| 方阵A的VOLTERRA乘子的判定与证明 |
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| 引用本文： | 胡玉臣,姜泽宏.方阵A的VOLTERRA乘子的判定与证明[J].长春工程学院学报(自然科学版),2000(1). |
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| 作者姓名： | 胡玉臣 姜泽宏 |
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| 作者单位： | 空军长春飞行学院数学室 长春130022
(胡玉臣)，长春工程学院基础部 长春1300l2(姜泽宏) |
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| 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。
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| 关 键 词： | 矩阵 Volterra乘子 对角占优矩阵 |
The judgement and provement of VOLTERRA multiplier of squarematrix A |
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| Hu Yuchen.The judgement and provement of VOLTERRA multiplier of squarematrix A[J].Journal of Changchun Institute of Technology(Natural Science Edition),2000(1). |
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| Authors: | Hu Yuchen |
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| Institution: | Changchun Air College of flight |
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| Abstract: | 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. |
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| Keywords: | matrix volterra multiplier diagonally domi-nant matrix |
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