标题： 时间平均能量衰减出现时的混沌运动 显示英文标题

标题： Chaotic motion at the emergence of the time averaged energy decay

摘要： 一个系统加环境保守模型用于描述当系统粒子的平均能量开始衰减时的非线性动力学。 系统粒子的动力学在环境振荡器的$N$值较低时是规则的，并在区间$13\le N\le15$内变得混沌，其中系统平均能量开始衰减。 为了描述非线性运动，我们估计李雅普诺夫指数（LE），确定功率谱和卡普兰-约克维数。 对于$N$的较大值，系统粒子的能量完全传递给环境，相应的 LEs 会下降。 数值证据表明粒子能量时间振荡的{\it 幅度}与平均能量衰减和捕获轨迹之间的联系。 显示英文摘要

摘要： A system plus environment conservative model is used to characterize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the $N$ environment oscillators and becomes chaotic in the interval $13\le N\le15$, where the system time averaged energy starts to decay. To characterize the nonlinear motion we estimate the Lyapunov exponent (LE), determine the power spectrum and the Kaplan-Yorke dimension. For much larger values of $N$ the energy of the system particle is completely transferred to the environment and the corresponding LEs decrease. Numerical evidences show the connection between the variations of the {\it amplitude} of the particles energy time oscillation with the time averaged energy decay and trapped trajectories.