论文标题
Lorenz系统的瞬态动力学，具有参数漂移
Transient dynamics of the Lorenz system with a parameter drift
论文作者
论文摘要
非自治动力系统有助于我们理解与其在自然界中实际发生的环境接触的真实系统的含义。在这里，我们关注的系统通过使用Lorenz系统进行插图，在小但不可忽略的速率下随时间变化的系统会随着时间而变化。这种系统通常在突然过渡到稳态之前显示长期的短暂动力学。这可以通过在相关的冷冻系统中的分叉交叉来解释。在涉及混乱的吸引子的情况下，我们出人意料地发现了将瞬态持续时间与参数变化率有关的缩放定律。此外，我们通过将参数逆转为其原始值来分析恢复瞬态动力学的生存能力，以替代参数漂移的系统的控制理论。我们获得了对与瞬态状态相对应的初始吸引子的轨迹变化率与轨迹的数量之间的关系。
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but non-negligible rates before settling at a stable value, by using the Lorenz system for illustration. This kind of systems commonly show a long-term transient dynamics previous to a sudden transition to a steady state. This can be explained by the crossing of a bifurcation in the associated frozen-in system. We surprisingly uncover a scaling law relating the duration of the transient to the rate of change of the parameter for a case where a chaotic attractor is involved. Additionally, we analyze the viability of recovering the transient dynamics by reversing the parameter to its original value, as an alternative to the control theory for systems with parameter drifts. We obtain the relationship between the paramater change rate and the number of trajectories that tip back to the initial attractor corresponding to the transient state.
