[Электронный ресурс]. - Электрон. дан. (499 Кб) : диссертации на соискание ученой степени кандидата-физико математических наук (перевод на английский язык) / А.Н. Горбань. - Электрон. дан. (499 Кб). - [Б. м. : б. и.], 1997. - Б. ц.
Аннотация: The paper gives the systematic analysis of singularities of transition processes in general dynamical systems. Dynamical systems depending on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ? of relaxation. This system of times contains: the time before the first entering of the motion into ?-neighbourhood of the limit set, the time of final entering in this neighbourhood and the time of stay of the motion outside the ?-neighbourhood of the limit set. The singularities of relaxation times as functions of (x0; k) under fixed ? are studied. A classification of different bifurcations (explosions) of limit sets is performed. The bifurcations fall into those with appearance of new limit points and bifurcations with appearance of new limit sets at finite distance from the existing ones. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The peculiarities of transition processes under perturbations are studied. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for smooth two-dimensional structural stable systems.
http://icm.krasn.ru/refextra.php?id=2806
Доп.точки доступа:
Gorban A.N.
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Singularities of Transition Processes In Dynamical Systems
[Electronic resource]. - Electronic text data : статья / A. N. Gorban. - Electronic text data // Electronic Journal of Differential Equations. - 1997. - Translation of Candidat (Ph.D) Thesis
Аннотация: The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ε of the relaxation. The singularities of relaxation times as functions of (x0,k) under fixed ε are studied. The classification of different bifurcations (explosions) of limit sets is performed. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.
Полный текст
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Горбань, Александр Николаевич
Аннотация: The paper gives a systematic analysis of singularities of transition processes in dynamical systems. General dynamical systems with dependence on parameter are studied. A system of relaxation times is constructed. Each relaxation time depends on three variables: initial conditions, parameters k of the system and accuracy ε of the relaxation. The singularities of relaxation times as functions of (x0,k) under fixed ε are studied. The classification of different bifurcations (explosions) of limit sets is performed. The relations between the singularities of relaxation times and bifurcations of limit sets are studied. The peculiarities of dynamics which entail singularities of transition processes without bifurcations are described as well. The analogue of the Smale order for general dynamical systems under perturbations is constructed. It is shown that the perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for the Morse-Smale systems.
Полный текст
Держатели документа:
ИВМ СО РАН : 660036, Красноярск, Академгородок, 50, стр.44
Доп.точки доступа:
Горбань, Александр Николаевич
PARAMETRIC ANALYSIS OF KINETIC-MODELS .2. INFLUENCE OF THE FORM OF BUFFER STEPS
[Text] / T. P. PUSHKAREVA, V. I. BYKOV // React. Kinet. Catal. Lett. - 1992. - Vol. 48, Is. 1. - P265-271, DOI 10.1007/BF02070095. - Cited References: 2
. - ISSN 0133-1736
РУБ Chemistry, Physical
Кл.слова (ненормированные):
Catalysis -- Mathematical models -- Bifurcations -- Buffer steps -- Parametric analysis -- Reaction oscillations -- Reaction kinetics
Аннотация: A series of mechanisms allowing oscillations and differring in the form of their buffer steps (step 3) (1) Z half arrow right over half arrow left X, (2) X + 2Z --> 3Z, (3) 2Z half arrow right over half arrow left 2Y (3') 2Z half arrow right over half arrow left Y, (3'') Z + X half arrow right over half arrow left Y has been considered. Detailed parametric analysis of local bifurcations of steady states and the influence of buffer steps on the oscillation characteristics are discussed.
WOS,
Scopus
Держатели документа:
Computing Center, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
PUSHKAREVA, T.P.; BYKOV, V.I.; Быков, Валерий Иванович
Кл.слова (ненормированные):
Catalysis -- Mathematical models -- Bifurcations -- Buffer steps -- Parametric analysis -- Reaction oscillations -- Reaction kinetics
Аннотация: A series of mechanisms allowing oscillations and differring in the form of their buffer steps (step 3) (1) Z half arrow right over half arrow left X, (2) X + 2Z --> 3Z, (3) 2Z half arrow right over half arrow left 2Y (3') 2Z half arrow right over half arrow left Y, (3'') Z + X half arrow right over half arrow left Y has been considered. Detailed parametric analysis of local bifurcations of steady states and the influence of buffer steps on the oscillation characteristics are discussed.
WOS,
Scopus
Держатели документа:
Computing Center, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
PUSHKAREVA, T.P.; BYKOV, V.I.; Быков, Валерий Иванович