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Zhao, Liang; Xie, Xiangdong; Yang, Liya; Chen, Fengde

Dynamic behaviors of a discrete Lotka-Volterra competition system with infinite delays and single feedback control. (English) Zbl 1406.92544

Abstr. Appl. Anal. 2014, Article ID 867313, 19 p. (2014).
Summary: A nonautonomous discrete two-species Lotka-Volterra competition system with infinite delays and single feedback control is considered in this paper. By applying the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Also, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that if the the discrete Lotka-Volterra competitive system with infinite delays and without feedback control is permanent, then, by choosing some suitable feedback control variable, the permanent species will be driven to extinction. That is, the feedback control variable, which represents the biological control or some harvesting procedure, is the unstable factor of the system. Such a finding overturns the previous scholars’ recognition on feedback control variables.

Cited in 4 Documents

MSC:

92D25 Population dynamics (general)
92D40 Ecology
93B52 Feedback control

Keywords:

discrete Lotka-Volterra competition system; feedback control; infinite delays
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\textit{L. Zhao} et al., Abstr. Appl. Anal. 2014, Article ID 867313, 19 p. (2014; Zbl 1406.92544)
Full Text: DOI

References:

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