文章基本信息

标题：Stability analysis of a discrete competitive system with nonlinear interinhibition terms
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作者：Jinhuang Chen ; Xiangdong Xie
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2017
卷号：2017
期号：1
页码：294
DOI：10.1186/s13662-017-1362-4
语种：English
出版社：Hindawi Publishing Corporation
摘要：We propose and study a discrete competitive system of the following form: x 1 ( n + 1 ) = x 1 ( n ) exp [ r 1 − a 1 x 1 ( n ) − b 1 x 2 ( n ) 1 + c 2 x 2 ( n ) ] , x 2 ( n + 1 ) = x 2 ( n ) exp [ r 2 − a 2 x 2 ( n ) − b 2 x 1 ( n ) 1 + c 1 x 1 ( n ) ] . $$ egin{aligned} &x_)(n+1)=x_)(n) xp{ iggl[r_)-a_)x_)(n)- rac {b_)x_,(n)}{1+c_,x_,(n)} iggr]}, \ &x_,(n+1)=x_,(n) xp{ iggl[r_,-a_,x_,(n)- rac {b_,x_)(n)}{1+c_)x_)(n)} iggr]}. nd{aligned}$$ We obtain some conditions for the local stability of the equilibria. Using the iterative method and the comparison principle of a difference equation, we also obtain a set of sufficient conditions that ensure the global stability of the interior equilibrium. Numeric simulations show the feasibility of the main results. Our results supplement and complement some known results.
关键词：local stability ; competitive ; global stability ; iterative method