Max-Plus动力系统极限环的Poincare映射方法
Poincare Map Method for Limit Cycles in a Max-Plus Dynamical System
摘要：
讨论了二维极大动力系统极限环的动力学性质。为了揭示极限环的稳定性，我们应用Poincare映射方法。该方法将二维系统化为由Poincare映射及其截面组成的一维分段线性离散动力系统。通过考虑原模型的逆系统，导出了其中一个极限环的盆。结果表明，所得到的盆地具有明显的层次结构。讨论了可积系统理论中的Poincare映射方法与分段线性映射方法在极限环问题中的关系。
英文摘要：
Dynamical properties of limit cycles in a two-dimensional max-plus dynamical system are discussed. We apply a Poincare map method to the limit cycles in order to reveal their stabilities. This method reduces the two dimensional system to a one-dimensional piecewise linear discrete dynamical system composed of the Poincare map and its cross section. Basins for one of the limit cycles are derived by considering the inverse system of the original model. It is found that the obtained basins show a hierarchic structure. Relationship between the Poincare map method and the method of piecewise linear mapping studied in integrable system theory for the limit cycles is discussed.
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