一类指数型离散Logistic迭代方程的动力学分析  

Dynamic Analysis of a Class of Exponential Discrete Logistic Iterative Equation

作　　者：刘玲伶[1] 李梅梅 LIU Lingling;LI Meimei(School of Sciences,Southwest Petroleum University,Chengdu 610500,China)

机构地区：[1]西南石油大学理学院,成都610500

出　　处：《重庆师范大学学报（自然科学版）》2021年第6期71-76,共6页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11771308);西南石油大学专项项目(No.2019CXTD08)。

摘　　要：【目的】研究一类种群生长模型x_(n+1)=x_(n)exp(r(1-ax_(n)-bx^(2)_(n))),r,a,b>0的稳定性和周期性。【方法】利用定性理论和分岔理论,讨论模型不动点的稳定性和退化现象以及周期点的存在性。【结果】给出模型不动点的稳定性条件以及发生倍周期分岔的参数条件,讨论了2;周期点的存在性,并给出了存在三周期点的充分条件。【结论】所得结果可以对符合模型的事物进行生长周期预测,为保护生物的人为干预活动提供参考。[Purposes]It studies the stability and periodic solution of a class of exponential discrete logistic iterative equation x_(n+1)=x_(n)exp(r(1-ax_(n)-bx^(2)_(n))),r,a,b>0.[Methods]By using qualitative theory and bifurcation theory,the stability,degenerate case of the fixed points and the existence of periodic solutions are discussed.[Findings]The stability condition of the fixed point and the bifurcation condition of period-doubling bifurcation are given.Furthermore,it discusses the existence of 2;periodic solution and give the sufficient condition of 3-periodic solution.[Conclusions]The obtained results can predict the growth of periodic solution and provide a reference for human intervention activities.

关 键 词：Logistic迭代方程 稳定性 倍周期分岔 LI-YORKE混沌 

分 类 号：O175.12[理学—数学]