Dynamic behaviors of a discrete Lotka-Volterra competitive system with the effect of toxic substances and feedback controls

Advances in Difference Equations

Zhanshuai Miao¹  Jiamin Liu¹  Fengde Chen¹  Liqiong Pu¹ 

[1] College of Mathematics and Computer Science, Fuzhou University, Fuzhou, P.R. China

关键词: feedback controls;    discrete;    toxic substances;    permanence;    extinction;    global stability;    34D23;    92B05;    34D40;   

DOI  :  10.1186/s13662-017-1130-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

By noting the fact that the intrinsic growth rate are not positive everywhere, we revisit Lotka-Volterra competitive system with the effect of toxic substances and feedback controls. The corresponding results about permanence and extinction for the species given in (Chen and Chen in Int. J. Biomath. 8(1):1550012, 2015) are extended. Furthermore, a very important fact is found in our results, that is, the feedback controls and toxic substances have no effect on the permanence and extinction of species. Moreover, we also derive sufficient conditions for the global stability of positive solutions. Finally, some numerical simulations show the feasibility of our main results.

【 授权许可】

CC BY