Dynamics in a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays

Advances in Difference Equations

Hong-Li Li¹  Ahmadjan Muhammadhaji¹  Azhar Halik¹ 

[1] College of Mathematics and System Sciences, Xinjiang University, Shengli Road, 830046, Urumqi, P.R. China;

关键词: Ratio-dependent competitive-competitive-cooperative system;    Time delay;    Permanence;    Feedback control;    Global attractivity;   

DOI  :  10.1186/s13662-021-03364-2

来源: Springer

【 摘 要 】

This study investigates the dynamical behavior of a ratio-dependent Lotka–Volterra competitive-competitive-cooperative system with feedback controls and delays. Compared with previous studies, both ratio-dependent functional responses and time delays are considered. By employing the comparison method, the Lyapunov function method, and useful inequality techniques, some sufficient conditions on the permanence, periodic solution, and global attractivity for the considered system are derived. Finally, a numerical example is also presented to validate the practicability and feasibility of our proposed results.

【 授权许可】

CC BY