摘要:
提出了一个分段Sprott系统,对其混沌机理进行了分析.根据Shilnikov定理,在满足异宿轨道基本特性、Shilnikov不等式和特征方程条件下,通过寻找该系统中由不稳定流形、异宿点和稳定流形三个几何不变集上所形成的一条异宿轨道,在分段Sprott系统中导出了存在异宿轨道时该系统中各个参数应符合的条件,并找到了一组对应的实参数,由此证明了异宿轨道的存在性.最后,根据这组对应的实参数,进行了电路设计与实验验证.
Abstract:
In this paper, a piecewise-linear Sprott system is proposed and its chaos mechanism is analyzed. According to the Shilnikov theorem, on the condition that the basic characteristics of heteroclinic orbit, Shilnikov inequality and eigenvalue equation are satisfied, by finding a heteroclinic orbit formed by three geometric invariant sets, namely the unstable manifold, heteroclinic point, and stable manifold, a set of real parameters in accordance with the condition of existence of heteroclnic orbit are obtained for this chaotic system. Thus, the existence of heteroclnic orbit has been proved. Finally, according to this set of real parameters, the circuit design and experimental verification has been carried out.
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