Contractively and global stability for discrete models of Lotka-Volterra type (Q2574433)

The author gives some new criteria for the global asymptotic stability of the following discrete model of nonautonomous Lotka-Volterra type: \[ N_i(p+1)= N_i(p)\exp\left\{r_i(p)(c_i(p)-b_i(p)N_i(p)-\sum^n_{j=1}\sum^m_{l=0}b^l_{ij}(p)N_j(p-l))\right\}, \] \[ N_i(0)=N_{i0}>0 \text{\;and\;} N_i(-l)=N_{i(-l)}\geq 0, \] where \(p=0,1,2,\ldots,\) \(r_i(p)>0, \lim\inf_{p\rightarrow\infty}r_i(p)>0, b_i(p)>0,b^0_{ii}(p)=0,\;b^l_{ij}(p)\geq 0, 1\leq i\leq n, 1\leq i\leq j\leq n,\;0\leq l\leq m. \)