摘要：A nonlinear amensalism model of the form d N 1 d t = r 1 N 1 ( 1 − ( N 1 P 1 ) α 1 − u ( N 2 P 1 ) α 2 ) , d N 2 d t = r 2 N 2 ( 1 − ( N 2 P 2 ) α 3 ) , $$ egin{aligned} & rac{dN_)}{dt}= r_)N_) iggl(1- iggl( rac{N_)}{P_)} iggr)^{ lpha _)}-u iggl( rac{N_,}{P_)} iggr)^{ lpha_,} iggr), \ & rac{dN_,}{dt}= r_,N_, iggl(1- iggl( rac{N_,}{P_,} iggr)^{ lpha_"} iggr), nd{aligned}$$ where r i , P i , u , i = 1 , 2 , α 1 , α 2 , α 3 $r_{i}, P_{i}, u, i=1, 2, lpha_), lpha_,, lpha_"$ are all positive constants, is proposed and studied in this paper. The dynamic behaviors of the system are determined by the sign of the term 1 − u ( P 2 P 1 ) α 2 $1-u ( rac{P_,}{P_)} )^{ lpha_,} $ . If 1 − u ( P 2 P 1 ) α 2 > 0 $1-u ( rac {P_,}{P_)} )^{ lpha_,}>0$ , then the unique positive equilibrium D ( N 1 ∗ , N 2 ∗ ) $D(N_)^{*},N_,^{*})$ is globally attractive, if 1 − u ( P 2 P 1 ) α 2 < 0 $1-u ( rac{P_,}{P_)} )^{ lpha_,}<0$ , then the boundary equilibrium C ( 0 , P 2 ) $C(0, P_,)$ is globally attractive. Our results supplement and complement the main results of Xiong, Wang, and Zhang (Advances in Applied Mathematics 5(2):255–261, 2016).
关键词：Amensalism model ; Differential inequality theory ; Global stability
