Well-posedness of a ratio-dependent Lotka–Volterra system with feedback control

Boundary Value Problems

Yuqian Zhou¹  Changyou Wang¹  Rui Li²  Yonghong Li³ 

[1] College of Applied Mathematics, Chengdu University of Information Technology;College of Automation, Chongqing University of Posts and Telecommunications;College of Science, Chongqing University of Posts and Telecommunications;

关键词: Predator-prey system;    Feedback control;    Permanence;    Attractivity;    Periodic solution;   

DOI  :  10.1186/s13661-018-1039-2

来源: DOAJ

【 摘 要 】

Abstract The main purpose of this article is to consider a Lotka–Volterra predator–prey system with ratio-dependent functional responses and feedback controls. By using a comparison theorem and constructing a suitable Lyapunov function as well as developing some new analysis techniques, we establish a set of easily verifiable sufficient conditions which guarantee the permanence of the system and the global attractivity of a positive solution for the predator–prey system. Furthermore, some conditions for the existence, uniqueness, and stability of a positive periodic solution for the corresponding periodic system are obtained by using the fixed point theory and some new analysis method. In additional, some numerical solutions of the equations describing the system are given to verify that the obtained criteria are new, general, and easily verifiable.

【 授权许可】

Unknown