Neimark-Sacker, flip and transcritical bifurcation in a symmetric system
of difference equations with exponential terms
In this paper, we study the conditions under which the following
symmetric system of difference equations with exponential terms:
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.