We first propose a class of generalized homogeneous vector fields which include existing ones as special cases. Then we establish a necessary and sufficient condition for $D$-stability of more general homogeneous cooperative systems. The decay rate is also explicitly estimated. Two numerical examples are worked out to show the effectiveness of the main result.

中文翻译：

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$d$齐次合作系统的稳定性

我们首先提出一类广义的齐次矢量场，其中包括现有的特殊情况。然后，我们为$d$-更通用的同类合作系统的稳定性。还明确估计了衰减率。通过两个数值例子说明了主要结果的有效性。