The intent of this work is to explore the generation mechanism of four mixed-mode vibration types triggered by the pitchfork bifurcation delay phenomenon in a driven van der Pol-Duffing oscillator. The four mixed-mode vibration types can be named “delayed sup-pitchfork/sup-Hopf” type for Homoclinic connection, symmetric “delayed sup-pitchfork/sup-Hopf” type, “point/point” type for delayed sup-pitchfork and “delayed sup-pitchfork/delayed Homoclinic” type, respectively. Our study proves that the pitchfork bifurcation delay phenomenon deserves a prominent role in the occurrence of the four mixed-mode vibration types, which enriches the dynamical behaviors of the bifurcation delay phenomenon as well as the possible routes to mixed-mode vibrations.

这项工作的目的是探索驱动 van der Pol-Duffing 振荡器中由干草叉分叉延迟现象触发的四种混合模式振动类型的产生机制。四种混合模式振动类型可以命名为“delayed sup-pitchfork/sup-Hopf”型用于同宿连接，对称“delayed sup-pitchfork/sup-Hopf”型，“point/point”型用于延迟sup-pitchfork和分别为“延迟 sup-pitchfork/延迟同宿”类型。我们的研究证明干草叉分叉延迟现象在四种混合模式振动类型的发生中应该发挥突出作用，这丰富了分叉延迟现象的动力学行为以及混合模式振动的可能途径。