摘要
提出两类广义梯度系统,即广义斜梯度系统和具有对称负定矩阵的广义梯度系统,并研究了这两类广义梯度系统的性质.在满足一定的条件下,把Tzénoff方程化成这两类广义梯度系统方程.进一步利用这两类广义梯度系统的性质来研究Tzénoff方程解的稳定性,分别给出解是稳定、渐进稳定和不稳定的条件,并举例说明结果的应用.
Two kinds of generalized gradient systems,namely generalized skew gradient system and generalized gradient system with symmetric negative definite matrix,are proposed,and the properties of these two kinds of generalized gradient systems are studied.The conditions under which the Tzénoff equations can be considered as one of the two generalized gradient systems are obtained.The characteristics of the generalized gradient systems can be used to study the stability of solution of the Tzénoff equations,and the conditions for the solution to be stable,asymptotically stable and unstable are given. Some examples are used to illustrate the application of the results.
引文
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