方阵A的VOLTERRA乘子的判定与证明  

The judgement and provement of VOLTERRA multiplier of squarematrix A

作　　者：胡玉臣[1] 姜泽宏[2] 

机构地区：[1]空军长春飞行学院数学室,长春130022 [2]长春工程学院基础部

出　　处：《长春工程学院学报（自然科学版）》2000年第0期8-9,共2页Journal of Changchun Institute of Technology：Natural Sciences Edition

摘　　要：在研究Lotka-Volterra方程正平衡点的稳定性态时,如果存在正对角矩阵D={d1,d2,A,dn},使得 DA+ATD为正定矩阵,则 Lotka-Volterra方程的正平衡点在第一卦限是全局稳定的。因此,问题在于寻找使 DA+ATD为正定的矩阵 D存在的条件,矩阵D也称为A的Volterra乘子。给出了实方阵A存在Volterra乘子的几个新的充分性条件,并逐一加以证明。When studying of positive equilbrium point stability of Lotka - Volterra equation, if there exists posi- tive diagonal matrx D = { d1, d2, A, dn. } to make DA + ATD to be positive definite matrix,then the positive eguilibrium point of Lotka - Volterra in the fist quadrant is stable in the overall situation. Therefore the question is to search for the existing condition which makes DA + ATD is positive definite matrix D, (matrix D can also be called AT Volter- ra multiplier ). The paper provides several new abundant conditions of Volterra existing in the real square matrix and proves them one by one.

关 键 词：矩阵 VOLTERRA乘子 对角占优矩阵 

分 类 号：O151.21[理学—数学]