Permanence and global asymptotic stability for a generalized nonautonomous Lotka-Volterra competition system (Q455023)

The paper is concerned with the following generic \(N\)-dimensional Lotka-Volterra competition model NEWLINE\[NEWLINE u_i^\prime =u_i\left[a_i(t)-\sum _{j=1}^Nb_{ij}(t)f_{ij}(u_i,u_j)\right],\quad i=1,\dotsc,N,\;N\geq 2. NEWLINE\]NEWLINE Under certain averaging conditions on the functional coefficients, it is shown that such systems become weakly permanent or permanent, respectively, and the difference between two solutions tends to zero as \(t\) tends to infinity. The paper improves similar results by Ahmad and Lazer, which are known to hold for the less general system NEWLINE\[NEWLINE u_i^\prime =u_i\left[a_i(t)-\sum _{j=1}^Nb_{ij}(t)u_j\right],\quad i=1,\dotsc,N,\;N\geq 2. NEWLINE\]