Alexandru Negrescu: On the stability of a predator-prey system of difference equations, 287-300

Abstract:

Using the centre manifold theory, we study the stability of the zero equilibrium of a system of two difference equations in the special case when one of the eigenvalues is equal to $1$ and the other eigenvalue has the absolute value less than $1$. The proposed system describes the dynamics of a single two-stage population that is practicing cannibalism.

Key Words: Difference equations, stability, centre manifold, cannibalism.

2010 Mathematics Subject Classification: Primary 39A30; Secondary 92D25.