Accurately detecting a homoclinic cycle and chaos in a concrete system takes a huge challenge. This paper gives a sufficient condition of coexisting homoclinic cycles (degenerate) with respect to a saddle-focus in a class of three-dimensional piecewise systems with two switching manifolds. Furthermore, by constructing the Poincaré map, it is rigorously shown that chaotic behavior is induced by the coexisting cycles without necessary symmetry in the considered system, which is evidently different from the usual dynamics in smooth system theory that a pair of symmetrical homoclinic cycles can generate chaos but the asymmetric ones cannot. It finally provides an example to illustrate the effectiveness of the results established.

准确检测混凝土系统中的同宿循环和混沌是一项巨大的挑战。本文给出了在具有两个切换流形的一类三维分段系统中关于鞍焦点并存同宿循环（退化）的充分条件。此外，通过构建庞加莱图，严格表明混沌行为是由所考虑系统中没有必要对称性的共存循环引起的，这与光滑系统理论中一对对称同宿循环可以产生的通常动力学明显不同混乱，但不对称的不能。最后提供了一个例子来说明所建立结果的有效性。