Some remarks on five-dimensional survival models

• Autorzy: Kowgier H.
• Języki publikacji: EN

Abstrakty

EN

In the paper has been showed on selected models how survival probabilities of five populations change with an assumption that they reached an equilibrium level given by the same number of individuals. For this purpose, a comparative simulation was used made by means of SDE-SOLVER complete computer software package. Five- dimensional Lotka-Volterra models were examined: the deterministic type, the Gaussian type in a stochastic version, and the Gaussian-Poissonian type. In addition, by means of MATHEMATICA 4.0 computer programme, formulas were derived making determination of equilibrium stationary points of the five-dimensional Lotka-Volterra system possible. Also, a stability analysis of the received equilibrium points was made in selected cases. As shown by the practice, application area for the given models is rather wide (see also [4]).

Słowa kluczowe

EN

computer simulation; five-dimensional Lotka-Volterra models; equilibrium stationary points; survival probabilities

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Foundations of Computing and Decision Sciences
• Rocznik: 2011
• Tom: Vol. 36, No. 3-4
• Strony: 243--258
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kowgier H.

• Department of Econometrics and Statistics, Faculty of Economics and Management, University of Szczecin, Mickiewicza 64, 71-101 Szczecin, Poland

Bibliografia

• [1] Elliot R.J., Stochastic Calculus and Applications, Springer-Verlag, New York, 1980.
• [2] Janicki A., Izydorczyk A, Komputerowe metody w modelowaniu stochastycznym, WNT, Warszawa, 2001.
• [3] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Springer-Verlag, New York, 1980.
• [4] Kowgier H., On a Certain Stochastic Optimization Related to the Black-Scholes Model, Polish Journal of Environmental Sudies, Vol. 16, No. 4A, HARD, Olsztyn, 2007.
• [5] Kowgier H., On Four-Dimensional Lotka-Volterra Models, Polish Journal of Environmental Studies, Vol.18. No.3B, HARD, Olsztyn, 2009.
• [6] Muszyński J., Myszkis A.D.: Równania różniczkowe zwyczajne, PWN, Warszawa, 1984.
• [7] Schuster H. G., Deterministic Chaos, Copyright by VCH Verlagsgesellschaft, 1988.
• [8] Sobczyk K., Stochastic Differential Equations with Applications to Physics and Engineering, Copyright © Kluwer Academic Publishers B.V., 1991.