## Permanence and global attractivity of the discrete Gilpin-Ayala type population model.(English)Zbl 1127.92038

Summary: We propose a discrete Gilpin-Ayala competition model and a discrete Gilpin-Ayala type multispecies competition-predator model. For the general nonautonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained. For the periodic case, sufficient conditions which ensure the existence of a unique globally stable positive periodic solution of the system are obtained. An example together with its numeric simulations shows the feasibility of the main results.

### MSC:

 92D40 Ecology 39A11 Stability of difference equations (MSC2000) 92D25 Population dynamics (general)
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### References:

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