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Permanence and asymptotic behavior of the \(N\)-species nonautonomous Lotka-Volterra competitive systems. (English) Zbl 0959.34039

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 Q. Peng and L.-S. Chen [Comput. Math. Appl. 27, No. 12, 53-60 (1994; Zbl 0798.92023)].

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
92D25 Population dynamics (general)
34D23 Global stability of solutions to ordinary differential equations

Citations:

Zbl 0798.92023
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References:

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