Stability Analysis for Discrete Dynamical Models using Mathematica

Stability is one of the most important concepts in Discrete Dynamical Systems. Behaviour of orbits in the neighbourhood of xed points can tell much about the behaviour of the system. Although in literature there are some computer codes to nd stability types of the xed points, they are generally lack of non-hyperbolic xed points for one-dimensional models and center manifolds for two-dimensional models. We give Mathematica codes for the stability of one-dimensional and two-dimensional models with non-hyperbolic cases and center manifolds. These codes will be useful for whom dealing with real world problems including population growth, compound interest and annuities, radioactive decay and pollution control etc

Stability Analysis of the Beddington Model with Allee Effect

We investigate the stability of the equilibria and the invariant manifolds of the host-parastoid model due to Beddington, Free, and Lawton [2] subject to the Allee effect