Nonnegative Solutions of Systems with Fractional-Rational Right-Hand Sides and Localization of Attractors

Abstract: For autonomous systems of ordinary differential equations with fractional-rationalright-hand sides for which the nonnegative orthant is positively invariant, sufficient conditions forthe existence of nontrivial localizing sets corresponding to coordinate functions are found.Conditions for the existence of an attractor for such systems are established, and its position isinvestigated. For systems modeling population dynamics, the relationship of the results obtainedhere with the conditions for the extinction or survival of populations is indicated.