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
a1,
a2,
a3,
b1,
b2,
b3 are real constants and the initial values conditions
x0,
y0 and
z0 are real numbers. The stability of those systems in the special case when one of the eigenvalues has absolute value equal to 1 and the other two eigenvalues have absolute value less than 1, using centre manifold theory, is investigated.