PERMANENCE AND POSITIVE BOUNDED SOLUTIONS OF KOLMOGOROV PREDATOR-PREY SYSTEM

Our main purpose is to present some criteria for the perma- nence and existence of a positive bounded solution of Kolmogorov predator- -prey system. Under certain conditions, it is shown that the system is per- manent and there exists a solution which is dened on the whole R and whose components are bounded from above and from below by positive constants. where aik(t); cik(t); djk(t); ejk(t), bi(t); rj(t) are continuous and bounded on R. A fundamental ecological question associated with the study of multispecies population interactions is the long-term coexistence of the involved popula- tions. Such questions also arise in many other situations (see (3)). Mathemat- ically, this is equivalent to the so-called permanence of the populations. We