  Mathematical modelling and numerical simulations of interaction populations
are crucial topics in systems biology. The interactions of ecological models
may occur among individuals of the same species or individuals of different
species. Describing the dynamics of such models occasionally requires some
techniques of model analysis. Choosing appropriate techniques of model analysis
is often a difficult task. We define a prey (mouse) and predator (cat) model.
The system is modelled by a pair of non-linear ordinary differential equations
using mass action law, under constant rates. A proper scaling is suggested to
minimize the number of parameters. More interestingly, we propose a homotopy
technique with n expanding parame- ters for finding some analytical approximate
solutions. Furthermore, using the local sensitivity method is another important
step forward in this study because it helps to identify critical model
parameters. Numerical simulations are provided using Matlab for different
parameters and initial conditions.
