Geometric approach for global asymptotic stability for three species competitive Gompertz models

This paper deals with the three dimensional competitive models with Gompertz growth in population dynamics. By using the geometric criterion and time average property to Gompertz models, a new criterion on the global asymptotical stability of the models is established. Furthermore, based on this criterion, a partial affirmative answer to Jiang–Niu–Zhu's open problems is given.