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
md5=8f955869afeb23a2b2f473cf32bec74b" title="Click to view the MathML source">a1,
md5=7c566ad9ed0e6d26164c2e0a702057be" title="Click to view the MathML source">a2,
md5=a4799aeb699a30fa775abd016d434320" title="Click to view the MathML source">a3,
md5=99ff3bf90a5e37197502932804bd62a3" title="Click to view the MathML source">b1,
md5=2749d696ff017c52f12d39dc437a1b16" title="Click to view the MathML source">b2,
md5=867a949030655d4ff4c90881ffa2a8f9" title="Click to view the MathML source">b3 are real constants and the initial values conditions
md5=b99ce840cf43effad7b2681a256d557c" title="Click to view the MathML source">x0,
md5=6ac2315f925119f1818bc84ee2690c4a" title="Click to view the MathML source">y0 and
md5=c776f9d83bb80730f40d6737ab7bd605" title="Click to view the MathML source">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.