具有两个鸭点的奇摄动平面系统中的双鸭圈
Double canard cycles in singularly perturbed planar systems with two canard points
摘要：
考虑具有两个鸭点的奇摄动平面系统中包含两个鸭的双鸭圈。以往的工作研究了具有单参数层方程的奇摄动平面系统的复杂振动，包括松弛振动和鸭式环，这些系统恰好具有一个鸭式点、两个跳跃点或一个鸭式点和一个跳跃点。基于规范形理论、Blow-up技术和Melnikov理论，研究了两个非退化鸭点处两个Hopf破缺机制诱导的双鸭环.最后，我们将所得结果应用于一类具有二次阻尼的三次Lienard方程。
英文摘要：
We consider double canard cycles including two canards in singularly perturbed planar systems with two canard points. Previous work studied the complex oscillations including relaxation oscillations and canard cycles in singularly perturbed planar systems with one-parameter layer equations, which have precisely one canard point, two jump points or one canard point and one jump point. Based on the normal form theory, blow-up technique and Melnikov theory, we investigate double canard cycles induced by two Hopf breaking mechanisms at two non-degenerate canard points. Finally, we apply the obtained results to a class of cubic Lienard equations with quadratic damping.
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