A singular perturbation problem from the artificial compressible system to the incompressible system is considered for a doubly diffusive convection when a Hopf bifurcation from the motionless state occurs in the incompressible system. It is proved that the Hopf bifurcation also occurs in the artificial compressible system for small singular perturbation parameter, called the artificial Mach number. The time periodic solution branch of the artificial compressible system is shown to converge to the corresponding bifurcating branch of the incompressible system in the singular limit of vanishing artificial Mach number.

中文翻译：

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双扩散对流方程Hopf分支的奇异极限II：分支和稳定性

当在不可压缩系统中发生从静止状态发生的霍普夫分岔时，考虑了从双重压缩对流的双重扩散对流，考虑了从人工可压缩系统到不可压缩系统的奇异摄动问题。事实证明，霍夫分叉也发生在对小奇异摄动参数的人工可压缩系统中，称为人工马赫数。人工可压缩系统的时间周期解分支显示为在消失的人工马赫数奇异极限下收敛到不可压缩系统的相应分支分支。