一类具有季节交替的n维Gilpin-Ayala竞争模型的动力学

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摘要：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Rn+中的所有非平凡轨道。

关键词：季节交替；Gilpin-Ayala竞争模型；周期解；庞加莱映射；负载单形

中图分类号：O 175.13文献标志码：A

文章编号：1000-5013（2024）03-0417-06

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

CHEN Meixiang，XIE Xizhuang

（School of Mathematical Sciences，Huaqiao University，Quanzhou 362021，China）

Abstract：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 Rn+ of the system.

Keywords：seasonal succession；Gilpin-Ayala competition model；periodic solution；Poincaré mapping；carrying simplex

1 预备知识

季节性更替是自然界的普遍现象，深深影响着种群的生存与增长，群落的结构和组成[1]。（剩余3404字）