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Zbl 1019.39004
Chen, Yuming; Zhou, Zhan
Stable periodic solution of a discrete periodic Lotka-Volterra competition system.
(English)
[J] J. Math. Anal. Appl. 277, No.1, 358-366 (2003). ISSN 0022-247X

Consider the following discrete Lotka-Volterra competition system $$\cases x(n+1)= x(n)\exp \biggl[r_1(n) \bigl(1-x(n)/K_1(n)-\mu_2(n) y(n) \bigr) \biggr],\\ y(n+1)=y(n) \exp\biggl[r_2(n) \bigl(1-\mu_1(n)x(n)-y(n) /K_2 (n)\bigr) \biggr] \endcases$$ where $K_i(n)$, $r_i(n)$ and $\mu_i(n)$, $i=1,2$ are bounded non-negative sequences. Sufficient conditions are given for the persistence of the system, i.e. the existence of a compact subset $E\subset \bbfR^2_+$ such that each solution will eventually enter and remain in $E$. The existence and stability of periodic solution is established, too.
[Dobiesław Bobrowski (Poznań)]
MSC 2000:
*39A11 Stability of difference equations

Keywords: Lotka-Volterra competition system; persistence; periodic solution; global stability

Cited in: Zbl 1125.39008

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