Neimark-Sacker, flip and transcritical bifurcation in a symmetric system
of difference equations with exponential terms
Abstract
In this paper, we study the conditions under which the following
symmetric system of difference equations with exponential terms:
\[ x_{n+1}
=a_1\frac{y_n}{b_1+y_n}
+c_1\frac{x_ne^{k_1-d_1x_n}}{1+e^{k_1-d_1x_n}},\]
\[ y_{n+1}
=a_2\frac{x_n}{b_2+x_n}
+c_2\frac{y_ne^{k_2-d_2y_n}}{1+e^{k_2-d_2y_n}}\]
where $a_i$, $b_i$, $c_i$, $d_i$, $k_i$, for $i=1,2$,
are real constants and the initial values $x_0$, $y_0$ are real
numbers, undergoes Neimark-Sacker, flip and transcritical bifurcation.
The analysis is conducted applying center manifold theory and the normal
form bifurcation analysis.
, 
