矩阵方程∑rk=0AkXBk=F的解

讨论矩阵方程∑rk=0AkXBk=F存在惟一解的充要条件,并给出了两种迭代求解法.     

在共振点附近的一类二阶泛函微分方程的解析解

在复域C内研究一类包含未知函数迭代的二阶微分方程x″(z)=G(z,x(z),x~2(z),…,x~m(z))解析解的存在性.通过Schr(?)der变换,即x(z)=y(αy~(-1)(z)),把这类方程转化为一种不含未知函数迭代的泛函微分方程α~2y″(αz)y″(z)-αy′(αz)y″(z)= (y′(z))~3G(y(z),y(αz),…,y(α~mz)),并给出它的局部可逆解析解.本文不仅讨论了双曲型情形0<|α|<1和共振的情形(α是一个单位根),而且还在Brjuno条件下讨论了共振点附近的情形(即单位根附近).     

矩阵方程∑k=0^rA^kXB^k=F的解

讨论矩阵方程∑k=0^rA^kXB^k=F存在惟一解的充要条件，并给出了两种迭代求解法．     

Influence of Noise on Stability of the Ecosystem

Based on a simplified predator-prey model,the influence of noise on the ecosystem has been studied.The results show the following facts.(i)For all parameter values,the existence of noise maintains the oscillatory state of the ecosystem,and enough strong noise can destroy the ecosystem,which means the annihilation of the species.(ii)Comparing to oscillation with small amplitude,while the ecosystem oscillates explosively with large amplitude,it is more likely to lose balance.In addition,the small-amplitude oscillation takes on higher level of regularity.All the numerical results are reasonable comparing to the general knowledge about ecosystem.