Temat: Global Stability - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Differential conditions to verify the Jacobian Conjecture
Autorzy:: Drużkowski, Ludwik
Tutaj, Halszka
Tematy:: jacobian conditions
global injectivity
global stability; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Powiązania:: https://bibliotekanauki.pl/articles/1311973.pdf Link otwiera się w nowym oknie
Opis:: Let F be a polynomial mapping of ℝ², F(O) = 0. In 1987 Meisters and Olech proved that the solution y(·) = 0 of the autonomous system of differential equations ẏ = F(y) is globally asymptotically stable provided that the jacobian of F is everywhere positive and the trace of the matrix of the differential of F is everywhere negative. In particular, the mapping F is then injective. We give an n-dimensional generalization of this result.
Dostawca treści:: Biblioteka Nauki

Artykuł

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Skocz do pozycji: 2.

Tytuł:: Global stability of positive standard and fractional nonlinear feedback systems
Autorzy:: Kaczorek, T.
Tematy:: global stability
fractional order
positive
nonlinear system; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/200986.pdf Link otwiera się w nowym oknie
Opis:: The global stability of positive continuous-time standard and fractional order nonlinear feedback systems is investigated. New sufficient conditions for the global stability of these classes of of positive nonlinear systems are established. The effectiveness of these new stability conditions is demonstrated on simple examples of positive nonlinear systems.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: On the global asymptotic stability problem and the Jacobian conjecture
Autorzy:: Drużkowski, L. M.
Tematy:: hipoteza jakobianu
global stability problem
Jacobian Conjecture; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/1839158.pdf Link otwiera się w nowym oknie
Opis:: In this survey, we recall the formulation of the problems and give a review of some nontrivial results in the area. Let F = (F1,...,Fn] : R^n - --> R^n be a C^1 map and let F'(x) and Jac F(x) = det F'(x) denote the Jacobian matrix and the jacobian of F at a point x belongs to R^n, respectively. The Global Asymptotic Stability Problem (GASP) reads as follows: Assume that F(0] = 0 and at any point x belongs to R^n all eigenvalues of F'(x) have negative real parts. Then consider the associated system of differential equations x'j(t] = Fj(x1(t), ...,Xn(t)), j = 1,...,n. The question is whether the solution x[t] = 0 is globally asymptotically stable. If n > 2, then the answer is negative (even if F is a a polynomial automorphism), so from now on (GASP) denotes (GASP) restricted to R^2. In 1963, Olech showed that under the (GASP) assumption (i. e., Jac F[x) > 0 and Trace F'(x) = [...] < 0 for any x belong to R^2) the conclusion of (GASP) is equivalent to the injectivity of F. In 1994, Fessler, and independently Gutierrez, proved the injectivity of F and, due to the above mentioned Olech's equivalence, gave the affirmative answer to the two-dimensional (GASP). Let K denote R or C, n > 1. The Jacobian Conjecture can be formulated as follows: If F = (F1, ... ,Fn) : K^n --> K^n is a polynomial map with a constant nonzero jacobian, then F is a polynomial automorphism (i.e. there exists F^-1 and F^-1 is also a polynomial map). Although the Jacobian Conjecture is still unsolved even in the case of n = 2, it is convenient, to consider the so called Generalized Jacobian Conjecture (for short (GJC)): the Jacobian Conjecture holds for every n > 1. We give a review of some interesting conditions equivalent to the Jacobian Conjecture, including Meisters and Olech's result on the existence of a poly-flow solution of the associated Ważewski equation x'(t) = [F'(x(t))]^-1 (a). We also present, a reduction of (GJC) to the case of F of degree 3 and of special forms, then some partial results, and (JC)'s relations with other problems.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: New sufficient conditions of global stability of nonlinear positive electrical circuits
Autorzy:: Kaczorek, Tadeusz
Tematy:: global stability
sufficient conditions
positive
nonlinear
electrical
circuit; Pokaż więcej
Wydawca:: Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Powiązania:: https://bibliotekanauki.pl/articles/378228.pdf Link otwiera się w nowym oknie
Opis:: The global stability of electrical circuits composed of positive linear parts and nonlinear static element with given characteristic and positive gain feedbacks is investigated. New sufficient conditions for the global stability of this class of nonlinear positive electrical circuits are established. These new stability conditions are demonstrated on simples examples of positive nonlinear electrical circuits.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Ananysis of a predator-prey model with disease in the predator species
Autorzy:: Radziński, Piotr
Foryś, Urszula
Tematy:: predator-prey model, eco-epidemiology, local and global stability; Pokaż więcej
Wydawca:: Polskie Towarzystwo Matematyczne
Powiązania:: https://bibliotekanauki.pl/articles/747413.pdf Link otwiera się w nowym oknie
Opis:: In the paper we analyse a diffusive predator-prey model with disease in predator species proposed by Qiao et al. (2014). In the original article there appears a mistake in the procedure of the model undimensionalisation. We make a correction in this procedure and show that some changes in the model analysis are necessary to obtain results similar to those presented by Qiao et al.We propose corrected conditions for global stability of one of existing equilibria -- disease free steady state and endemic state in the case without diffiusion as well as in the model with diffusion. On the basis of the corrected analysis we present new stability results.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 6.

Tytuł:: On the stability of some systems of exponential difference equations
Autorzy:: Psarros, N.
Papaschinopoulos, G.
Schinas, C.J.
Tematy:: difference equations
asymptotic behaviour
global stability
centre manifold
biological dynamics; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255823.pdf Link otwiera się w nowym oknie
Opis:: In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
Dostawca treści:: Biblioteka Nauki

Artykuł

na półce

Skocz do pozycji: 7.

Tytuł:: Global stability of positive discrete-time time-varying nonlinear feedback systems
Autorzy:: Kaczorek, Tadeusz
Sajewski, Łukasz
Tematy:: global stability
discrete-time
positive
feedback
time-varying
nonlinear system; Pokaż więcej
Wydawca:: Uniwersytet Technologiczno-Humanistyczny im. Kazimierza Pułaskiego w Radomiu
Powiązania:: https://bibliotekanauki.pl/articles/2058440.pdf Link otwiera się w nowym oknie
Opis:: The global stability of positive discrete-time time-varying nonlinear systems with time-varying scalar feedbacks is investigated. Sufficient conditions for the asymptotic stability of discrete-time positive time-varying linear systems are given. The new conditions are applied to discrete-time positive time-varying nonlinear systems with time-varying feedbacks. Sufficient conditions are established for the global stability of the discrete-time positive time-varying nonlinear systems with feedbacks.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: THREATS AND OPPORTUNITIES OF THE UKRAINIAN CRISIS: IMPACT ON THE GLOBAL STABILITY
Autorzy:: Krasota, Olena
Tematy:: Global Stability
the Ukrainian Crisis
crisis triggers
consequences of the crisis; Pokaż więcej
Wydawca:: Wyższa Szkoła Biznesu i Przedsiębiorczości w Ostrowcu Świętokrzyskim
Powiązania:: https://bibliotekanauki.pl/articles/483940.pdf Link otwiera się w nowym oknie
Opis:: The current Ukrainian crisis has various effects, both domestic and international, on the political, economic, and social agenda. The crisis is also inexorably linked to the issue of national security of many states and is undoubtedly changing the geopolitical situation in the world. This paper examines and compares the causes and implications of the two Ukrainian crises: the one of 2008 – 2009 and the most recent one of 2014 – 2015 by looking at their main triggers and consequences. The paper also intends to provide an insight on the potential threats and new opportunities for further development of the Ukrainian and global economies.
Dostawca treści:: Biblioteka Nauki

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na półce

Skocz do pozycji: 9.

Tytuł:: Global Financial Stability Assessment
Autorzy:: Frączek, Bożena
Wydawca:: Uni-edition GmbH, Berlin
Opis:: This paper focuses on issues of assessment of financial system stability. The author presents basic definition and meaning of financial stability as well as the concept of instability. However, special attention is paid to measurement of financial stability. In this paper is presented the possibility of assessment of financial stability through the prism of the instability which is easier to define and quantify. In many cases, the methods for measuring and assessing financial stability rely on finding and measuring the potential sources of risk that are the causes of instability. An example such approach could be method of assessing the global financial stability which was developed by the International Monetary Fund (IMF) Staff. It take into account four broad risks and two underlying conditions as the underlying factors affecting financial stability. The result of this method is the Global Financial Stability Map GFSM, which shows (graphical representation) the periodic improvement or deterioration in global financial stability through the prism of these factors.
Bożena Frączek
Dostawca treści:: Repozytorium Centrum Otwartej Nauki

Inne

na półce

Skocz do pozycji: 10.

Tytuł:: Global stability of nonlinear feedback systemswith positive descriptor linear parts
Autorzy:: Kaczorek, T.
Tematy:: global stability
positive descriptor
nonlinear
feedback system
globalna stabilność
nieliniowość
system informacji zwrotnej; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/200005.pdf Link otwiera się w nowym oknie
Opis:: The global (absolute) stability of nonlinear systems with negative feedbacks and positive descriptor linear parts is addressed. Transfer matrices of positive descriptor linear systems are analyzed. The characteristics u = f (e) of the nonlinear parts satisfy the condition k₁e ≤ f (e) ≤ k2e for some positive k₁, k₂. It is shown that the nonlinear feedback systems are globally asymptotically stable if the Nyquist plots of the positive descriptor linear parts are located in the right-hand side of the circles (– 1/k1, – 1/k2).
Dostawca treści:: Biblioteka Nauki

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