Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Dynamics of a non-autonomous ratio-dependent predator—prey system

Meng Fana1, Qian Wanga1 and Xingfu Zoua2

a1 Department of Mathematics, Northeast Normal University, Changchun, Jilin 130024, People's Republic of China (

a2 Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF A1C 5S7, Canada (


We investigate a non-autonomous ratio-dependent predator–prey system, whose autonomous versions have been analysed by several authors. For the general non-autonomous case, we address such properties as positive invariance, permanence, non-persistence and the globally asymptotic stability for the system. For the periodic and almost-periodic cases, we obtain conditions for existence, uniqueness and stability of a positive periodic solution, and a positive almost-periodic solution, respectively.

(Received May 31 2001)

(Accepted March 26 2002)