关键词: 多卷混沌吸引子, 异宿环, 混沌不变集, Shilnikov 理论, 分片仿射系统

Abstract: To elucidate the generation mechanism of multi-scroll chaotic attractors, this paper investigates a class of three-dimensional $n$-zone $(n≥2)$ piecewise affine systems. By analyzing the geometric structure of stable and unstable manifolds, sufficient conditions are established for the coexistence of $n−1$ heteroclinic cycles. Inspired by the Shilnikov-type theory , suitable cross-sections are constructed near the heteroclinic cycles, and the corresponding Poincaré map is derived. A rigorous analysis of the Poincaré map reveals the existence of a chaotic invariant set in the system. Numerical simulations are provided to support the theoretical results. The findings suggest that the multi-scroll chaotic structure may originate from the coexistence and interaction of multiple heteroclinic cycles.

Key words: Multi?scroll chaotic attractor, Heteroclinic cycle, Chaotic invariant set, Shilnikov?type theory, Piecewise affine system