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\title{\textbf{On the stability of some systems of exponential difference equations}}
\author{
\textbf{C. J. Schinas}\\
Department of Electrical and Computer Engineering\\
Democritus University of Thrace\\
Xanthi, 67100, Greece\\
e-mail: cschinas@ee.duth.gr\\}
\date{}
\maketitle

\begin{abstract}
In this paper  we  prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some  extensions of an one-dimensional biological model. The stability of these systems is investigated  in the special case when one of the eigenvalues has absolute value equal to 1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we  study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
\end{abstract}

\noindent \textbf{Keywords:} Difference equations, asymptotic behaviour, global stability, centre manifold, biological dynamics.

\vspace{4 mm}

\noindent \textbf{Co-authors:} G. Papaschinopoulos, N. Psarros


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