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On permanence and global stability in a general Gilpin-Ayala competition predator-prey discrete system. (English) Zbl 1125.39008
The authors propose a general discrete multispecies Gilpin-Ayala competition predator-prey model. By using difference inequality and the technique developed by Y. Chen and Z. Zhou [J. Math. Anal. Appl. 277, 358–366 (2003; Zbl 1019.39004)], sufficient conditions are established for the permanence and the global stability. An example is also included.

MSC:
39A11 Stability of difference equations (MSC2000)
39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
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