一类具有季节交替的n维Gilpin-Ayala竞争模型的动力学

Dynamics of A n-Dimensional Gilpin-Ayala Competition Model With Seasonal Succession

研究一类具有季节交替的n维Gilpin-Ayala竞争模型。利用单调动力系统的理论,当n=1时,系统存在着阈值动力学。根据离散竞争映射的负载单形理论,证得n维系统存在一个(n-1)维的负载单形。结果表明:(n-1)维的负载单形吸引了系统在R^(n)_(+)中的所有非平凡轨道。

A type of n dimensional Gilpin-Ayala competition models with seasonal succession are studied.Using the theory of monotonic dynamical systems,when n=1,the system has threshold dynamics.Using the theory of carrying simplex of discrete competitive mappings,the existence of a(n-1)dimensional carrying simplex in the n dimensional system is proved.The result shows that(n-1)dimensional carrying simplex attracts all nontrivial orbits in R^(n)_(+)of the system.