The C1 Property of Carrying Simplices for a Class of Competitive Systems of ODEs

In this paper we consider a class of dissipative competitive systems of ODEs on the nonneptive orthant C. We assume, among others, that the system restricted to any face of C is weakly persistent. It is proved that the carrying simplex is a C1 manifold-with-corners. In the proof we analyze the asymptotic behavior of the linearization of the original system