Wyniki wyszukiwania - Biblioteka Nauki

1

Versal deformations of $D_q$-invariant 2-parameter families of planar vector fields

100%

Świrszcz G.

Annales Polonici Mathematici

|

1995

|

tom 62

|

nr 3

265-281

EN

The paper deals with 2-parameter families of planar vector fields which are invariant under the group $D_q$ for q ≥ 3. The germs at z = 0 of such families are studied and versal families are found. We also give the phase portraits of the versal families.

2

The Generalized Saddle-Node Bifurcation of Degenerate Solution

100%

Liu P. , Wang Y.-W.

Commentationes Mathematicae

|

2005

|

tom 45

|

nr 2

EN

In this paper we discuss the bifurcation problem for the abstract operator equation of the form $F (u, \lambda) = \theta$ with a parameter $\lambda$, where $F\colon X \times R \to Y$ is a $C^1$ mapping, $X, Y$ are Banach spaces. By the bounded linear generalized inverse $A^+$ of $A = F_u (u_0 , \lambda_0 )$, an abstract bifurcation theorem for the case $\operatorname{dim}N (F_u (u_0 , \lambda_0 )) \geq \operatorname{codim} R(F_u (u_0 , \lambda_0 )) = 1$ has been obtained.

3

Generic saddle-node bifurcation for cascade second order ODEs on manifolds

88%

Medveď M.

Annales Polonici Mathematici

|

1998

|

tom 68

|

nr 3

211-225

EN

Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.

4

Bifurcations in an electro-vibroimpact system with friction

88%

Ho J. H. , Woo K. C.

|

2008

|

tom Vol. 46 nr 3

511-520

EN

Bifurcation phenomena of an electro-vibroimpact system have been investigated by means of numerical analysis. It has been shown that the system undergoes transition from chaotic motion to periodic motion as the control frequency of the solid state relay (one of the system parameters) varies. A close co-relationship with an experimental bifurcation diagram has been observed. Periodic motion has been identified to yield better system performance over chaotic motion. The foundation of implementing an optimal feedback control strategy is established.

PL

W artykule przedstawiono zjawiska bifurkacyjne zachodzące w układzie maszyny elektro-wibracyjnej z uderzeniami za pomocą analizy numerycznej. Pokazano, że układ wykazuje przejście z ruchu chaotycznego do periodycznego przy zmianach częstości sterującej (jednego z parametrów układu) pracą bezstykowego przekaźnika mocy. Zaobserwowano bliską współzależność otrzymanych diagramów bifurkacyjnych z wynikami doświadczalnymi. Stwierdzoną lepszą wydajność urządzenia dla zakresu parametrów zapewniających ruch periodyczny. Sformułowano podstawy do określenia i wdrożenia optymalnej strategii sterowania układu opartej na sprzężeniu zwrotnym.

5

Dimension Reduction and Domains of Attraction of Nonlinear Dynamical Systems

88%

Hochlenert D.

|

tom Vol. 35, No. 4

32-48

EN

The appropriate modeling of technical systems usually results in dynamical systems having many or even an infinite number of degrees of freedom. Moreover, nonlinearities play an important role in many applications, so that the arising systems of nonlinear differential equations are difficult to analyze. However, it is well known that the asymptotic behavior of some high dimensional systems can be described by corresponding systems of much smaller dimension. The present paper deals with the dimension reduction of nonlinear systems close to a bifurcation point. Using the ideas of normal form theory, the asymptotic dynamics of the system is extracted by a nonlinear coordinate transformation. The solutions of the reducedordsr system are analyzed analytically with respect to their stability and their domains of attraction. Furthermore, the inverse of the near-identity transformations is used to construct adapted Lyapunov functions for the original system to estimate the attractors of the solutions as well. The procedure is applied to the Duffing equation and the equations of motion of a railway wheelset and compared with numerical solutions.

6

Finite element analysis of the hemodynamics in the human carotid artery bifurcation

88%

Postelnicu A. , Minea D.

|

2000

|

tom Vol. 5, no 4

759-772

EN

The present paper brings new lights on blood flow patterns in rigid artery bifurcation models, differing in angle of bifurcation. Using the ANSYS 5.4/FLOTRAN package, a numerical analysis in two dimensions was performed, under physiologically relevant flow conditions. For two bifurcation models, one with large angle the other with a small one, the distributions of velocities, shear-stress and pressure in the domain of carotid artery bifurcation have been obtained. It is argued and proved that the vascular geometry at the bifurcation level represents a risk factor in atherogenesis, the relevant factors for this process being the flow separation, reversal flow regions and wall shear stress.

7

Numerical Analysis of Flow Bifurcations in a Closed-Off Channel

75%

Sobieski W.

|

2009

|

tom nr 12

259-271

EN

This article describes the results of numerical simulations of fluid flow in a closed-off channel with a plain nozzle. Simulations were performed with the application of the Finite Volume Procedure in the Multi Flower 2D non-commercial application. The main objective of the study was to determine the effect of channel geometry on flow structure. A total of 27 system configurations were analyzed for nine geometry variants and three pressure variants in the feed nozzle. Based on the obtained results, five main flow types were determined, including Hopf bifurcation structures. This paper presents simulation results and it analyzes the observed flow types in view of general bifurcation conditions. The final section of this paper describes the attempts at repeating numerical simulations with the use of the FLUENT commercial application. This simulation makes a reference to an earlier experiment carried out by DYBAN et al. (1971), and it is a continuation of previous research described in detail by BADUR, SOBIESKI (2001).

PL

Artykuł przedstawia badania numeryczne przepływu płynu przez ślepo zakończony kanał z umieszczoną wewnątrz prostą dyszą zasilającą. Symulacje wykonano metodą objętości skończonych z zastosowaniem niekomerycjnego pakietu Multi Flower 2D. Podstawowym celem badań było określenie wpływu geometrii kanału na strukturę przepływu. Badania wykonano dla 27 konfiguracji układu - dziewięciu wariantów geometrii i trzech wariantów ciśnień w dyszy zasilającej. Analiza wyników doprowadziła do wytypowania pięciu głównych struktur przepływowych, w tym również struktur o charakterze bifurkacji Hopfa. W pracy zestawiono wyniki symulacji w formie zbiorczej, a także przeanalizowano zaobserwowane typy przepływów pod kątem ogólnych uwarunkowań bifurkacji. W końcowej części opisano próby powtórzenia symulacji numerycznych za pomocą komercyjnego pakietu FLUENT. Badania symulacyjne nawiązują do eksperymentu (DYBAN et al. 1971) i są kontynuacją wcześniejszych prac, opisanych szczegółowo w artykule (BADUR, SOBIESKI 2001).

8

Bifurcation and chaos in drive systems

75%

Kratochvil C. , Houfek L. , Houfek M. , Krejsa J.

|

2006

|

tom z. 31

89-94

EN

The paper is focused on analysis of dynamic properties of controlled drive systems. It describes the possible ways of stability analysis. Paper is also focused on bifurcation of steady states and possible oceurence of chaotic behavior.

9

A comparison of center-manifold reduction of nonlinear integro-differential flutter equation and approximate set of ordinary differential equations

75%

Grzędziński J.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

|

1999

|

tom nr 9

7-14

EN

A nonlinear integro-differential flutter equation of a thin airfoil placed in an incompressible flow is solved by two different methods. The first method involves the center-manifold reduction and gives the asymptotic limit cycle amplitude and frequency in terms of power series expansions. The second method replaces the integro-differential equation by an approximate set of first-order ordinary differential equations which are solved by using bifurcation and continuation software package. A comparison of these two methods shows that the domain of a good agreement between them varies significantly depending on the parameters of the problem.

10

Metody numeryczne wyznaczania zakresów drgań podharmonicznych i chaotycznych

75%

Łuczko J.

|

2006

|

tom R. 103, z. 11-M

39-62

PL

W niniejszym artykule zaproponowano analityczno-numeryczne metody badania wpływu parametrów na charakterystyki dynamiczne układu oraz typ wzbudzanych drgań. Do badania zjawiska rezonansu podharmonicznego zastosowano analizę bifurkacyjną. Do wyznaczania zakresów drgań podharmoniczych, prawie okresowych i chaotycznych zastosowano metody numerycznego całkowania oraz analizy widmowej. Na przykładach oscylatorów typu Duffinga i Van der Pola pokazano możliwości metod do analizy układów nieliniowych.

EN

In the paper some analytical and numerical methods of investigation of non-linear systems were proposed. The post-bifurcation analysis was used to explain the phenomenon of sub-harmonic resonance. Zones of the sub-harmonic, quasi-periodic and chaotic vibrations were estimated by the methods of numerical integration and spectrum analysis. The approach was illustrated by numerical examples which consider the forced vibration of the Duffing and Van der Pol oscillators.

11

On bifurcation of extremals of one class of variational calculus tasks with multiparametrical perturbation

75%

Ashimov A. A. , Sagadiyev K. A. , Borovskiy Y. V. , Iskakov N. A. , Ashimov A. A.

|

2007

|

tom Vol. 33, no 4

85-91

EN

A bifurcation of the extremals of one variational calculus task on the choice of optimum laws for a parametrical regulation of a dynamic system in the given finite set of algorithms is under consideration. An assertion about conditions sufficient for the existence of the specified variational calculus task's solution is formulated and proved. A defintion of a bifurcation point under a multiparametrical perturbation of the given variational calculus task is provided. An assumption on the sufficient conditions for its existence is formulated and proved. A numerical algorithm of calculating a bifurcation value of a parameter is offered. The findings are illustrated by the example of calculated set of bifurcation points of the extremals of the variational calculus task on the choice of optimum laws for a parametrical regulation of the market economy mechanisms in the given finite set of algorithms on the basis of a mathematical model of the economic system of the country, which is suggested in order to investigate the influence of state expenditures upon its evolution. The research findings could be applied to the process of development and implementation of an effective state economic policy.

12

Flexible and Robust Patterning by Centralized Gene Networks

75%

Vakulenko S. , Radulescu O.

|

2012

|

tom Vol. 118, nr 4

345-369

EN

We investigate the possibility of programming arbitrarily complex space-time patterns, and transitions between such patterns, by gene networks. We consider networks with two types of nodes. The v-nodes, called centers, are hyperconnected and interact one to another via u-nodes, called satellites. This centralized architecture realizes a bow-tie scheme and possesses interesting properties. Namely, this organization creates feedback loops that are capable to generate any prescribed patterning dynamics, chaotic or periodic, or stabilize a number of prescribed equilibrium states. We show that activation or silencing of a node can sharply switch the network dynamics, even if the activated or silenced node is weakly connected. Centralized networks can keep their flexibility, and still be protected against environmental noises. Finding an optimized network that is both robust and flexible is a computationally hard problem in general, but it becomes feasible when the number of satellites is large. In theoretical biology, this class of models can be used to implement the Driesch-Wolpert program, allowing to go from morphogen gradients to multicellular organisms.

13

Local properties of the solution set of the operator equation in Banach spaces in a neighbourhood of a bifurcation point

75%

Janczewska J.

Open Mathematics

|

2004

|

tom 2

|

nr 4

561-572

EN

In this work we study the problem of the existence of bifurcation in the solution set of the equation F(x, λ)=0, where F: X×R k →Y is a C 2-smooth operator, X and Y are Banach spaces such that X⊂Y. Moreover, there is given a scalar product 〈·,·〉: Y×Y→R 1 that is continuous with respect to the norms in X and Y. We show that under some conditions there is bifurcation at a point (0, λ0)∈X×R k and we describe the solution set of the studied equation in a small neighbourhood of this point.

14

Ambiguities in input-output behavior of driven nonlinear systems close to bifurcation

75%

Reit M. , Berens M. , Mathis W.

|

nr 2

15

Zjawisko synchronizacji drgań i wzbudzenia asynchronicznego w oscylatorze Lienarda

63%

Łuczko J.

|

2008

|

tom R. 105, z. 1-M

193-201

PL

W niniejszym artykule zbadano wpływ parametrów oscylatora Lienarda na charakter wzbudzanych drgań. Do wyznaczania zakresów drgań podharmonicznych i prawie okresowych zastosowano metody numerycznego całkowania skojarzone z metodami analizy widmowej. W celu wyjaśnienia zjawiska synchronizacji drgań i wzbudzenia asynchronicznego sporządzono również diagramy bifurkacyjne. Ruch układu zilustrowano na płaszczyznach fazowych. W przypadku niejednoznacznych rozwiązań wyznaczono zbiory przyciągania.

EN

The paper has investigated the influence of the parameters of Lienard's oscillator on the character of the excited vibrations. Methods of numerical integration combined with spectral analysis have been used to determine the regions of subharmonic and quasi-periodic vibration regimes. Bifurcation diagrams have been used to explain the phenomenon of vibration synchronization and that of the asynchronic excitation of vibrations. The motion of the studied system has been illustrated in phase planes. In the case of non-unique solutions an analysis has been performed to determine the basins of attraction.

16

Możliwości wykorzystania elementów teorii bifurkacji do analizy pracy systemu elektroenergetycznego

63%

Małyszko O.

|

2008

|

tom R. 84, nr 7

154-157

PL

W artykule zasygnalizowano możliwość wykorzystania elementów teorii bifurkacji do kontroli pracy systemu elektroenergetycznego. Pokazano to na dwóch przykładach. W pierwszym przedstawiono metodę kontroli stabilności systemu poprzez pomiar największego wykładnika Lapunowa natomiast w drugim przykładzie opisano metodę wyznaczania on-line impedancji zwarciowej systemu również z wykorzystaniem wykładników Lapunowa.

EN

The paper presents a method of control of power system stability and a method of estimation on-line of power system impedance. These methods are shown as an example of possibility of bifurcation theory elements utilization for analysis of power system. Both methods based on using Lyapunov exponents.

17

Dynamika nieliniowego modelu konkurencji doskonałej z heterogenicznymi oczekiwaniami po stronie podażowej

63%

Kruszewski R.

Przegląd Zachodniopomorski

|

2013

|

nr 3/1

169-182

EN

We investigate the dynamics of the proposed demand-supply model with heterogeneous expectations, a linear demand curve, and nonlinear supply curve. The possible price behaviour is be described. W investigate, how the dynamics of the model depend on parameters.

18

Bistability phenomenon in fluid dynamic

63%

Tesar V.

|

1999

|

tom Z. 44 (221)

161-170

EN

Several interesting fluid flow fields exhibit lack of unicity: instead of a single solution, they have two stable regimes - with an unstable equilibrium between them, which however becomes stable at low Reynolds numbers. A particular example is a trapped vortex ring held by a special cavity on periphery of a fluid jet. Dynamic models of this bistability show interesting bifurcation properties, period doubling phenomenon and existence of chaotic regimes indicating that this may be an important underlying effect for turbulence.

PL

Kilka interesujących obszarów przepływu płynu wykazuje brak jednoznaczności: zamiast pojedynczego rozwiązania posiadają one dwa stabilne stany - z niestabilną równowagą między nimi, która jednakże staje się stabilna przy niskich liczbach Reynoldsa. Szczególnym przykładem jest stabilizujący pierścień wirowy otrzymany przez specjalne wgłębienie na obrzeżu strumienia płynu. Model dynamiczny tej bistabilności wykazuje interesujące rozgałęziające własności, okresowe zjawisko zdwajania i istnienie stanów chaotycznych powoduje, że może to być istotny wspomagający efekt turbulencji.

19

Kontrola pracy systemu elektroenergetycznego z wykorzystaniem elementów teorii bifurkacji

63%

Małyszko O.

|

2012

|

tom R. 80, nr 8

37-40

PL

Przedstawiono możliwość zastosowania w praktyce elementów teorii bifurkacji i chaosu do analizy i kontroli pracy systemu elektroenergetycznego.

EN

The paper presents a possibility of practical application of bifurcation and chaos theory components in analysis and control of operation of electric power system.

20

Czy problem bifurkacji w mechanice gruntów jest ważny?

63%

Sikora Z.

|

2007

|

tom z. 111

373-382

PL

W artykule przedstawiono zastosowanie hypoplastycznego prawa konstytutywnego do przedstawienia pewnej klasy zagadnień związanych z bifurkacją rozwiązań zagadnień brzegowych. Sformułowano podstawowe twierdzenia i definicje teorii bifurkacji, za pomocą których, w dyskretnych punktach kwadratury Gaussa, istnieje możliwość stwierdzenia występowania punktów bifurkacji. Wykrycie punktu bifurkacji w obszarze rozwiązania pozwala określić warunki tworzenia się lokalizacji deformacji.

EN

A general form of hypoplastic constitutive equation utilized for formulation of specific bifurcation theory is presented. Some important theorems and definitions of possible bifurcation point and bifurcated solutions are drawn up. The procedure of bifurcation points presented in its computational form can be realized at least at the discrete Gauss points at which the localization of deformation might be possible. The relevancy of the bifurcation problem is underlined and its applicability m finite element methods is appreciated.