A dynamic model with two discontinuously coupled bi-nonlinear oscillators and multiple non-smooth constraints is presented, which increases the complexity of the system. The dynamic behaviors of the system with asymmetric clearances are investigated by the continuation platform Computational Continuation Core (abbreviated as COCO) and rich bifurcation phenomena are revealed. In the case of bilateral soft constraints, the asymmetric constrained system has four initial states which are not exactly the same as the initial states of the system with one-sided elastic constraint. For each case, the whole motion process of the oscillator is analyzed by path-following method. Numerical simulation shows that there are many co-dimension-one bifurcations, for example, period-doubling bifurcation, Neimark–Sacker bifurcation and saddle–node bifurcation which can change the stability of the motions. Furthermore, three different co-dimension-two bifurcations, i.e., grazing-saddle–node bifurcation, saddle–node-Neimark–Sacker bifurcation and Neimark–Sacker-grazing bifurcation, are found through the intersections of grazing, saddle–node and Neimark–Sacker co-dimension-one bifurcation curves.

提出了具有两个不连续耦合的双非线性振荡器和多个非光滑约束的动力学模型，这增加了系统的复杂性。通过计算平台连续核（简称COCO）研究了具有非对称间隙的系统的动力学行为，并揭示了丰富的分叉现象。在双边软约束的情况下，非对称约束系统具有四个初始状态，这与具有单侧弹性约束的系统的初始状态不完全相同。针对每种情况，通过路径跟踪法分析了振荡器的整个运动过程。数值模拟表明，存在许多共维一分叉，例如，倍频分叉，Neimark–Sacker分叉和鞍形节点分叉可以改变运动的稳定性。此外，通过吃草，鞍形节点和Neimark-N的交点发现了三个不同的共维两个分叉，即放牧-鞍-节点分叉，鞍形-节点-Neimark-Sacker叉形和Neimark-Sacker-放牧分叉。 Sacker维数一分叉曲线。