DISCRETIZATION OF A MATHEMATICAL MODEL FOR TUMOR-IMMUNE SYSTEM INTERACTION WITH PIECEWISE CONSTANT ARGUMENTS
DISCRETIZATION OF A MATHEMATICAL MODEL FOR
TUMOR-IMMUNE SYSTEM INTERACTION WITH
PIECEWISE CONSTANT ARGUMENTS
Senol Kartal1 and Fuat
Gurcan2
1Department of Mathematics, Nevsehir Hacı Bektas
Veli University, Nevsehir, Turkey 2Department of Mathematics, Erciyes
University, Kayseri, Turkey 2 Faculty of Engineering and Natural
Sciences, International University of Sarajevo, Hrasnicka cesta 15, 71000,
Sarejevo, BIH
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.
KEYWORDS
piecewise constant arguments; difference equation; stability;
bifurcation.
SOURCE URL
VOLUME LINK
.png)
Comments
Post a Comment