Limit cycles in a generalized Gause-type predator-prey system

来源期刊：中南大学学报(英文版)2001年第4期

论文作者：CHEN Hai-bo LIU Yi-rong

文章页码：283 - 286

Key words：generalized Gause-type predator-prey system; boundedness; periodic solution; existence

Abstract: The qualitative behavior of solutions for a generalized Gause-type predator-prey systemwas studied.A large number of biological and bioeconomic models are special cases of this system .The system was investigated in the regionD={(x,y)|x>0,y>0} because of the biological meaning of the system .The authors derived some sufficient conditions for the boundedness of the solutions and the existence of limit cycles of the system ,which ensure that the system has at least one limit cycle.The theory of limit sets of autonomous plane systems and the theoremof cycle field of Poincare-Bendixson are efficiently employed in the research .The main results and their consequences presented not only generalize some known results,but also improve some corresponding results of other authors.