Local Stability in 3D Discrete Dynamical Systems: Application to a Ricker Competition Model

Abstract EN

A survey on the conditions of local stability of fixed points of three-dimensional discrete dynamical systems or difference equations is provided.

In particular, the techniques for studying the stability of nonhyperbolic fixed points via the centre manifold theorem are presented.

A nonlinear model in population dynamics is studied, namely, the Ricker competition model of three species.

In addition, a conjecture about the global stability of the nontrivial fixed points of the Ricker competition model is presented.