Electron. J. Diff. Equ., Vol. 2013 (2013), No. 22, pp. 1-9.

Permanence for a competition and cooperation model of enterprise cluster with delays and feedback controls

Ping Liu, Yongkun Li

Abstract:
In this article, based on population ecology theory, we present a competition and cooperation system of the enterprise cluster with time delays and feedback controls. By using differential inequalities, we obtain sufficient conditions for the permanence of the system, which shows that the time delay, feedback control and initial production have an influence on the persistent properties of the system. We further interpret our result from the economic point of view. Some suggestions about enterprise cluster are put forward through the analysis of our results.

Submitted October 4, 2012. Published January 25, 2013.
Math Subject Classifications: 34C11, 91B55, 92D25, 93B52.
Key Words: Enterprise cluster; permanence; competition and cooperation model; time delay; feedback control.

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Ping Liu
Department of Mathematics, Yunnan University
Kunming, Yunnan 650091, China
email: liuping@ynu.edu.cn
Yongkun Li
Department of Mathematics, Yunnan University
Kunming, Yunnan 650091, China
email: yklie@ynu.edu.cn

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