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Permanence and global stability for nonautonomous $$N$$-species Lotka-Volterra competitive system with impulses. (English) Zbl 1200.34051
The authors consider the following $$N$$-species Lotka-Volterra competitive system with impulsive effects
\begin{aligned} & \dot x_i(t)= x_i(t)\Biggl[a_i(t)- \displaystyle\sum^n_{j=1} b_{ij}(t) x_j(t)\Biggr],\quad t\neq t_k,\\ & x_i(t^+_k)= h_{i\alpha}x_i(t_k),\quad i= 1,2,\dots, n,\;k= 1,2,\dots,\end{aligned}\tag{1}
where $$a_i$$ and $$b_{ij}$$ $$(i,j= 1,2,\dots)$$ are bounded and continuous. The authors find sufficient conditions for the permanence, persistance and extinction of (1).

##### MSC:
 34C60 Qualitative investigation and simulation of ordinary differential equation models 34A37 Ordinary differential equations with impulses 34D05 Asymptotic properties of solutions to ordinary differential equations 92D25 Population dynamics (general)
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