The Proof Of Hofbauer-so-takeuchi Conjecture In The Case Of N=5

In this thesis, the global stability of a class of two species Lotka-Volterra com-petition system is considered. In1996, J. Hofbauer, J.W.-H. So and Y. Takeuchi proposed aconjecture, which was proved by the proposer in the cases of n=2and n=3. In1999, basedon the H-S-T paper, Zhengyi Lu and Guojie Wang proposed a PD algorithm and showed thatthe conjecture to be true in the case of n=4. In this paper, through promoting PD algorithm,combining SWDS algorithm and adopting the parallel computing technology, we proved thatthe conjecture is true in the case of n=5.