of the centre of the displacement, an explaining origin of dynamic chaos by infinite ruptures of the second sort in co-ordinates of the centre of displacement is designed. It is shown, that these ruptures are generated by transition through a zero corresponding a component of a vector of states.

References: 
  1. Кузнецов С. П. Динамический хаос. М. : Физмат- лит, 2006. 294 с.
  2. Подчукаев В. А. Аналитические методы теории ав- томатичекого управления. М. : Физматлит, 2002. 256 с.
  3. Воеводин В. В., Кузнецов Ю. А. Матрицы и вы- числения. М. : Наука, 1984. 320 с.
  4. Пензов Ю. Е. Аналитическая геометрия. Саратов : Изд-во Сарат. ун-та, 1972. 364 c.
  5. Подчукаев В. А., Звягина А. С. Новое доказатель- ство гипотезы Ж. А. Пуанкаре // Докл. Академии воен. наук. 2009. № 5(40). С. 115–123.
  6. Бронштейн И. Н., Семендяев К. А. Справочник по математике для инженеров и учащихся втузов. М. : Наука, 1986. 544 с.