Transformation of polynomial differential systems in the positive orthant
Résumé
We study polynomial n-dimensional differential systems when the (n-dimensional) variable keeps the same sign; that is, the system is defined inside one of the orthants. We show it is always possible to transform the system into a quadratic Lotka-Volterra type system. We give several tools to study these last systems; we deduce indications on the global behaviour of the original system.