【作者】 郭迎；

【导师】 林怡平；

【作者基本信息】 昆明理工大学 ， 应用数学， 2003， 硕士

【摘要】 本文研究了高维Lotka-Volterra系统的周期解。首先讨论N维Lotka-Volterra系统的稳定性，然后对该系统利用线性变换进行化简，讨论了N维Lotka-Volterra系统的周期解及分支方向问题。在此基础上，详细讨论了四维和五维Lotka-Volterra系统的周期解及分支方向，最后，构造了一类五维Lotka-Volterra的系统有周期解的例子。更多还原

【Abstract】 This thesis deals with the periodic solution of n-dimensional Lotka-volterra systems. Firstly, we discuss the stability of the periodic solution of n-dimensional Lotka-volterra systems, then simplify the complex systems and analyse the stable periodic orbits of n-dimensional differential systems and n-dimensional Lotka-volterra systems. Then on the basis of these conclusions, the bifurcation and stability of periodic solution for 4-dimersonal and 5-dimensional systems will be discussed in detail. Finally, by using these results, we rebuild a 5-dimensional Lotka-volterra system.更多还原