**THE LOTKA-VOLTERRA MODEL**
**Conclusion**

This model can be considered as a first approach to this kind of problem. Indeed, it is clear that this model has great limitations.First of all, even in the absence of sharks, the population of sardines wouldn't increase without any limit. Moreover, in the absence of sardines, sharks would probably disappear in a very short lap of time (in fact, they would probably find something else to eat!). At least, we can see that this model doesn't take into account any competition within species.The fact that the system never reaches a stable state, whatever the parameters and initial conditions are (except if the initial conditions equal a critical point) isn't also very realistic, as well as the fact that the solutions are perfectly periodic (even if cycles can be observed in reality). That's why, numerous modifications of this model exist and can make it more realistic.Nevertheless, this model is interesting to study as it can give quite easily a first overview about this kind of problems.