We study the dynamics of a piecewise-smooth system of differential equations for which the existence of a strange Lorenz-type attractor had been rigorously proved previously and bifurcation mechanisms of its birth had been obtained. In this work we discuss the destruction of this attractor due to the appearance of sliding motions in its structure. Using qualitative and numerical methods, we study a complex sequence of attractor bifurcations that leaves in the system a globally stable limit cycle. We show that this sequence is based on C-bifurcations and bifurcations of multi-loop homoclinic trajectories.

中文翻译：

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分段光滑Lorenz型系统中混沌吸引子的分支

我们研究了微分方程的分段光滑系统的动力学，对于该系统，以前已严格证明了奇异的Lorenz型吸引子的存在，并获得了其诞生的分叉机理。在这项工作中，我们讨论了由于吸引子在其结构中的出现而造成的破坏。使用定性和数值方法，我们研究了吸引子分支的复杂序列，该序列在系统中留下了全局稳定的极限环。我们显示此序列基于C-分叉和多环同宿轨迹的分叉。