Global Stability of a Competitive Model with State-Dependent Delay

• DOI: 10.1007/s10884-015-9475-5
• Publication Date: 2015-08-04T09:41:48Z
• Authors: Yunfei Lv; Rong Yuan; Yongzhen Pei; Tongtong Li
• Keywords: Stability theory; Population model

This article deals with a stage-structured model with state-dependent delay which is assumed to be an increasing function of the population density with lower and upper bound. Firstly, according to the principle of linearized stability (Theorem 3.6, Hartung et al. in Handbook of differential equations: ordinary differential equations, 2006), we study the local stability of system in combination with the positivity and boundedness of solutions. By using the comparison principle obtained and an iterative method, the global stability of the equilibria is completely analyzed. Our results show how the interaction between interspecific and intraspecific competition affects the coexistence of both species.