摘要
A.J. Schwartz [9] studied C2 dynamical system on compact and connected 2-dimensional manifold of class C2 and its minimal set Ω. We investigate the minimal set Ω of a 4-dimensional irreducible and competitive system. Under the condition divf≥0, we prove that Ω can only be a singular point or a closed orbit homeomorphic to S1. We also give the composition of limit set of such system in R4 and discuss the orbital behavior of a mathematical model in economics
A.J. Schwartz [9] studied C2 dynamical system on compact and connected 2-dimensional manifold of class C2 and its minimal set Ω. We investigate the minimal set Ω of a 4-dimensional irreducible and competitive system. Under the condition divf≥0, we prove that Ω can only be a singular point or a closed orbit homeomorphic to S1. We also give the composition of limit set of such system in R4 and discuss the orbital behavior of a mathematical model in economics
