Global stability in discrete models of nonautonomous Lotka-Volterra type (Q1876321)

The author considers the discrete version of a non-autonomous Lotka Volterra model \[ N_i(p+1) = N_i(p)\exp\{c_i(p)-a_i(p)N_i(p)-\sum_{j=1}^{n}\sum_{\ell=0}^{m}a_{ij}^{\ell}(p)N_j(p-k_\ell)\} \] \[ 1\leq i\leq n\;,\;p=0,1,2,\ldots; N_i(p)=N_{ip}\geq 0,\;p\geq 0\;, N_{i0}>0,\;1\leq i\leq n \] with bounded coefficients. Several theorems on existence, uniqueness and persistence (non-zero limit for \(t\rightarrow\infty\) of the solutions) are formulated and proved. Throughout the paper the analogy with the continuous time version -- the differential equations model -- is followed.