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1
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Some classes of linear extentions of dynamical system on a torus.

100%
Morawiak M. R.
Mathematica Applicanda
|
2017
|
tom 45
|
nr 2
PL
W pracy przedstawiono metodę konstrukcji funkcji Lapunowa dla pewnych klas liniowych rozszerzeń układów dynamicznych na torusie. Pierwsza część artykułu zawiera wstęp teoretyczny, w którym przedstawione zostały m.in. defnicje funkcji Greena-Samojlenki oraz regularności układu równań różniczkowych. W drugiej części udowodniono twierdzenie, które umożliwia ustalenie regularności układu poprzez konstrukcję funkcji Lapunowa. Przedstawione zostały także przykłady, które pokazują jak wielkie możliwości daje to twierdzenie przy badaniu regularności układów równań różniczkowych.
EN
In this article was presented a method of construction of the Lyapunov function for some classes of linear extensions of dynamical systems. The article contains two parts. In the first part were presented the basic definitions as Green-Samoilenko function and regularity of the system. The second part contains the theorem, which allows to determine regularity of the system by using the Lyapunov function. In the second part are also two example, which show how to construct the Lyapunov function.
2
Content available remote

Model based analysis of signaling pathways

100%
Smieja J.
International Journal of Applied Mathematics and Computer Science
|
2008
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tom 18
|
nr 2
139-145
EN
The paper is concerned with application of mathematical modeling to the analysis of signaling pathways. Two issues, deterministic modeling of gene transcription and model-driven discovery of regulatory elements, are dealt with. First, the biological background is given and the importance of the stochastic nature of biological processes is addressed. The assumptions underlying deterministic modeling are presented. Special emphasis is put on describing gene transcription. A framework for including unknown processes activating gene transcription by means of first-order lag elements is introduced and discussed. Then, a particular interferon-β induced pathway is introduced, limited to early events that precede activation of gene transcription. It is shown how to simplify the system description based on the goals of modeling. Further, a computational analysis is presented, facilitating better understanding of the mechanisms underlying regulation of key components in the pathway. The analysis is illustrated by a comparison of simulation and experimental data.
3
Content available remote

Set arithmetic and the enclosing problem in dynamics

100%
Mrozek M., Zgliczyński P.
Annales Polonici Mathematici
|
2000
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tom 74
|
nr 1
237-259
EN
We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.
4
Content available remote

Random Dynamical Systems with Jumps and with a Function Type Intensity

100%
Kubieniec J.
Annales Mathematicae Silesianae
|
2016
|
tom 30
|
nr 1
63-87
EN
In paper [4] there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant λ. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when λ is not constant but a Lipschitz function.
5
Content available remote

Randomly connected dynamical systems - asymptotic stability

100%
Horbacz K.
Annales Polonici Mathematici
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1998
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tom 68
|
nr 1
31-50
EN
We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.
6
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Speeds of convergence of orbits of non-elliptic semigroups of holomorphic self-maps of the unit disk

100%
Bracci F.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2019
|
tom 73
|
nr 2
EN
We introduce three quantities related to orbits of non-elliptic continuous semigroups of holomorphic self-maps of the unit disk, the total speed, the orthogonal speed, and the tangential speed and show how they are related and what can be inferred from those.
7
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An unconditionally stable nonstandard finite difference method applied to a mathematical model of HIV infection

88%
Obaid H., Ouifki R., Patidar K.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 2
357-372
EN
We formulate and analyze an unconditionally stable nonstandard finite difference method for a mathematical model of HIV transmission dynamics. The dynamics of this model are studied using the qualitative theory of dynamical systems. These qualitative features of the continuous model are preserved by the numerical method that we propose in this paper. This method also preserves the positivity of the solution, which is one of the essential requirements when modeling epidemic diseases. Robust numerical results confirming theoretical investigations are provided. Comparisons are also made with the other conventional approaches that are routinely used for such problems.
8
Content available remote

Stability and stabilizability of a class of uncertain dynamical systems with delays

88%
Saadni M. S., Mehdi D.
International Journal of Applied Mathematics and Computer Science
|
2005
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tom 15
|
nr 3
321-329
EN
This paper deals with a class of uncertain systems with time-varying delays and norm-bounded uncertainty. The stability and stabilizability of this class of systems are considered. Linear Matrix Inequalities (LMI) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established.
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