Introduction

Many of the most intersting dynamics in the biological world have to do with interactions between species. Mathematical models are required if we hope to simulate these dynamics.
One of the first models to incorprate interactions between predators and preys was proposed in 1925 by the American biophysicist Alfred Lotka and the Italian mathematician Vito Volterra.
This model forms the basis of many models used today in the analysis of poulation dynamics.
Here we deal with two species models, but it should be kept in mind that Lotka-Volterra models may be extended to much more species in interraction. Moreover these equations can be used for multi species competition models.
In chapter 1 we are interested in the basic model of Lotka-Volterra, and analyse the equilibrium point.
In chapter 2 we used a close model involving a logistic growth.