Wyniki wyszukiwania - BazTech

1

Existence of periodic positive solutions to nonlinear Lotka-Volterra competition

Benhadri Mimia, Caraballo Tomas, Zeghdoudi Halim

Opuscula Mathematica

|

2020

|

Vol. 40, no. 3

341--360

EN

We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating arguments. The main tool we use to obtain our result is the Krasnoselskii fixed point theorem. In particular, this paper improves important and interesting work [X.H. Tang, X. Zhou, On positive periodic solution of Lotka-Volterra competition systems with deviating arguments, Proc. Amer. Math. Soc. 134 (2006), 2967-2974]. Moreover, as an application, we also exhibit some special cases of the system, which have been studied extensively in the literature.

2

Zastosowanie uproszczonych charakterystyk częstotliwościowych do analizy kanału komunikacyjnego o zmiennych w czasie parametrach

Grzyb S., Orłowski P.

Pomiary Automatyka Kontrola

|

2014

|

R. 60, nr 5

317--320

PL

Celem niniejszej pracy jest przedstawienie możliwości zastosowania uproszczonych charakterystyk częstotliwościowych do analizy dyskretnego, niestacjonarnego modelu kanału komunikacyjnego. W pierwszej części artykułu zaprezentowano przegląd literatury oraz skrócony opis modelu matematycznego zatoru w sieciach komputerowych. W dalszej części pracy zapisano uogólniony model układu przy pomocy notacji operatorowej oraz zastosowano metodę do wyznaczania przybliżonych charakterystyk częstotliwościowych : amplitudowej i fazowej. W ostatniej części pracy wyznaczono dla przyjętych wartości macierzy układu uproszczone charakterystyki częstotliwościowe oraz przebiegi czasowe.

EN

The purpose of this paper is to present the possibilities of applying simplified frequency characteristics to the analysis of a discrete, non-stationary model of the communication channel. In the first part of the paper a review of the literature and a brief description of the mathematical model of congestion in computer networks are presented. The model is a linear, non-stationary, discrete dynamical system model that allows modelling of delays for any long duration. Such a model stored in the state variables enables the use of existing synthesis methods of control to avoid congestion and minimize their effects It is presented in equations (3)-(4). The following part delivers a generalized model of the system using the operator notation and the method determining the approximate frequency characteristics: amplitude and phase. It is described by relations (6)-(11). The last section is focused on delivering the simplified frequency characteristics. The results of calculations are presented in Fig. 2. The waveforms for the assumed values of the system matrix can be seen in Figs. 4, 5 and 6.

3

Model matematyczny kanału komunikacyjnego z zatorem w sieciach o zmiennych w czasie parametrach

Grzyb S., Orłowski P.

Pomiary Automatyka Kontrola

|

2013

|

R. 59, nr 11

1151--1154

PL

W pracy zaproponowano model matematyczny kanału komunikacyjnego z zatorem w węźle zatłoczonym, blokadami w węzłach pośrednich i parametrach zmiennych w czasie. Do opisu matematycznego wykorzystany jest liniowy, niestacjonarny, dyskretny model układu dynamicznego. Umożliwia on modelowanie opóźnień o dowolnie długim czasie trwania. Model taki zapisany w przestrzeni zmiennych stanu daje możliwość wykorzystanie istniejących metod syntezy sterowania do unikania zatorów i minimalizacji ich skutków. W pracy przedstawiono wyniki symulacji komputerowej opracowanego modelu.

EN

The paper presents a mathematical model of a communication channel with frequent congestion in intermediate nodes and time-varying delay. The first part of the paper is focused on description of some TCP protocol modifications, which adapted this protocol to be more effective and fault resistant in data transporting. This efficiency can be observed especially in an environment with frequent congestion and data loss. Regardless of the modifications of different transport protocols and the increase in the link bandwidth, to make full use of the computer network bandwidth it is necessary to develop some mechanisms allowing control of the transmitted packets at the network nodes. There is presented mathematical estimation of a real network segment built of many active network nodes and connections. This solution is a linear, non-stationary, discrete dynamical system model that allows modelling of delays for any long duration. Such a model stored in the state variables enables the use of existing synthesis methods of control to avoid congestion and minimize their effects. A block diagram of a network part with delay varying in time is presented in Fig. 1. A network part participating in packet forwarding may consists of a significant number of nodes. The last part of this paper presents the results of a simulation of the developed model in a form of the step response. The graph of this response is shown in Figs. 2 and 3.

4

Fixed points and stability in neutral nonlinear differential equations with variable delays

Ardjouni A., Djoudi A.

Opuscula Mathematica

|

2012

|

Vol. 32, no. 1

5-19

EN

By means of Krasnoselskii's fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307-3315], and also those of T.A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499-519] and B. Zhang [Nonlinear Anal. 63 (2005), e233-e242]. In the end we provide an example to illustrate our claim.