Permanence and asymptotic behavior of the \(N\)-species nonautonomous Lotka-Volterra competitive systems (Q1568730)

The authors study the permanence and global asymptotic behavior for the \(n\)-species Lotka-Volterra competitive systems \[ {dx_i\over dt}=x_i \left(b_i(t)- \sum^n_{j=1} a_{ij}(t)x_j\right), \quad i=1,2, \dots,n, \] where all parameters are time dependent and asymptotically approximate periodic functions, respectively. The authors obtain sufficient conditions for the permanence and global asymptotic stability of the system. They extend related results for \(n=2\) by \textit{Q. Peng} and \textit{L.-S. Chen} [Comput. Math. Appl. 27, No. 12, 53-60 (1994; Zbl 0798.92023)].