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1

Asymptotic stability of solutions for a diffusive epidemic model

Bouaziz Khelifa, Douaifia Redouane, Abdelmalek Salem

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

553--573

EN

The aim of this paper is to study the existence and the asymptotic stability of solutions for an epidemiologically emerging reaction-diffusion model. We show that the model has two types of equilibrium points to resolve the proposed system for a fairly broad class of nonlinearity that describes the transmission of an infectious disease between individuals. The model is analyzed by using the basic reproductive number R0 . Finally, we present the numerical examples simulations that clarifies and confirms the results of the study throughout the paper.

2

Stability of an Electrical System Used in Transport

Lungoci C., Gałuszka A.

Przegląd Elektrotechniczny

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2010

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R. 86, nr 5

64-68

EN

The paper deals with the stability aspects around the defined equilibrium point of an electrical system used in the traction regime of a DC motor. The electrical schema of the system is presented and the mathematical model is constructed. After defining the equilibrium point, the stability around it is analyzed, using several mathematical criteria. Implementing a modern controller, mathematical results are verified by computations and conclusions regarding the mathematical methods of stability analysis are done.

PL

Artykuł dotyczy stabilności wokół zdefiniowanego punktu równowagi modelu układu elektrycznego złożonego z dwóch źródeł energii, dwóch elementów sterujących, oraz obciążenia trakcyjnego. Zaprezentowano schemat takiego układu oraz skonstruowano odpowiadający mu model matematyczny. Zastosowano klasyczne kryteria do analizy zachowania się układu zlinearyzowanego wokół punktu równowagi.

3

Coupled analytical and numerical approach to uncovering new regulatory mechanisms of intracellular processes

Śmieja J.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 4

781-788

EN

The paper deals with the analysis of signaling pathways aimed at uncovering new regulatory processes regulating cell responses. First, general issues of comparing simulation and experimental data are discussed, and various aspects of data normalization are covered. Then, a model of a particular signaling pathway, induced by Interferon-\beta, is briefly introduced. It serves as an example illustrating how mathematical modeling can be used for inferring the structure of a regulatory system governing the dynamics of intracellular processes. In this pathway, experimental results suggest that a hitherto unknown process is responsible for a decrease in the levels of one of the important molecules used in the pathway. Then, equilibrium points of the model are analyzed, allowing the rejection of all but one explanation of the phenomena observed experimentally. Numerical simulations confirm that the model can mimic the dynamics of the processes in the pathway under consideration. Finally, some remarks about the applicability of the method based on an analysis of equilibrium points are made.

4

Constrained equilibrium point of maximal monotone operator via variational inequality

Przeworski M., Zagrodny D.

Journal of Applied Analysis

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1999

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Vol. 5, nr 1

147-152

EN

Herein a sufficient condition for q to belong to Q∩T-1(0) is provided, where Q is a weakly compact convex subset of a real reflexive Banach space E and T : E→→E* is a maximal monotone operator.

5

Punkty stałe odwzorowań wielowartościowych

Kryszewski W.

Roczniki Polskiego Towarzystwa Matematycznego. Seria 2: Wiadomości Matematyczne

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1998

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[Z] 34

9-30