论文标题
最高动力学系统中极限周期的Poincare Map方法
Poincare Map Method for Limit Cycles in a Max-Plus Dynamical System
论文作者
论文摘要
讨论了二维最大值动态系统中极限循环的动力学特性。我们将Poincare地图方法应用于极限周期以揭示其稳定性。该方法将二维系统降低到由PoinCare Map及其横截面组成的一维线性离散动力系统。通过考虑原始模型的反系统来得出一个极限周期之一的盆地。发现所获得的盆地显示出层次结构。讨论了在限制周期中的集成系统理论中研究的庞康咖啡图方法与分段线性映射的方法之间的关系。
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.
