Abstract
The paper discusses a nonautonomous discrete time Lotka-Volterra competitive system with pure delays and feedback controls. New sufficient conditions for which a part of then-species is driven to extinction are established by using the method of multiple discrete Lyapunov functionals.
Highlights
The coexistence and global stability of population models are of the interesting subjects in mathematical biology
We see that for general discrete n-species population systems the results for which a part of the n-species is driven to extinction and the surplus part of the n-species remains the permanence, up to now, are still not obtained
Let Z denote the set of all nonnegative integers
Summary
The coexistence and global stability of population models are of the interesting subjects in mathematical biology. Muroya in 6, 7 considered the following general nonautonomous discrete n-species Lotka-Volterra systems: Ni p 1. Liao et al in 8 discussed the following general discrete nonautonomous n-species competitive system with feedback controls:. We see that in 9, 10 the authors studied the following nonautonomous continuous Lotka-Volterra competitive system with pure delays and feedback controls:. We see that for general discrete n-species population systems the results for which a part of the n-species is driven to extinction and the surplus part of the n-species remains the permanence, up to now, are still not obtained. Motivated by the above works, in this paper we study the following discrete nonautonomous Lotka-Volterra competitive system with pure delays and feedback controls n xi k 1 xi k exp⎩ri k j aij k xj k − τij n σij j bijl.
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