The permanence and periodic solution of a competitive system with infinite delay, feedback control, and Allee effect

oleh: Lei Shi, Hua Liu, Yumei Wei, Ming Ma, Jianhua Ye

Format: Article
Diterbitkan: SpringerOpen 2018-10-01

Deskripsi

Abstract This paper is devoted to study the permanence and periodic solution of a competitive system with infinite delay, feedback control, and the Allee effect. We derive sufficient conditions for the permanence and existence of a periodic solution in a competitive system with infinite delay, feedback control, and the Allee effect by using the differential inequality theory and constructing the Lyapunov function. We provide explicit estimates of the lower and upper bounds of the population density. This study reveals that the Allee effect plays an essential role in the permanence and increases the risk of population extinction.