DISCRETIZATION OF A MATHEMATICAL MODEL FOR
TUMOR-IMMUNE SYSTEM INTERACTION WITH
PIECEWISE CONSTANT ARGUMENTS
S. Kartal1, und and Fuat Gurcan2. DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WITH PIECEWISE CONSTANT ARGUMENTS, 1 (1):
1-9(Mai 2014)
Zusammenfassung
The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
%0 Journal Article
%1 noauthororeditor
%A Kartal1, Senol
%A and Fuat Gurcan2,
%D 2014
%E Mathematics, Applied
%E ), Sciences: An International Journal (MathSJ
%J DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WITH PIECEWISE CONSTANT ARGUMENTS
%K tag
%N 1
%P 1-9
%T DISCRETIZATION OF A MATHEMATICAL MODEL FOR
TUMOR-IMMUNE SYSTEM INTERACTION WITH
PIECEWISE CONSTANT ARGUMENTS
%U http://airccse.com/mathsj/papers/1114mathsj05.pdf
%V 1
%X The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
@article{noauthororeditor,
abstract = {The present study deals with the analysis of a Lotka-Volterra model describing competition between tumor
and immune cells. The model consists of differential equations with piecewise constant arguments and
based on metamodel constructed by Stepanova. Using the method of reduction to discrete equations, it is
obtained a system of difference equations from the system of differential equations. In order to get local
and global stability conditions of the positive equilibrium point of the system, we use Schur-Cohn criterion
and Lyapunov function that is constructed. Moreover, it is shown that periodic solutions occur as a
consequence of Neimark-Sacker bifurcation.
},
added-at = {2018-02-02T10:50:15.000+0100},
author = {Kartal1, Senol and and Fuat Gurcan2},
biburl = {https://www.bibsonomy.org/bibtex/2d0fef88f25c25b0f7c4afba46567b955/mathsj},
editor = {Mathematics, Applied and ), Sciences: An International Journal (MathSJ},
interhash = {d89115d812fccf0ea7d64fad2dce5d4d},
intrahash = {d0fef88f25c25b0f7c4afba46567b955},
issn = {2200-0011},
journal = {DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WITH PIECEWISE CONSTANT ARGUMENTS},
keywords = {tag},
language = {english},
month = may,
number = 1,
pages = {1-9},
timestamp = {2018-02-02T10:50:15.000+0100},
title = {DISCRETIZATION OF A MATHEMATICAL MODEL FOR
TUMOR-IMMUNE SYSTEM INTERACTION WITH
PIECEWISE CONSTANT ARGUMENTS},
url = {http://airccse.com/mathsj/papers/1114mathsj05.pdf},
volume = 1,
year = 2014
}