Nagatani Takashi
Department of Mechanical Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 2):046103. doi: 10.1103/PhysRevE.66.046103. Epub 2002 Oct 9.
We study the effect of speedup on the dynamical behavior of a single cyclic bus in a bus system with many bus stops. We present a nonlinear-map model of a cyclic bus to take into account the speedup. When the cyclic bus is delayed, the bus speeds up to retrieve the delay. It is found that the cyclic bus exhibits chaotic motion with increasing speedup. The chaotic motion depends on both speedup and the number of bus stops. Also, it is shown that the dynamical transition between the chaotic and periodic motions occurs with the increase of bus stops. The dependence of the recurrence time (one period) and Liapunov exponent on both speedup and the number of bus stops is calculated for distinct dynamic states. It is shown that the speedup has a significant effect on the bus motion. For a piecewise linear-map model, the cyclic bus does not exhibit the chaotic motion but a complex oscillatory motion with multiple periods occurs.
我们研究了加速对具有多个公交站点的公交系统中单个循环公交动态行为的影响。我们提出了一个考虑加速因素的循环公交非线性映射模型。当循环公交出现延误时，它会加速以弥补延误。研究发现，随着加速的增加，循环公交会呈现出混沌运动。混沌运动既取决于加速，也取决于公交站点的数量。此外，还表明随着公交站点数量的增加，混沌运动和周期运动之间会发生动态转变。针对不同的动态状态，计算了循环时间（一个周期）和李雅普诺夫指数对加速和公交站点数量的依赖性。结果表明，加速对公交运动有显著影响。对于分段线性映射模型，循环公交不会呈现混沌运动，而是会出现具有多个周期的复杂振荡运动。
