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Some new results on nonautonomous Lotka-Volterra competitive systems with delays. (English) Zbl 0947.34066
The authors consider the following \(N\)-species nonautonomous Lotka-Volterra type system with finite or infinite delays: \[ \begin{split} x_i'(t)= x_i(t)\Bigl[ b_i(t)- a_i(t)x_i (t)-\sum^n_{j=1} a_{ij}(t)x_j \bigl(t- \tau_{ij} (t)\bigr) \\ -\sum^n_{j=1}\int^0_{-\sigma_{ij}} c_{ij}(t,s) x_j (t+s)ds \Bigr], \quad i=1,2, \dots,n.\end{split}\tag{1} \] They establish a series of criteria under which a part of the \(n\) species is driven to extinction while the remaining part of the \(n\) species is persistent or uniformly persistent, or coexists globally asymptotically stably.
The results in the paper generalize and improve some known results on nondelayed \(N\)-species Lotka-Volterra type competitive systems.
Reviewer: V.Petrov (Plovdiv)

MSC:
34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
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