On permanence and global stability in a general Gilpin–Ayala competition predator–prey discrete system

In this paper, we propose a discrete multispecies general Gilpin–Ayala competition predator–prey model. By using new difference inequality and developing the analysis technique of Chen and Zhou [Y. Chen, Z. Zhou, Stable periodic solution of a discrete periodic Lotka–Volterra competition system, J. Math. Anal. Appl. 277 (2003) 358–366], sufficient conditions are established for the permanence and the global stability. An example shows the feasibility of our results.