We study the stability of the zero equilibrium of the following system of difference equations, which is a natural extension of an one-dimensional biologicalmodel:
where
source">a1,
source">a2,
source">a3,
32804bd62a3" title="Click to view the MathML source">b1,
source">b2,
source">b3 are real constants and the initial values conditions
source">x0,
source">y0 and
source">z0 are real numbers. The stability of those systems in the special case when one of the eigenvalues has ab
solute value equal to 1 and the other two eigenvalues have ab
solute value less than 1, using centre manifold theory, is investigated.