Busenberg, S.van den Driessche, P.2010-03-042010-03-0419902010-03-04http://hdl.handle.net/1828/2319A general criterion is established for showing the non-existence of periodic solutions and closed phase polygons of differential equations. Several known criteria of this type are obtained as special cases. An extension is obtained for functional differential equations and several applications are given for specific special cases including homogeneous systems and population dynamics equations.ennonexistence of periodic solutionsBendixson-Dulac criterionhomogeneous differential equationsfunctional differential equationspopulation dynamics systemstechnical reports (mathematics and statistics)Technical ReportDepartment of MathematicsDepartment of Mathematics and Statistics