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AbstractWe propose and study a discrete competitive system of the following form: x1(n+1)=x1(n)exp[r1−a1x1(n)−b1x2(n)1+c2x2(n)],x2(n+1)=x2(n)exp[r2−a2x2(n)−b2x1(n)1+c1x1(n)]. $$\begin{aligned} &x_{1}(n+1)=x_{1}(n)\exp{\biggl[r_{1}-a_{1}x_{1}(n)- \frac {b_{1}x_{2}(n)}{1+c_{2}x_{2}(n)}\biggr]}, \\ &x_{2}(n+1)=x_{2}(n)\exp{\biggl[r_{2}-a_{2}x_{2}(n)- \frac {b_{2}x_{1}(n)}{1+c_{1}x_{1}(n)}\biggr]}. \end{aligned}$$ We obtain some conditions for the local stability… Click to show full abstract
AbstractWe propose and study a discrete competitive system of the following form: x1(n+1)=x1(n)exp[r1−a1x1(n)−b1x2(n)1+c2x2(n)],x2(n+1)=x2(n)exp[r2−a2x2(n)−b2x1(n)1+c1x1(n)]. $$\begin{aligned} &x_{1}(n+1)=x_{1}(n)\exp{\biggl[r_{1}-a_{1}x_{1}(n)- \frac {b_{1}x_{2}(n)}{1+c_{2}x_{2}(n)}\biggr]}, \\ &x_{2}(n+1)=x_{2}(n)\exp{\biggl[r_{2}-a_{2}x_{2}(n)- \frac {b_{2}x_{1}(n)}{1+c_{1}x_{1}(n)}\biggr]}. \end{aligned}$$ 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.
Journal Title: Advances in Difference Equations
Year Published: 2017
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